What to publish?

This might seem like a strange question. A snarky answer would be “everything!” But no, not really everything. Not all math deserves to be published, just like not all math needs to be done. Making this judgement is difficult and goes against the all too welcoming nature of the field. But if you want to succeed in math as a profession, you need to make some choices. This is a blog post about the choices we make and the choices we ought to make.

Bedtime questions

Suppose you tried to solve a major open problem. You failed. A lot of time is wasted. Maybe it’s false, after all, who knows. You are no longer confident. But you did manage to compute some nice examples, which can be turned into a mediocre little paper. Should you write it and post it on the arXiv? Should you submit it to a third rate journal? A mediocre paper is still a consolation prize, right? Better than nothing, no?

Or, perhaps, it is better not to show how little you proved? Wouldn’t people judge you as an “average” of all published papers on your CV? Wouldn’t this paper have negative impact on your job search next year? Maybe it’s better to just keep it to yourself for now and hope you can make a breakthrough next year? Or some day?

But wait, other people in the area have a lot more papers. Some are also going to be on a job market next year. Shouldn’t you try to catch up and publish every little thing you have? People at other universities do look at the numbers, right? Maybe nobody will notice this little paper. If you have more stuff done by then it will get lost in the middle of my CV, but it will help get the numbers up. Aren’t you clever or what?

Oh, wait, maybe not! You do have to send your CV to your letter writers. They will look at all your papers. How would they react to a mediocre paper? Will they judge you badly? What in the world should you do?!?

Well, obviously I don’t have one simple answer to that. But I do have some thoughts. And this quote from a famous 200 year old Russian play about people who really cared how they are perceived:

Chatsky: I wonder who the judges are! […]

Famusov: My goodness! What will countess Marya Aleksevna say to this?

[Alexander Griboyedov, Woe from Wit, 1823, abridged.]

You would think our society had advanced at least a little…

Who are the champions?

If we want to find the answers to our questions, it’s worth looking at the leaders of the field. Let’s take a few steps back and simply ask — Who are the best mathematicians? Ridiculous questions always get many ridiculous answers, so here is a random ranking by some internet person: Newton, Archimedes, Gauss, Euler, etc. Well, ok — these are all pretty dead and probably never had to deal with a bad referee report (I am assuming).

Here is another random list, from a well named website research.com. Lots of living people finally: Barry Simon, Noga Alon, Gilbert Laporte, S.T. Yau, etc. Sure, why not? But consider this recent entrant: Ravi P. Agarwal is at number 20, comfortably ahead of Paul Erdős at number 25. Uhm, why?

Or consider Theodore E. Simos who is apparently the “Best Russian Mathematician” according to research.com, and number 31 in the world ranking:

Uhm, I know MANY Russian mathematicians. Some of them are truly excellent. Who is this famous Simos I never heard of? How come he is so far ahead of Vladimir Arnold who is at number 829 on the list?

Of course, you already guessed the answer. It’s obvious from the pictures above. In their infinite wisdom, research.com judges mathematicians by the weighted average of the numbers of papers and citations. Arnold is doing well on citations, but published so little! Only 157 papers!

Numbers rule the world

To dig a little deeper into this citation phenomenon, take a look at the following curious table from a recent article “Extremal mathematicians“ by Carlos Alfaro:

If you’ve been in the field for awhile, you are probably staring at this in disbelief. How do you physically write so many papers?? Is this even true???

Yes, you know how Paul Erdős did it — he was amazing and he had a lot of coauthors. No, you don’t know how Saharon Shelah does it. But he is a legend, and you are ok with that. But here we meet again our hero Ravi P. Agarwal, the only human mathematician with more papers than Erdős. Who is he? Here is what the MathSciNet says:

Note that Ravi is still going strong — in less than 3 years he added 125 papers. Of these 1727 papers, 645 are with his favorite coauthor Donal O’Regan, number 3 on the list above. Huh? What is going on??

What’s in a number?

If the number of papers is what’s causing you to worry, let’s talk about it. Yes, there is also number of citations, the h-index (which boils down to the number of citations anyway), and maybe other awful measurements of research productivity. But the number of papers is what you have a total control over. So here are a few strategies how you can inflate the number that I learned from a close examination of publishing practices of some of the “extremal mathematicians”. They are best employed in combination:

(a) Form a clique. Over the years build a group of 5-8 close collaborators. Keep writing papers in different subsets of 3-5 of them. This is easier to do since each gets to have many papers while writing only a fraction. Make sure each papers cites heavily all other subsets from the clique. To an untrained eye of an editor, these would appear to be experts who are able to referee the paper.

(b) Form a cartel. This is a strong for of a clique. Invent an area and call yourselves collaborative research in that area. Make up a technical name, something like “analytic and algebraic topology
of locally Euclidean metrizations of infinitely differentiable Riemannian manifolds“. Apply for collaborative grants, organize conferences, publish conference proceedings, publish monographs, start your own journal. From outside it looks like a normal research activity, and who is to judge after all?

(c) Publish in little known, not very selective or shady journals. For example, Ravi P. Agarwal published 26 papers in Mathematics (MDPI Journal) that I discussed at length in this blog post. Note aside: since Mathematics is not indexed by the MathSciNet, the numbers above undercount his total productivity.

(d) Organize special issues with these journals. For example, here is a list of 11(!) special issues Agarwal served as a special editor with MDPI. Note the breadth of the collection:

(e) Become an editor of an established but not well managed journal and publish a lot there with all your collaborators. For example, T.E. Simos has a remarkable record of 150 (!) papers in the Journal of Mathematical Chemistry, where he is an editor. I feel that Springer should be ashamed of such a poor oversight of this journal, but nothing can be done I am sure since the journal has a healthy 2.413 impact factor, and Simos’s hard work surely contributed to its rise from just 1.056 in 2015. OTOH, maybe somebody can convince the MathSciNet to stop indexing this journal?

Let me emphasize that nothing on the list above is unethical, at least in a way the AMS or the NAS define these (as do most universities I think). The difference is quantitative, not qualitative. So these should not be conflated with various paper mill practices such as those described in this article by Anna Abalkina.

Disclaimer: I strongly recommend you use none of these strategies. They are abusing the system and have detrimental long term effects to both your area and your reputation.

Zero-knowledge publishing

In mathematics, there is another method of publishing that I want to describe. This one is borderline unethical at best, so I will refrain from naming names. You figure it out on your own!

Imagine you want to prove a major open problem in the area. More precisely, you want to become famous for doing that without actually getting the proof. In math, you can’t get there without publishing your “proof” in a leading area journal, better yet one of the top journals in mathematics. And if you do, it’s a good bet the referees will examine your proof very carefully. Sounds like a fail-proof system, right?

Think again! Here is an ingenuous strategy that I recently happen to learn. The strategy is modeled on the celebrated zero-knowledge proof technique, although the author I am thinking of might not be aware of that.

For simplicity, let’s say the open problem is “A=? Z”. Here is what you do, step by step.

1. You come up with a large set of problems P,Q,R,S,T,U,V,W,X,Y which are all equivalent to Z. You then start a well publicized paper factory proving P=Q, W=X, X=Z, Q=Z, etc. All these papers are correct and give a good vibe of somebody who is working hard on the A=?Z problem. Make sure you have a lot of famous coauthors on these papers to further establish your credibility. In haste, make the papers barely readable so that the referees don’t find any major mistakes but get exhausted by the end.
2. Make another list of problems B,C,D,E,F,G which are equivalent to A. Keep these equivalences secret. Start writing new papers proving B=T, D=Y, E=X, etc. Write them all in a style similar to previous list: cumbersome, some missing details, errors in minor arguments, etc. No famous people as coauthors. Do try to involve many grad students and coauthors to generate good will (such a great mentor!) They will all be incorrect, but none of them would raise a flag since by themselves they don’t actually prove A=Z.
3. Populate the arXiv with all these papers and submit them to different reputable journals in the area. Some referees or random readers will find mistakes, so you fix one incomprehensible detail with another and resubmit. If crucial problems in one paper persist, just drop it and keep going through the motions on all other papers. Take your time.
4. Eventually one of these will get accepted because the referees are human and they get tired. They will just assume that the paper they are handling is just like the papers on the first list – clumsily written but ultimately correct. And who wants to drag things down over some random reduction — the young researcher’s career is on the line. Or perhaps, the referee is a coauthor of some of the paper on the first list – in this case they are already conditioned to believe the claims because that’s what they learned from the experience on the joint paper.
5. As soon as any paper from the second list is accepted, say E=X, take off the shelf the reduction you already know and make it public with great fanfare. For example, in this case quickly announce that A=E. Combined with the E=X breakthrough, and together with X=W and W=Z previously published in the first list, you can conclude that A=Z. Send it to the Annals. What are the referees going to do? Your newest A=E is inarguable, clearly true. How clever are you to have figured out the last piece so quickly! The other papers are all complicated and confusing, they all raise questions, but somebody must have refereed them and accepted/published them. Congratulations on the solution of A=Z problem! Well done!

It might take years or even decades until the area has a consensus that one should simply ignore the erroneous E=X paper and return to “A=?Z” the status of an open problem. The Annals will refuse to publish a retraction — technically they only published a correct A=E reduction, so it’s all other journals’ fault. It will all be good again, back to normal. But soon after, new papers such as G=U and B=R start to appear, and the agony continues anew…

From math to art

Now that I (hopefully) convinced you that high numbers of publications is an achievable but ultimately futile goal, how should you judge the papers? Do they at least make a nonnegative contribution to one’s CV? The answer to the latter question is “No”. This contribution can be negative. One way to think about is by invoking the high end art market.

Any art historian would be happy to vouch that the worth of a painting hinges heavily on the identity of the artist. But why should it? If the whole purpose of a piece of art is to evoke some feelings, how does the artist figures into this formula? This is super naïve, obviously, and I am sure you all understand why. My point is that things are not so simple.

One way to see the a pattern among famous artists is to realize that they don’t just create “one off” paintings, but rather a “series”. For example, Monet famously had haystack and Rouen Cathedral series, Van Gogh had a sunflowers series, Mondrian had a distinctive style with his “tableau” and “composition” series, etc. Having a recognizable very distinctive style is important, suggesting that painting in series are valued differently than those that are not, even if they are by the same artist.

Finally, the scarcity is an issue. For example Rodin’s Thinker is one of the most recognizable sculptures in the world. So is the Celebration series by Jeff Koons. While the latter keep fetching enormous prices at auctions, the latest sale of a Thinker couldn’t get a fifth of the Yellow Balloon Dog price. It could be because balloon animals are so cool, but could also be that there are 27 Thinkers in total, all made from the same cast. OTOH, there are only 5 balloon dogs, and they all have distinctly different colors making them both instantly recognizable yet still unique. You get it now — it’s complicated…

What papers to write

There isn’t anything objective of course, but thinking of art helps. Let’s figure this out by working backward. At the end, you need to be able to give a good colloquium style talk about your work. What kid of papers should you write to give such a talk?

1. You can solve a major open problem. The talk writes itself then. You discuss the background, many famous people’s attempts and partial solutions. Then state your result and give an idea of the proof. Done. No need to have a follow up or related work. Your theorem speaks for itself. This is analogous to the most famous paintings. There are no haystacks or sunflowers on that list.
2. You can tell a good story. I already wrote about how to write a good story in a math paper, and this is related. You start your talk by telling what’s the state of the sub-area, what are the major open problems and how do different aspects of your work fit in the picture. Then talk about how the technology that you develop over several papers positioned you to make a major advance in the area that is your most recent work. This is analogous to the series of painting.
3. You can prove something small and nice, but be an amazing lecturer. You mesmerize the audience with your eloquence. For about 5 minutes after your talk they will keep thinking this little problem you solved is the most important result in all of mathematics. This feeling will fade, but good vibes will remain. They might still hire you — such talent is rare and teaching excellence is very valuable.

That’s it. If you want to give a good job talk, there is no other way to do it. This is why writing many one-off little papers makes very little sense. A good talk is not a patchwork quilt – you can’t make it of disparate pieces. In fact, I heard some talks where people tried to do that. They always have coherence of a portrait gallery of different subjects by different artists.

Back to the bedtime questions — the answer should be easy to guess now. If your little paper fits the narrative, do write it and publish it. If it helps you tell a good story — that sounds great. People in the area will want to know that you are brave enough to make a push towards a difficult problem using the tools or results you previously developed. But if it’s a one-off thing, like you thought for some reason that you could solve a major open problem in another area — why tell anyone? If anything, this distracts from the story you want to tell about your main line of research.

How to judge other people’s papers

First, you do what you usually do. Read the paper, make a judgement on the validity and relative importance of the result. But then you supplement the judgement with what you know about the author, just like when you judge a painting.

This may seem controversial, but it’s not. We live in an era of thousands of math journals which publish in total over 130K papers a year (according to MathSciNet). The sheer amount of mathematical research is overwhelming and the expertise has fractured into tiny sub-sub-areas, many hundreds of them. Deciding if a paper is a useful contribution to the area is by definition a function of what the community thinks about the paper.

Clearly, you can’t poll all members of the community, but you can ask a couple of people (usually called referees). And you can look at how previous papers by the author had been accepted by the community. This is why in the art world they always write about recent sales: what money and what museum or private collections bought the previous paintings, etc. Let me give you some math examples.

Say, you are an editor. Somebody submits a bijective proof of a binomial identity. The paper is short but nice. Clearly publishable. But then you check previous publications and discover the author has several/many other published papers with nice bijective proofs of other binomial identities, and all of them have mostly self-citations. Then you realize that in the ocean of binomial identities you can’t even check if this work has been done before. If somebody in the future wants to use this bijection, how would they go about looking for it? What will they be googling for? If you don’t have good answers to these questions, why would you accept such a paper then?

Say, you are hiring a postdoc. You see files of two candidates in your area. Both have excellent well written research proposals. One has 15 papers, another just 5 papers. The first is all over the place, can do and solve anything. The second is studious and works towards building a theory. You only have time to read the proposals (nobody has time to read all 20 papers). You looks at the best papers of each and they are of similar quality. Who do you hire?

That depends on who you are looking for, obviously. If you are a fancy shmancy university where there are many grad students and postdocs all competing with each other, none working closely with their postdoc supervisor — probably the first one. Lots of random papers is a plus — the candidate clearly adapts well and will work with many others without need for a supervision. There is even a chance that they prove something truly important, it’s hard to say, right? Whether they get a good TT job afterwards and what kind of job would that be is really irrelevant — other postdocs will be coming in a steady flow anyway.

But if you want to have this new postdoc to work closely with a faculty at your university, someone intent on building a something valuable, so that they are able to give a nice job talk telling a good story at the end, hire the second one. They first is much too independent and will probably be unable to concentrate on anything specific. The amount of supervision tends to go less, not more, as people move up. Left to their own devices you expect from these postdocs more of the same, so the choice becomes easy.

Say, you are looking at a paper submitted to you as an editor of an obscure journal. You need a referee. Look at the previous papers by the authors and see lots of the repeated names. Maybe it’s a clique? Make sure your referees are not from this clique, completely unrelated to them in any way.

Or, say, you are looking at a paper in your area which claims to have made an important step towards resolving a major conjecture. The first thing you do is look at previous papers by the same person. Have they said the same before? Was it the same or a different approach? Have any of their papers been retracted or major mistakes found? Do they have several parallel papers which prove not exactly related results towards the same goal? If the answer is Yes, this might be a zero-knowledge publishing attempt. Do nothing. But do tell everyone in the area to ignore this author until they publish one definitive paper proving all their claims. Or not, most likely…

P.S. I realize that many well meaning journals have double blind reviews. I understand where they are coming from, but think in the case of math this is misguided. This post is already much too long for me to talk about that — some other time, perhaps.

The insidious corruption of open access publishers

The evil can be innovative. Highly innovative, in fact. It has to be, to survive. We wouldn’t even notice it otherwise. This is the lesson one repeatedly learns from foreign politics, where authoritarian or outright dictatorial regimes keeps coming up with new and ingenuous uses of technology to further corrupt and impoverish their own people. But this post is about Mathematics, the flagship MDPI journal.

What is MDPI?

It’s a for profit publisher of online-only “open access” journals. Are they legitimate or predatory? That’s a good question. The academic world is a little perplexed on this issue, although maybe they shouldn’t be. It’s hard for me to give a broad answer given that it publishes over 200 journals, most of which have single word wonder titles like Data, Diseases, Diversity, DNA, etc.

If “MDPI” doesn’t register, you probably haven’t checked your spam folder lately. I am pretty sure I got more emails inviting me to be a guest editor of various MDPI journals than from Nigerian princes. The invitations came in many fields (or are they?), from Sustainability to Symmetry, from Entropy to Axioms, etc. Over the years I even got some curious invites from such titles as Life and Languages. I can attest that at the time of this writing I am alive and can speak, which I suppose qualifies me to be guest editor of both..

I checked my UCLA account, and the first email from I got from MDPI was on Oct 5, 2009, inviting me to be guest editor in “Algorithms for Applied Mathematics” special issue of Algorithms. The most remarkable invitation came from a journal titled “J“, which may or may not have been inspired by the single letter characters in the James Bond series, or perhaps by the Will Smith character in Men in Black — we’ll never know. While the brevity is commendable, it serves the same purpose of creatively obscuring the subject in all these cases.

While I have nothing to say about all MDPI journals, let me leave you with some links to people who took MDPI seriously and decided to wade on the issue. Start with this 2012 Stack Exchange discussions on MDPI and move to this Reddit discussion from 3 months ago. Confused enough? Then read the following:

1. Christos Petrou, MDPI’s Remarkable Growth, The Scholarly Kitchen (August 10, 2020)
2. Dan Brockington, MDPI Journals: 2015-2020 (March 29, 2021)
3. Paolo Crosetto, Is MDPI a predatory publisher? (April 12, 2021)
4. Ángeles Oviedo-García, Journal citation reports and the definition of a predatory journal: The case of MDPI, Research Evaluation (2021). See also this response by MDPI.

As you can see, there are issues with MDPI, and I am probably the last person to comment on them. We’ll get back to this.

What is Mathematics?

It’s one of the MDPI journals. It was founded in 2013 and as of this writing published 7,610 articles. More importantly, it’s not reviewed by the MathSciNet and ZbMath. Ordinarily that’s all you need to know in deciding whether to submit there, but let’s look at the impact factor. The numbers differ depending on which version you take, but the relative picture is the same: it suggests that Mathematics is a top 5-10 journal. Say, this comprehensive list gives 2.258 for Mathematics vs. 2.403 for Duke, 2.200 for Amer. Jour. Math, 2.197 for JEMS, 1.688 for Advances Math, and 1.412 for Trans. AMS. Huh?

And look at this nice IF growth. Projected forward it will be #1 journal in the whole field, just what the name would suggest. Time to jump on the bandwagon! Clearly somebody very clever is managing the journal guiding it from obscurity to the top in just a few years…

Now, the Editorial Board has 11 “editors-in-chief” and 814 “editors”. Yes, you read the right — it’s 825 in total. Well, math is a broad subject, so what did you expect? For comparison, Trans. AMS has only about 25 people on its Editorial Board, so they can’t possibly cover all of mathematics, right? Uhm…

So, who are these people? I made an effort and read the whole list of these 825 chosen ones. At least two are well known and widely respected mathematicians, although neither lists being an editor of Mathematics on their extended CVs (I checked). Perhaps, ashamed of the association, but not ashamed enough to ask MDPI to take their name off the list? Really?

I also found three people in my area (understood very broadly) that I would consider serious professionals. One person is from my own university albeit from a different department. One person is a colleague and a friend (this post might change that). Several people are my “Facebook or LinkedIn friends” which means I never met them (who doesn’t have those?) That’s it! Slim pickings for someone who knows thousands of mathematicians…

This journal is popular, seriously?

Yes, it is. No doubt about it. Just look at this self-reported graph below. That’s a lot of papers, almost all of them in the past few years. For comparison, Trans. AMS publishes about 300 papers a year, while Jour. AMS in the past few years averaged about 25 papers a year.

The reasons for popularity are also transparent: they accept all kinds of nonsense.

To be fair, honest acceptance rates are hard to come by, so we really don’t know what happens to lower tier math journals. I remember when I came to be an editor of Discrete Math. it had the acceptance ratio of 30% which I considered outrageously high. I personally aimed for 10-15%. But I imagine that the acceptance ratio is non-monotone as a function of the “journal prestige” since there is a lot of self-selection happening at the time of submission.

Note that the reason for self-selection (when it comes to top journals) is the high cost of waiting for a decision which can often take upwards of a year. A couple of year-long rejections for a paper and its prospects are looking dim as other papers start appearing (including your own) which can prove stronger result by better/cleaner arguments. Now try explaining to the editor why your old weaker paper should be published in favor of all this new shining stuff…

This is yet another place where MDPI is innovative. They make a decision within days:

So the authors contemplating where to submit face a stark alternative: either their paper will be accepted with high probability within days, or — who knows… All these decisions are highly personal and dependent on particularities of author’s country, university, career stage, etc., but overall it’s hard to blame them for sending their work to Mathematics.

What makes MDPI special?

Mostly the way it makes money. It forgoes print subscription mode altogether, and has a 1800 CHF (about $1,960) “article processing charge” (APC). This is not unusual per se, e.g. Trans. AMS, Ser. B charges $2,750 APC while Forum of Mathematics, Sigma charges $1500 which is a deep discount from Cambridge’s “standard” $3,255 APC. What is unusual is the sheer volume of business MDPI makes from these charges essentially by selling air. They simply got ahead of competitors by being shameless. Indeed, why have high standards? That’s just missing out on so much revenue…

This journal is predatory, right?

Well, that’s what the MDPI link items 1-4 are about (see above). When it comes to Mathematics, I say No, at least not in a sense that’s traditionally understood. However, this doesn’t make it a legitimate research publication, not for a second! It blurs the lines, it corrupts the peer review, it leeches off academia, and it collects rents by selling air. Now that I made my views clear, let me explain it all.

What people seem to be hung up about is the idea that you can tell who is predatory by looking at the numbers. Number of submissions, number of citations, acceptance percentage, number of special issues, average article charge, etc. These numbers can never prove that MDPI does anything wrong. Otherwise MDPI wouldn’t be posting them for everyone to see.

Reading MDPI response in item 4. is especially useful. They make a good point — there is not good definition of a “predatory journal”, since the traditional “pay-to-play” definition simply doesn’t apply. Because when you look at the stats — Mathematics looks like a run-of-the-mill generic publication with high acceptance ratio, a huge number of ever corrupting special issues, and very high APC revenue. Phrased differently and exaggerating a bit, they are a mixture of Forum of Mathematics, Sigma or Trans. AMS, Ser. B. in being freely accessible, combined with the publication speed and efficiency of Science or Nature, but the selectivity of the arXiv (which does in fact reject some papers).

How do you tell they are illegitimate then?

Well, it’s the same logic as when judging life under an authoritarian regime. On paper, they all look the same, there is nothings to see. Indeed, for every electoral irregularity or local scandal they respond with what-about-your-elections. That’s how it goes, everybody knows.

Instead, what you do is ask real people to tell their stories. The shiny facade of the regime quickly fades away when one reads these testimonials. For life in the Soviet Union, I recommend The Gulag Archipelago and Boys in Zinc which bookend that sordid history.

So I did something similar and completely unscientific. I wrote to about twenty authors of Mathematics papers from the past two years, asking them to tell their stories, whether their papers were invited or contributed, and if they paid and how much. I knew none of them before writing, but over a half of the authors kindly responded with some very revealing testimonials which I will try to summarize below.

What exactly does the Mathematics do?

(1) They spam everyone who they consider “reputable” to be “guest editors” and run “special issues”. I wrote before how corrupt are those, but this is corruption on steroids. The editors are induced by waiving their APCs and by essentially anyone their choose. The editors seem to be given a budget to play with. In fact, I couldn’t find anyone whose paper was invited (or who was an editor) and paid anything, although I am sure there are many such people from universities whose libraries have budgeted for open source journals.

(2) They induce highly cited people to publish in their journal by waiving APCs. This is explicitly done in an effort to raise impact factors, and Mathematics uses h-index to formalize this. The idea seems to be that even a poor paper by a highly cited author will get many more citation than average, even if they are just self-citations. They are probably right on this. Curiously, one of my correspondents looked up my own h-index (33 as I just discovered), and apparently it passed the bar. So he quickly proposed to help me publish my own paper in some special issue he was special editing this month. Ugh…

(3) They spam junior researchers asking them to submit to their numerous special issues, and in return to accept their publishing model. They are asked to submit by nearly guaranteeing high rates of processing and quick timeline. Publish or perish, etc.

(4) They keep up with appearances and do send each paper to referees, usually multiple referees, but requiring them to respond in two weeks. The paper avoids being carefully refereed and that allows a quick turnaround. Furthermore, the refereeing assignments are made more or less at random to people in their database completely unfamiliar with the subject. They don’t need to be, of course, all they need is to provide a superficial opinion. From what I hear, when the referee recommends rejection the journal doesn’t object — there is plenty of fish in the sea…

(5) Perhaps surprisingly, several people expressed great satisfaction with the way refereeing was done. I attribute this to superficial nature of the reports and the survivor bias. Indeed, nobody likes technical reports which make you deal with proof details, and all the people I emailed had their papers accepted (I wouldn’t know the names of people whose papers were rejected).

(6) The potential referees are induced to accept the assignment by providing 100 CHF vouchers which can be redeemed at any MDPI publication. Put crudely, they are asked to accept many refereeing assignments, say Y/N at random, and you can quickly publish your own paper (as long as it’s not a complete garbage). One of my correspondents wrote that he exchanged six vouchers worth 600 CHF onto one APC worth 1600 CHF at the time. He meant that this was a good deal as the journal waived the rest, but from what I heard others got the same or similar deal.

(7) Everyone else who has a university library willing to pay APC is invited to submit for the same reasons as (4). And people do contribute. Happily, in fact. Why wouldn’t they — it’s not their money and they get to have a quick publication in a journal with high IF. Many of my correspondents reported to be so happy, they later published several other papers in various MDPI journals.

(8) According to my correspondents, other than the uncertain reputation, the main problem people faced was typesetting, especially when it came to references. Mathematics is clearly very big on that, it’s why they succeeded to begin with. One author reported that the journal made them write a sentence

The first part of the bibliography […], numbered in chronological order from [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,….]

Several others reported long battles with the bibliography style to the point of threatening to withdraw the paper, at which point the journal cave all reported. But all in all, there were unusually few complaints other than on a follow up flood of random referee invitations.

(9) To conclude, the general impression of authors seem to be crystalized in the following quote by one of them:

I think what happened is MDPI just puts out a ton of journals and is clearly just interested in profiting from them (as all publishers are, in a sense…) and some of their particular journals have become more established and reputed than others, some seem so obscure I think they really are just predatory, but others have risen above that, and Mathematics is somewhere in the middle of that spectrum.

What gives?

As I mentioned before, in my opinion Mathematics is not predatory. Rather, it’s parasitic. Predatory journals take people’s own cash to “publish” their paper in some random bogus online depositary. The authors are duped out of cash with the promise of a plausibly looking claim of scientific recognition which they can use for their own advancement. On the other hand, Mathematics does nothing nothing other journals don’t do, and the authors seem to be happy with the outcome.

The losers are the granting foundations and university libraries which shell out large amounts for a subpar products (compared to Trans. AMS, Ser B., Forum Math Sigma, etc.) as they can’t tell the difference between these journals, or institutionally not allowed to do so. In the spirit of “road to hell is paved with good intentions“, this is an unintended consequence of the Elsevier boycott which brought the money considerations out of the shadows and directly led to founding of the open access journals with their misguided budget model.

MDPI clearly found a niche allowing them to monetize on mediocre papers while claiming high impact factors from a minority of papers by serious researchers. In essence it’s the same scam as top journals are playing with invited issues (see my old blog post again), but in reverse — here the invited issues are pushing the average quality of the journal UP rather than DOWN.

As I see it, Mathematics corrupts the whole peer review process by monetizing it to the point that APC becomes a primary consideration rather than the mathematical contribution of the paper. In contrast with the Elsevier, the harm MDPI does is on an intangible level — the full extend of it might never become clear as just about all papers the Mathematics publishes will never be brought to public scrutiny (the same is true for most low-tier journal). All I know is that the money universities spend on Mathematics APCs are better be spent on just about anything else supporting actual research and education.

What happens to math journal in the future?

I already tried answering this eight years ago, with a mixed success. MDPI shows that I was right about moving to online model and non-geographical titles, but wrong about thinking that journals will further specialize. Journals like Mathematics, Algorithms, Symmetry, etc. are clear counterexamples. I guess I was much too optimistic about the future without thinking through the corrupt nature the money brings to the system.

So what now? I think the answer is clear, at least in Mathematics. The libraries should stop paying for open access. Granting agencies should prohibit grants be used for paying for publications. Mathematicians should simply run away any time someone brings up the money. JUST SAY NO.

If this means that journals like Forum Math. would have to die or get converted to another model — so be it. The right model of arXiv overlay is cheap and accessible. There is absolutely no need for a library to pay for Trans. AMS, Ser. B. publication if the paper is already freely available on the arXiv, as is the fact with the vast majority of their papers. It’s hard to defend giving money to Cambridge Univ. Press or AMS, but giving it to MDPI is just sinful.

Finally, if you are on the Mathematics editorial board, please resign and never tell anyone that you were there. You already got what you wanted, your paper is published, your name is on the cover of some special issue (they print them for the authors). I might be overly optimistic again, but when it comes to MDPI, shame might actually work…

How to fight the university bureaucracy and survive

The enormity of the university administration can instill fear. How can you possibly fight such a machine? Even if an injustice happened to you, you are just one person with no power, right? Well, I think you can. Whether you succeed in your fight is another matter. But at least you can try… In this post I will try to give you some advise on how to do this.

Note: Initially I wanted to make this blog post light and fun, but I couldn’t think of a single joke. Somehow, the subject doesn’t inspire… So read this only if it’s relevant to you. Wait for future blog posts otherwise…

Warning: Much of what I say is relevant to big state universities in the US. Some of what I say may also be relevant to other countries and university systems, I wouldn’t know.

Basics

Who am I to write about this? It is reasonable to ask if any of this is based on my personal experience of fighting university bureaucracies. The answer is yes, but I am not willing to make any public disclosures to protect privacy of all parties involved. Let me just say that over the past 20 years I had several relatively quiet and fairly minor fights with university bureaucracies some of which I won rather quickly by being right. Once, I bullied my way into victory despite being in the wrong (as I later learned), and once I won over a difficult (non-personal) political issue by being cunning and playing a really long game that took almost 3 years. I didn’t lose any, but I did refrain from fighting several times. By contrast, when I tried to fight the federal government a couple of times (on academic matters), I lost quickly and decisively. They are just too powerful….

Should you fight? Maybe. But probably not. Say, you complained to the administration about what you perceive to be an injustice to you or to someone else. Your complaint was denied. This is when you need to decide if you want to start a fight. If you do, you will spend a lot of effort and (on average) probably lose. The administrations are powerful and know what they are doing. You probably don’t, otherwise you won’t be reading this. This blog post might help you occasionally, but wouldn’t change the big picture.

Can you fight? Yes, you can. You can win by being right and convince bureaucrats to see it this way. You can win by being persistent when others give up. You can also win by being smart. Big systems have weaknesses you can exploit, see below. Use them.

Is there a downside to winning a fight? Absolutely. In the process you might lose some friends, raise some suspicions from colleagues, and invite retribution. On a positive side, big systems have very little institutional memory — your win and the resulting embarrassment to administration will be forgotten soon enough.

Is there an upside to losing a fight? Actually, yes. You might gain resect of some colleagues as someone willing to fight. In fact, people tend to want being friends/friendly with such people out of self-preservation. And if your cause is righteous, this might help your reputation in and beyond the department.

Why did I fight? Because I just couldn’t go on without a fight. The injustice, as I perceived it, was eating me alive and I had a hunch there is a nonzero chance I would win. There were some cases when I figured the chances are zero, and I don’t need the grief. There were cases when the issue was much too minor to waste my energy. I don’t regret those decision, but having grown up in this unsavory part of Moscow, I was conditioned to stand up for myself.

Is there a cost of not fighting? Yes, and it goes beyond the obvious. First, fighting bureaucracy is a skill, and every skill takes practice. I remember when tried to rent an apartment in Cambridge, MA — some real estate agents would immediately ask if I go to Harvard Law School. Apparently it’s a common practice for law students to sue their landlords, an “extra credit” homework exercise. Most of these lawsuits would quickly fail, but the legal proceeding were costly to the owners.

Second, there is a society cost. If you feel confident that your case is strong, you winning might set a precedent which could benefit many others. I wrote on this blog once how I dropped (or never really started) a fight against the NSF, even though they clearly denied me the NSF Graduate Fellowship in a discriminatory manner, or at least that’s what I continue to believe. Not fighting was the right thing to do for me personally (I would have lost, 100%), but my case was strong and the fight itself might have raised some awareness to the issue. It took the NSF almost 25 years to figure out that it’s time to drop the GREs discriminatory requirement.

Axioms

1. If it’s not in writing it never happened.
2. Everyone has a boss.
3. Bureaucrats care about themselves first and foremost. Then about people in their research area, department and university, in that order. Then undergraduates. Then graduate students. You are the last person they care about.

How to proceed

Know your adversary. Remember — you are not fighting a mafia, a corrupt regime or the whole society. Don’t get angry, fearful or paranoid. Your adversary is a group of good people who are doing their jobs as well as they can. They are not infallible, but probably pretty smart and very capable when it comes to bureaucracy, so from game theory point of view you may as well assume they are perfect. When they are not, you will notice that — that’s the weakness you can exploit, but don’t expect that to happen.

Know your rights. This might seem obvious, but you would be surprised to know how many academics are not aware they have rights in a university system. In fact, it’s a feature of every large bureaucracy — it produces a lot of well meaning rules. For example, Wikipedia is a large project which survived for 20 years, so unsurprisingly it has a large set of policies enforced by an army of admins. The same is probably true about your university and your department. Search on the web for the faculty handbook, university and department bylaws, etc. If you can’t find the anywhere, email the assistant to the Department Chair and ask for one.

Go through the motions. Say, you think you were slighted. For example, your salary was not increased (enough), you didn’t get a promotion, you got too many committee duties assigned, your sabbatical was not approved, etc. Whatever it is, you are upset, I get it. Your first step is not to complain but go through the motions, and email inquiries. Email the head of the department, chair of the executive committee, your faculty dean, etc., whoever is the decision maker. Calmly ask to explain this decision. Sometimes, this was an oversight and it’s corrected with a quick apology and “thanks for bringing this up”. You win, case closed. Also, sometimes you either get a convincing explanation with which you might agree — say, the university is on salary freeze so nobody got a salary increase, see some link. Again, case closed.

But in other cases you either receive an argument with which you disagree (say, “the decision was made based on your performance in the previous year”), a non-answer (say, “I am on sabbatical” or “I will not be discussing personal matters by email”), or no answer at all. These are the cases that you need to know how to handle and all such cases are a little different. I will try to cover as much territory as possible, but surely will miss some cases.

Ask for advice. This is especially important if you are a junior mathematician and feel a little overwhelmed. Find a former department chair, perhaps professor emeritus, and have an quiet chat. Old-timers know the history of the department, who are the university administrators, what are the rules, what happened to previous complaints, what would fly and what wouldn’t, etc. They might also suggest who else you should talk to that would be knowledgeable and help dealing with an issue. With friends like these, you are in a good shape.

Scenarios

Come by for a chat. This is a standard move by a capable bureaucrat. They invite you for a quick discussion, maybe sincerely apologize for “what happened” or “if you are upset” and promise something which they may or may not intend to keep. You are supposed to leave grateful that “you are heard” and nothing is really lost from admin’s point of view. You lost.

There is only one way to counter this move. Agree to a meeting — play nice and you might learn something. Don’t record in secret — it’s against the law in most states. Don’t ask if you can record the conversation — even if the bureaucrat agrees you will hear nothing but platitudes then (like “we in our university strive to make sure everyone is happy and successful, and it is my personal goal to ensure everyone is treated fairly and with respect”). This defeats the purpose of the meeting moving you back to square one.

At the meeting do not agree with anything, never say yes or no to anything. Not even to the routine “No hard feelings?” Just nod, take careful notes, say “thank you so much for taking time to have this meeting” and “This information is very useful, I will need to think it over”. Do not sign anything. If offered a document to sign, take it with you. If implicitly threatened, as in “Right now I can offer you this for you, but once you leave this office I can’t promise… ” (this is rare but does happen occasionally), ignore the threat. Just keep repeating “Thank you so much for informing me of my options, I will need to think it over.” Go home, think it over and talk to somebody.

Get it all in writing. Within a few hours after the meeting, email to the bureaucrat an email with your notes. Start this way: “Dear X, this is to follow up on the meeting we had on [date] regarding the [issue]. I am writing this to ensure there is no misunderstanding on my part. At the meeting you [offered/suggested/claimed/threatened] …. Please let me know if this is correct and what are the details of …”

A capable bureaucrat will recognize the move and will never go on record with anything unbecoming. They will accept the out you offered and claim that you indeed misunderstood. Don’t argue with that — you have them where you want it. In lieu of the misunderstanding they will need to give a real answer to your grievance (otherwise what was the point of the meeting?) Sometimes a bureaucrat will still resort to platitudes, but now that they are in writing, that trick is harder to pull off, and it leads us to a completely different scenario (see below).

Accept the win. You might receive something like this: “We sincerely apologize for [mistake]. While nothing can be done about [past decision], we intend to [compensate or rectify] by doing…” If this is a clear unambiguous promise in writing, you might want to accept it. If not, follow up about details. Do not pursue this any further and don’t make it public. You got what you wanted, it’s over.

Accept the defeat. You might learn that administration acted by the book, exactly the way the rules/bylaws prescribe, and you were not intentionally discriminated in any way. Remain calm. Thank the bureaucrat for the “clarification”. It’s over.

Power of CC. If you receive a non-answer full of platitudes or no email reply at all (give it exactly one week), then follow up. Write politely “I am afraid I did not receive an answer to [my questions] in my email from [date]. I would really appreciate your response to [all issues I raised]. P.S. I am CC’ing this email to [your boss, boss of your boss, your assistant, your peers, other fellow bureaucrats, etc.] to let them know of [my grievance] and in case they can be helpful with this situation.” They will not “be helpful”, of course, but that’s not the point. The CC move itself has an immense power driven by bureaucrats’ self-preservation. Most likely you will get a reply within hours. Just don’t abuse the CC move — use it when you have no other moves to play, as otherwise it loses its power.

Don’t accept a draw. Sometimes a capable bureaucrat might reply to the whole list on CC and write “We are very sorry [your grievance] happened. This is extremely atypical and related to [your unusual circumstances]. While this is normally not appropriate, we are happy to make an exception in your case and [compensate you].” Translation: “it’s your own fault, you brought it on yourself, we admit no wrongdoing, but we are being very nice and will make you happy even though we really don’t have to do anything, not at all.” While other bureaucrats will recognize the move and that there is an implicit admission of fault, they will stay quiet — it’s not their fight.

Now, there is only one way to counter this, as far as I know. If you don’t follow up it’s an implicit admission of “own fault” which you don’t want as the same issue might arise again in the future. If you start explaining that it’s really bureaucrat’s fault you seem vindictive (as in “you already got what you wanted, why do you keep pushing this?”), and other bureaucrats will close ranks leaving you worse off. The only way out is to pretend to be just as illogical as the bureaucrat pretends to be. Reply to the whole CC list something like “Thank you so much for your apology and understanding of my [issue]. I am very grateful this is resolved to everyone’s satisfaction. I gratefully accept your sincere apology and your assurances this will not happen again to me nor anyone else at the department.”

A capable bureaucrat will recognize they are fighting fire with fire. In your email you sound naïve and sincere — how do you fight that? What are they going to do — reply “actually, I didn’t issue any apology as this was not my fault”? Now that seem overly defensive. And they would have to reply to the whole CC list again, which is not what they want. They are aware that everyone else knows they screwed up, so reminding everyone with a new email is not in their interest. And there is a decent chance you might reply to the whole CC list again with all that sugarcoated unpleasantness. Most likely, you won’t hear from them again, or just a personal (non-CC’d) email which you can ignore regardless of the content.

Shifting blame or responsibility. That’s another trick bureaucrats employ very successfully. You might get a reply from a bureaucrat X to the effect saying “don’t ask me, these are rules made by [people upstairs]” or “As far as I know, person Y is responsible for this all”. This is great news for you — a tacit validation of your cause and an example of a bureaucrat putting their own well-being ahead of the institution. Remember, your fight is not with X, but with the administration. Immediately forward both your grievance and the reply to Y, or to X’s boss if no names were offered, and definitely CC X “to keep your in the loop of further developments on this issue”. That immediately pushes bureaucracy into overdrive as it starts playing musical chairs in the game “whose fault is that and what can be done”.

Like with musical chairs, you might have to repeat the procedure a few times, but chances are someone will eventually accept responsibility just to stop this embarrassment from going circles. By then, there will be so many people on the CC chain, your issue will be addressed appropriately.

Help them help you. Sometimes a complaint puts the bureaucrat into a stalemate. They want to admit that injustice happened to you, but numerous university rules forbid them from acting to redress the situation. In order to violate these rules, they would have to take the case upstairs, which brings its own complications to everyone involved. Essentially you need to throw them a lifeline by suggesting some creative solution to the problem.

Say, you can write “while I realize the deadline for approval of my half-year sabbatical has passed, perhaps the department can buyout one course from my Fall schedule and postpone teaching the other until Spring.” This moves the discussion from the “apology” subject to “what can be done”, a much easier bureaucratic terrain. While the bureaucrat may not agree with your proposed solution, your willingness to deal without an apology will earn you some points and perhaps lead to a resolution favorable to all parties.

Now, don’t be constrained in creativity of when thinking up such a face saving resolution. It is a common misconception that university administrations are very slow and rigid. This is always correct “on average”, and holds for all large administrative systems where responsibility is distributed across many departments and individuals. In reality, when they want to, such large systems can turn on a dime by quickly utilizing its numerous resources (human, financial, legal, etc.) I’ve seen it in action, it’s jaw-dropping, and it takes just one high ranking person to take up the issue and make it a cause.

Making it public. You shouldn’t do that unless you already lost but keep holding a grudge (and have tenure to protect you). Even then, you probably shouldn’t do it unless you are really good at PR. Just about every time you make grievances public you lose some social points with people who will hold it against you, claim you brought it on yourself, etc. In the world of social media your voice will be drowned and your case will be either ignored or take life of its own, with facts distorted to fit a particular narrative. The administration will close ranks and refuse to comment. You might be worse off than when you started.

The only example I can give is my own combative blog post which remains by far my most widely read post. Everyone just loves watching a train wreck… Many people asked why I wrote it, since it made me a persona non grata in the whole area of mathematics. I don’t have a good answer. In fact, that area may have lost some social capital as a result of my blog post, but haven’t changed at all. Some people apologized, that’s all. There is really nothing I can do and they know it. The truth is — my upbringing was acting up again, and I just couldn’t let it go without saying “Don’t F*** with Igor Pak”.

But you can very indirectly threaten to make it public. Don’t do it unless you are at an endgame dealing with a high ranking administrator and things are not looking good for you. Low level university bureaucrats are not really afraid for their jobs. For example, head of the department might not even want to occupy the position, and is fully protected by tenure anyway. But deans, provosts, etc. are often fully vested into their positions which come with substantial salary hike. If you have a sympathetic case, they wouldn’t want to be featured in a college newspaper as denying you some benefits, regardless of the merit. They wouldn’t be bullied into submission either, so some finesse is needed.

In this case I recommend you find an email of some student editor of a local university newspaper. In your reply to the high ranking administrator write something like “Yes, I understand the university position in regard to this issue. However, perhaps [creative solution]”. Then quietly insert the editor’s email into CC. In the reply, the administrator will delete the email from CC “for privacy reasons”, but will google to find out who is being CC’ed. Unable to gauge the extend of newspaper’s interest in the story, the administrator might chose to hedge and help you by throwing money at you or mollifying you in some creative way you proposed. Win–win.

Final word

I am confident there will be people on all sides who disagree collectively with just about every sentence I wrote. Remember — this blog post is a not a recommendation to do anything. It’s just my personal point of view on these delicate matters which tend to go undiscussed, leaving many postdocs and junior faculty facing alone their grievances. If you know a good guide on how to deal with these issues (beyond Rota’s advice), please post a link in the comments. Good luck everyone! Hope you will never have to deal with any of that!

What if math dies?

Over the years I’ve heard a lot about the apparent complete uselessness and inapplicability of modern mathematics, about how I should always look for applications since without them all I am doing is a pointless intellectual pursuit, blah, blah, blah.  I had strangers on the plane telling me this (without prompting), first dates (never to become second dates) wondering if “any formulas changed over the last 100 years, and if not what’s the point“, relatives asking me if I ever “invented a new theorem“, etc.

For whatever reason, everyone always has an opinion about math.  Having never been accused of excessive politeness I would always abruptly change the subject or punt by saying that the point is “money in my Wells Fargo account“.  I don’t even have a Wells Fargo account (and wouldn’t want one), but what’s a small lie when you are telling a big lie, right?

Eventually, you do develop a thicker skin, I suppose.  You learn to excuse your friends as well meaning but uneducated, journalists as maliciously ignorant, and strangers as bitter over some old math learning experience (which they also feel obliged to inform you about).  However, you do expect some understanding and respect from fellow academics. “Never compare fields” Gian-Carlo Rota teaches, and it’s a good advice you expect sensible people to adhere.  Which brings me to this:

The worst idea I’ve heard in a while

In a recent interview with Glenn Loury, a controversial UPenn law professor Amy Wax proposed to reduce current mathematics graduate programs to one tenth or one fifteenth of their current size (start at 54.30, see also partial transcript).  Now, I get it.  He is a proud member of the “intellectual dark web“, while she apparently hates liberal education establishment and wants to rant about it.  And for some reason math got lumped into this discussion.  To be precise, Loury provoked Wax without offering his views, but she was happy to opine in response.  I will not quote the discussion in full, but the following single sentence is revealing and worth addressing:

If we got rid of ninety percent of the math Ph.D. programs, would we really be worse off in any material respect?  I think that’s a serious question.

She followed this up with “I am not advocating of getting rid of a hundred percent of them.”  Uhm, thanks, I guess…

The inanity of it all

One is tempted to close ranks and ridicule this by appealing to authority or common sense.  In fact, just about everyone — from Hilbert to Gowers — commented on the importance of mathematics both as an intellectual endeavor and the source of applications.  In the US, we have about 1500-2000 new math Ph.D.’s every year, and according to the AMS survey, nearly all of them find jobs within a year (over 50% in academia, some in the industry, some abroad).

In fact, our math Ph.D. programs are the envy of the world.  For example, of the top 20 schools worldwide between 12 and 15 are occupied by leading US programs depending on the ranking (see e.g. here or there for recent examples, or more elsewhere).  Think about it: math requires no capital investment or infrastructure at all, so with the advent of personal computing, internet and the arXiv, there are little or no entry barriers to the field.  Any university in the world can compete with the US schools, yet we are still on the top of the rankings.  It is bewildering then, why would you even want to kill these super successful Ph.D. programs?

More infrastructurally, if there are drastic cuts to the Ph.D. programs in the US, who would be the people that can be hired to teach mathematics by the thousands of colleges whose students want to be math majors?  The number of the US math majors is already over 40,000 a year and keep growing at over 5% a year driven in part by the higher salary offerings and lifetime income (over that of other majors).  Don’t you think that the existing healthy supply and demand in the market for college math educators already determined the number of math Ph.D.’s we need to produce?

Well, apparently Wax doesn’t need convincing in the importance of math.  “I am the last person to denigrate pure mathematics.  It is a glory of mankind…”   She just doesn’t want people doing new research.  Or something.  As in “enough already.”  Think about it and transfer this thought to other areas.  Say — no new music is necessary — Bach and Drake said it all.  Or — no new art is necessary — Monet and Warhol were so prolific, museums don’t really have space for new works.  Right…

Economics matters

Let’s ask a different question: why would you want to close Ph.D. programs when they actually make money?  Take UCLA.  We are a service department, which makes a lot of money from teaching all kinds of undergraduate math courses + research grants both federal, state and industrial.  Annually, we graduate over 600 students with different types of math/stat majors, which constitutes about 1.6% of national output, the most of all universities.

Let’s say our budget is $25 mil (I don’t recall the figures), all paid for.  That would be out of UCLA budget of $7.5 billion of which less than 7% are state contributions.  Now compare these with football stadiums costs which are heavily subsidized and run into hundreds of millions of dollars.  If you had to cut the budget, is math where you start?

Can’t we just ignore these people?

Well, yes we can.  I am super happy to dismiss hurried paid-by-the-word know-nothing journalists or some anonymous YouTube comments.  But Amy Wax is neither.  She is smart and very accomplished:  summa cum laude from Yale, M.D. cum laude from Harvard Medical School, J.D. from Columbia Law School where she was an editor of Columbia Law Review, argued 15 cases in the US Supreme Court, is a named professor at UPenn Law School, has dozens of published research papers in welfare, labor and family law and economics.  Yep.

One can then argue — she knows a lot of other stuff, but nothing about math.  She is clearly controversial, and others don’t say anything of that nature, so who cares.  That sounds right, but so what?  Being known as controversial is like license to tell “the truth”…  er… what they really think.  Which can include silly things based on no research into our word.  This means there are numerous other people who probably also think that way but are wise enough or polite enough not to say it.  We need to fight this perception!

And yes, sometimes these people get into positions of power and decide to implement the changes.  Two cases are worth mentioning: the University of Rochester failed attempt to close its math Ph.D. program, and the Brown University fiasco.  The latter is well explained in the “Mathematical Apocrypha Redux” (see the relevant section here) by the inimitable Steven Krantz.  Rating-wise, this was a disaster for Brown — just read the Krantz’s description.

The Rochester story is rather well documented and is a good case of study for those feeling too comfortable.  Start with this Notices article, proceed to NY Times, then to protest description, and this followup in the Notices again.  Good news, right?  Well, I know for a fact that other administrators are also making occasional (largely unsuccessful) moves to do this, but I can’t name them, I am afraid.

Predictable apocalypse

Let’s take Amy Wax’s proposal seriously, and play out what would happen if 90-93% of US graduate programs in mathematics are closed on January 1, 2020.  By law.  Say, the US Congress votes to deny all federal funds to universities if they maintain a math Ph.D. program, except for the top 15 out of about 180 graduate programs according to US News.  Let’s ignore the legal issues this poses.  Just note that there are various recent and older precedents of federal government interfering with state and private schools (sometimes for a good cause).

Let’s just try to quickly game out what would happen.  As with any post-apocalyptic fiction, I will not provide any proofs or reasoning.  But it’s all “reality based”, as two such events did happened to mathematicians in the last century, one of them deeply affecting me: the German “academic reforms” in late 1930s (see e.g. here or there), and the Russian exodus in early 1990s (see e.g. here or there, or there).  Another personally familiar story is an implosion of mathematics at Bell Labs in late 1990s.  Although notable, it’s on a much smaller scale and to my knowledge has not been written about (see the discussion here, part 6).

First, there will be huge exodus of distinguished mathematics faculty from school outside of the 15 schools.  These include members of the National Academy of Sciences, numerous ICM speakers, other award winners, etc.  Some will move overseas (Canada, Europe, Japan, China, etc.), some will retire, some leave academia.  Some will simply stop doing research given the lack of mathematical activity at the department and no reward for doing research.

Second, outside of top 15, graduate programs in other subjects notice falling applications resulting in their sliding in world ranking.  These include other physical sciences, economics and computer science.  Then biological and social sciences start suffering.  These programs start having their own exodus to top 15 school and abroad.

Third, given the sliding of graduate programs across the board, the undergraduate education goes into decline across the country.  Top US high school students start applying to school abroad. Many eventually choose to stay in these countries who welcome their stem excellence.

Fourth, the hitech, fintech and other science heavy industries move abroad closer to educated employees.  United States loses its labor market dominance and starts bleeding jobs across all industries.   The stocks and housing market dip down.

Fifth, under strong public pressure the apocalyptic law is repealed and all 180 Ph.D. programs are reinstated with both state and federal financial support.  To everyone’s surprise, nobody is moving back.  Turns out, destroying is much faster and easier than rebuilding, as both Germany and Russia discovered back in the 20th century.  From that point on, January 1, 2020 became known as the day the math died.

Final message:

Dear Amy Wax and Glenn Loury!  Please admit that you are wrong.  Or at least plead ignorance and ask for forgiveness.  I don’t know if you will ever see this post or have any interest in debating the proposition I quoted, but I am happy to do this with you.  Any time, any place, any style.  Because the future of academia is important to all of us.

How many graduate students do we need?

In response to my previous post “Academia is nothing like a drug cartel“, a fellow blogger Adam Sheffer asks:

I was wondering what you think about a claim that I sometimes hear in this context – that one of the problems is that universities train too many Ph.D. students. That with a smaller number of math Ph.D. students the above will be less of a problem, and also that this way there will be a smaller number of people dealing with less “serious/important” topics (whatever this means exactly).

This question is certainly relevant to the “adjunct issue”.  I heard it before, but always found it somewhat confusing.  Specifically to the US, with its market based system, who exactly is supposed to decrease the number of Ph.D.’s?  The student themselves should realize how useless in the doctoral degree and stop applying?  The individual professors should refuse to accept graduate students?  The universities should do this together, in some kind of union?  The government?  All these questions are a bit different and need untangling.

I was going to write a brief reply, but after Adam asked this question I found a yet another example of lazy journalism by Slate’s “education columnist” Rebecca Schuman who argues:

It is, simply put,  irresponsible to accept so many Ph.D. students when you know graduate teaching may well be the only college teaching they ever do.

Of course, Dr. Schuman already has a Ph.D. (from our neighbor UC Irvine) — she just wants others not get one, perhaps to avoid her own fate of an adjunct at University of Missouri.  Needless to say, I cannot disagree more.  Let me explain.

Universities are not allowed to form a cartel

Let’s deal with the easy part.  If the American universities somehow conspired to limit or decrease the number of graduate students they accepts, this would be a classical example of anti-competitive behavior.  Simply put, the academia would form a cartel.  A textbook example of a cartel is OPEC which openly conspires to increase or decrease oil production in order to control world energy prices.  In the US, such activity is against the law due to to the Sherman Act of 1890, and the government/courts have been ruthless in its application (cf. European law to that effect).

One can argue that universities are non-profit institutions and by definition would not derive profit should they conspire, but the law makes no distinction on this, and this paper (co-authored by the celebrity jurist and economist Richard Posner) supports this approach.  And to those who think that only giants such as Standard Oil, AT&T or Microsoft have to worry about anti-trust, the government offers plenty of example of going after  small time cartels.  A notable recent case is Obama’s FTC going after Music Teachers National Association, who have a non-poaching of music students recommendation in their “code of ethics”.  Regardless what you think of that case, it is clear that the universities would never try to limit the number of graduate students in a similar manner.

Labor suppy and demand

As legions before her, Schuman laments that pospective grad students do not listen to “reason”:

Expecting wide-eyed, mind-loving intellectuals to embrace the eventual realities of their situations has not worked—yes, they should know better, but if they listened to reason, they wouldn’t be graduate students in the first place.  Institutions do know better, so current Ph.D. recruitment is dripping with disingenuousness.

But can you really be “wide-eyed” in the internet era?   There is certainly no shortage of articles by both journalists and academics on the “plight” of academic life – she herself links to sites which seem pretty helpful informing prospective graduate students (yes, even the link to Simpsons is helpful).   I have my own favorites: this, that, that and even that.  But all of these are misleading at best and ridiculous at worst.  When I mentioned them on MO, José Figueroa-O’Farrill called them a “parallel universe”, for a good reason.

You see, in this universe people make (mostly) rational decisions, wide-eyed or not.   The internet simply destroyed the information gap.  Faced with poor future income prospects, graduate students either choose to go elsewhere or demand better conditions at the universities.  Faced with a decreasing pool of candidates the universities make an effort to make their programs more attractive, and strive to expand the applicant pool by reaching out to underrepresented groups, foreign students, etc.  Eventually the equilibrium is reached and labor supply meets demand, as it always has.  Asking the universities (who “do know better”)  to have the equilibrium be reached at a lower point is equivalent to asking that Ph.D. programs become less attractive.  And I thought Schuman cares…

Impact of government actions

Now, when it comes to distorting of the labor market, the government is omnipotent and with a single bill can decrease the number of graduate students.  Let’s say, the Congress tomorrow enacts a law mandating a minimum wage of $60,000 a year for all graduate students.  Of course, large universities have small armies of lawyers and accountants who would probably figure out how to artificially hike up the tuition for graduate students and include it in their income, but let’s assume that the law is written to prevent any loopholes.  What would happen next?

Obviously, the universities wouldn’t be able to afford that many graduate graduate students.  The number of them will plunge.  The universities would have to cut back on the TA/recitation/discussion sessions  and probably hire more adjuncts to compensate for the loss.   In time, this would lower the quality of education or lead to huge tuition increases, or mostly likely a little bit of both.  The top private universities who would want to maintain small classes will become completely unaffordable for the middle class.  Meanwhile the poorer state universities will commodify their education by creating huge classes with multiple choice machine testing, SAT-style, and further diminishing student-faculty interaction.  In fact, to compensate for their increasing cost to universities, graduate students will be asked to do more teaching, thus extending their time-to-degree and decreasing the graduation rates.

Most importantly, this would probably have no positive effect on decreasing competition for tenure track jobs, since the academic market is international.  In other words, a decreasing american supply will be immediately compensated with an increasing european supply aided with inflow from emerging markets (ever increasing in quantity and quality production of Ph.D.’s in Asia).   In fact, there is plenty of evidence that this would have sharply negative effect on prospects of American students, as decreased competition would result in weaker research work (see below).

In summary, who exactly would be the winners of this government action?  I can think of only one group: lazy journalists who would have many new reasons to write columns complaining about the new status quo.

The out of control academics

Let’s go back to Schuman’s “it is [..] irresponsible to accept so many Ph.D. students” quote I mentioned above, and judge in on moral merits.  Irresponsible?  Really?  You are serious?  Is it also irresponsible to give so many football scholarships to college students if only a few of them can make it to the NFL?  Is it also irresponsible to have so many acting schools given that so few of the students become movie stars?  (see this list in my own little town).  In the previous post I already explain how graduate schools are apprenticeship programs.  Graduate schools give students a chance and an opportunity to succeed.  Some students do indeed, while others move to do something else, sometimes succeeding beyond expectations (see e.g. this humorous list).

What’s worse, Schuman implicitly assumes that the Ph.D. study can only be useful if directly applicable to obtain a professorship.  This is plainly false.  I notice from her CV that she teaches “The World of Kafka” and “Introduction to German Prose”.  Excellent classes I am sure, but how exactly the students are supposed to use this knowledge in real life?  Start writing in German or become a literary agent?   Please excuse me for being facetious – I hope my point is clear.

Does fewer students means better math?  (on average)

In effect, this is Adam’s speculation at the end of his question, as he suggested that perhaps fewer mathematics graduate students would decrease the number of  “less ‘serious/important’ topics”.  Unfortunately, the evidence suggests the opposite.  When there is less competition, this is a result of fewer rewards and consequently requires less effort to succeed.  As a result, the decrease in the number of math graduate students will lead to less research progress and increase in “less important” work, to use the above  language.

To see this clearly, think of sports.  Compare this list of Russian Major League baseball players with this list by that of Japanese.  What explains the disparity?  Are more Japanese men born with a gift to play baseball?  The answer is obvious.  Baseball is not very popular in Russia.  Even the best Russian players cannot compete in the american minor leagues.  Things are very different in Japan, where baseball is widely popular, so the talented players make every effort to succeed rather than opt for possibly more popular sport (soccer and hockey in Russian case).

So, what can be done, if anything?

To help graduate students, that is.  I feel there is a clear need to have more resources on non-academic options available for graduate student (like this talk or this article).   Institutionally, we should make it easier to cross register to other schools within the university and the nearby universities.  For example, USC graduate students can take UCLA classes, but I have never seen anyone actually doing that.  While at Harvard, I took half a dozen classes at MIT – it was easy to cross register and I got full credit.

I can’t think of anything major the universities can do.  Government can do miracles, of course…

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P.S.  I realize that the wage increase argument has a “fighting straw men” feel.  However, other government actions interfering with the market are likely to bring similarly large economic distortions of the academic market, with easily predictable negative consequences.  I can think of a few more such unfortunate efforts, but the burden is not on me but on “reformers” to propose what exactly do they want the government to do.

P.P.S.  We sincerely wish Rebecca Schuman every success in her search for a tenure track appointment.  Perhaps, when she gets such a position, she can write another article with a slightly sunnier outlook.

Academia is nothing like a drug cartel

It’s been awhile since I wanted to rant. Since the last post, really. Well, I was busy. But the time has come to write several posts.

This post is about a number of recent articles lamenting the prevalence of low paid adjuncts in many universities. To sensationalize the matter, comparisons were made with drug cartels and Ponzi schemes. Allegedly, this inequality is causing poverty and even homelessness and death. I imagine reading these articles can be depressing, but it’s all a sham. Knowingly or not, the journalists are perpetuating false stereotypes of what professors really do. These journalists seem to be doing their usual lazy work and preying on reader’s compassion and profound misunderstanding of the matter.

Now, if you are reading this blog, I am assuming you know exactly what professors do (Hint: not just teaching). But if you don’t, start with this outline by my old friend Daniel Liberzon, and proceed to review any or all of these links: one, two, three, four. When you are done, we can begin to answer our main semi-serious question:

What is academia, really, if it’s not a drug cartel or a Ponzi scheme?

I can’t believe this trivial question is difficult to some people, and needs a lengthy answer, but here it is anyway.

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Academia rewards industriousness and creativity

This might seem obvious – of course it does!  These are the main qualities needed to achieve success doing research. But reading the above news reports it might seem that Ph.D. is like a lottery ticket – the winnings are rare and random. What I am trying to say is that academia can be compared with other professions which involve both qualities. To make a point, take sculpture.

There are thousands of professional sculptors in the United States. The figures vary greatly, but same also holds for the number of mathematicians, so we leave it aside. The average salary of sculptors seems to be within reach from average salary in the US, definitely below that of an average person with bachelor degree. On the other hand, top sculptors are all multimillionaires. For example, recently a sculpture by Jeff Koons sold for $58.4 million. But at least it looked nice. I will never understand the success of Richard Serra, whose work is just dreadful. You can see some of his work at UCLA (picture), or at LACMA (picture).  Or take a celebrated and much despised 10 million dollar man Dale Chihuly, who shows what he calls “art” just about everywhere…  But reasonable people can disagree on this, and who am I to judge anyway?  My opinion does not matter, nor is that of almost anyone.  What’s important, is that some people with expertise value these creative works enough to pay a lot of money for them.  These sculptors’ talent is clearly recognized.

Now, should we believe on the basis of the salary disparity that the sculpture is a Ponzi scheme, with top earners basically robbing all the other sculptors of good living?  That would be preposterous, of course.  Same with most professors.  Just because the general public cannot understand and evaluate their research work and creativity, does not mean it’s not there and should not be valued accordingly.

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Academia is a large apprenticeship program

Think of graduate students who are traditionally overworked and underpaid. Some make it to graduate with a Ph.D. and eventually become tenured professors. Many, perhaps most, do not. Sounds like a drug cartel to you? Nonsense! This is exactly how apprenticeships works, and how it’s been working for centuries in every guild.  In fact, some modern day guilds don’t pay anything at all.

Students enter the apprenticeship/graduate program in hopes to learn from the teacher/professor and succeed in their studies. The very best do succeed. For example, this list of Rembrant‘s pupils/assistants reads somewhat similar to this list of Hilbert‘s students. Unsurprisingly, some are world famous, while others are completely forgotten. So it’s not about cheap labor as in drug cartels – this is how apprenticeships normally work.

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Academia is a big business

Think of any large corporation.  The are many levels of management: low, mid, and top-level.  Arguably, all tenured and tenure-track faculty are low level managers, chairs and other department officers (DGS, DUS, etc.) are mid-level, while deans, provosts and presidents/chancellors are top-level managers.  In the US, there is also a legal precedent supporting qualifying professors as management (e.g. professors are not allowed to unionize, in contrast with the adjunct faculty).  And deservingly so.  Professors hire TA’s, graders, adjuncts, support stuff, choose curriculum, responsible for all grades, run research labs, serve as PI’s on federal grants, and elect mid-level management.

So, why many levels?  Take UCLA.  According to 2012 annual report, we operate on 419 acres, have about 40 thousand students, 30 thousand full time employees (this includes UCLA hospitals), have $4.6 billion in operating revenue (of which tuition is only $580 million), but only about 2 thousand ladder (tenure and tenure-track) faculty.  For comparison, a beloved but highly secretive Trader Joe’s company has about $8 billion in revenue, over 20 thousand employees, and about 370 stores, each with 50+ employees and its own mid and low-level management.

Now that you are conditioned to think of universities as businesses and professors as managers, is it really all that surprising that regular employees like adjuncts get paid much less?  This works the same way as for McDonalds store managers, who get paid about 3 times as much as regular employees.

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Higher echelons of academia is a research factory with a side teaching business

Note that there is a reason students want to study at research universities rather than at community colleges.  It’s because these universities offer many other more advanced classes, research oriented labs, seminars, field works, etc.  In fact, research and research oriented teaching is really the main business rather than service teaching.

Think revenue.  For example, UCLA derives 50% more revenue from research grants than from tuition.  Places like MIT are giving out so many scholarships, they are loosing money on teaching (see this breakdown).  American universities cannot quit the undergraduate education, of course, but they are making a rational decision to outsource the low level service teaching to outsiders, who can do the same work but cheaper.  For example, I took English in Moscow, ESL at a community college in Brooklyn, French at Harvard, and Hebrew at University of Minnesota.  While some instructors were better than others, there was no clear winner as experience was about the same.

So not only the adjunct salaries are low for a reason, keeping them low is critical to avoid hiring more regular faculty and preventing further tuition inflation.  The next time you read about adjuncts barely making a living wage, compare this to notorious Bangalore call centers and how much people make over there (between $100 and $250 a month).

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Academia is a paradise of equality

College professors are different from drug gangsters not only in the level of violence, but also in a remarkable degree of equality between universities (but not between fields!)  Consider for example this table of average full professor salaries at the top universities.  The near $200,000 a year may seem high, but note that this is only twice that of average faculty at an average college.  Given that most of these top universities are located in the uber-expensive metropolitan areas (NYC, Boston, San Francisco, Los Angeles, etc.), the effect is even further diminished. 

Compare this with other professions.  Forget the sculptors mentioned above whose pay ratios can go into thousands, let’s take a relatively obscure profession of an opera singer (check how many do you know from this list).  Like academia and unlike sculpture, the operas are greatly subsidized by the governments and large corporations.  Still, perhaps unsurprisingly, there is a much greater inequality than in academia.  While some popular singers like Dmitri Hvorostovsky make over $3 million a year, the average salary is about $100,000 a year, giving a ratio of 30+.

In other words, given that some professors are much better than others when it comes to research (not me!), one can argue that they are being underpaid to subsidize the lackluster efforts of others.  No wonder the top academics suffer from the status-income disequilibrium.  This is the opposite of the “winner takes all” behavior argued by the journalists in an effort to explain adjuncts’ plight.

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Academia is an experience

People come to universities to spend years studying, and they want to enjoy those years.  They want to hear famous authors and thinkers, learn basic skills and life changing stories, make lasting friendships, play sports and simply have fun.  Sometimes this does not work out, but we are good at what we do (colleges have been perfecting their craft for hundreds of years).  Indeed, many students take away with them a unique deeply personal experience.  Take my story.  While at Moscow University, I heard lectures by Vladimir Arnold, attended Gelfand’s Seminar, and even went to a public lecture by President Roh Tae-woo.  It was fun.  While at Harvard, I took courses of Raoul Bott and Gian-Carlo Rota (at MIT), audited courses of such non-math luminaries as Stephan Thernstrom and William Mills Todd, III, and went to public lectures by people like Tim Berners-Lee, all unforgettable.

So this is my big NO to those who want to replace tenured faculty with adjuncts, leveling the academic salaries, and commodifying the education.  This just would not work; it is akin to calls for abolition of haute cuisine in favor of more fast food.  In fact, nobody really wants to do either of these.  The inexpensive education is already readily available in the form of community colleges.  In fact, students apply in large numbers trying to get to a place like UCLA, which offers a wide range of programs and courses.  And it’s definitely not because of our celebrity adjuncts.

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In conclusion

Academia is many things to many people.  There are many important reasons why the ladder faculty are paid substantially better than TA’s and adjuncts, reasons both substantive and economical.  But at no point does the academia resemble the Ponzi schemes and drug cartels, which are famous for creating the economic devastation and inequality (and, um, illegal).  If anything, the academia is the opposite, as it creates economic opportunities and evens the playing field.   And to those educational reformers who think they know better: remember, we heard it all before…

Admission blues: How to fix GRE Mathematics and tweak the Putnam Competition

I was thinking about the Putnam competition and the GRE Mathematics test in the context of graduate admissions.  Are they useful?  If yes, which one is more relevant?  After crunching some numbers, I concluded that while they are useful to some extend, there are problems with both.  Even worse, a number of students who fall in the gap between “very good” and “exceptional”, are ill served with either.

1. Graduate admissions in mathematics

As I mention in my earlier post, every year the US produces around 1,600 Ph.D.’s in mathematical sciences (math, applied math, statistics) from over 100 accredited programs, of which about 900 are US citizen and permanent residents.  If you restrict to mathematics alone, the numbers drop by about 25% to about 1200. The overall 10 year completion rate is about 50%  according to the Council of Graduate Schools study, so perhaps about 3,000-3,200 students start graduate programs.

As a general rule, graduate programs in mathematics explicitly ask for the GRE Subject test scores, but are often happy to hear about the Putnam results as well.  In fact, some “how to” guides now recommend taking Putnam exam (and Putnam prep classes!) on par with the GRE test and REU programs (see e.g. here and there).  How the schools use either data is probably quite a bit different, and is the other side of our main question.

2. GRE Mathematics Subject test in numbers

The GRE Subject tests are developed and administered by ETS, which is nominally non-profit, but with about 1 billion dollars in revenue.  For a quick comparison with a for-profit, non-profit and public institutions, e.g. New York Times Corp, Harvard and UCLA, had 2.3, 3.7 and 4.3 bln dollars in 2011 operating revenues, respectively.

From the official GRE test preparation publication:  “The questions are classified approximately as follows: calculus (50%), algebra (25%) and other topics (25%).”  This is already unfortunate, but more on that later.  Here are these “other topics”:

Introductory real analysis (sequences and series of numbers and functions, continuity, differentiability and integrability, elementary topology of R), discrete mathematics (logic, set theory, combinatorics, graph theory, and algorithms), general topology, geometry, complex variables, probability and statistics, and numerical  analysis.  The above descriptions of topics covered in the test should not be considered exhaustive […]  (emphasis mine – IP)

The GRE Guide gives .92 value for the KR20 reliability test, a solid measure suggesting the test has many questions leading to different scores between strong and weak students.  The students have 170 minutes for about 65 questions.  The scores are on the scale from 200 to 990, are rounded to nearest multiple of 10, with standard errors 31 points, and 44 for the differences.  In other words, if I understand correctly (the guide is vague on this), one should not reliably compare students with scores differing by 50 points of less.  I am doubtful most grad schools  follow that.

In the same GRE guide, ETS reports that there were about 12,800 test takers in four years (July 2008 to June 2011), roughly 3200 a year.  This loosely coincides with our graduate student data, as the students take on average one GRE Subject test.  In other words, all students with GRE scores get accepted somewhere.  So one should not be surprised to see a high correlation (but not necessarily causation) between grad school ranking and GRE Subject scores. Curiously, ETS’s own study says GRE General are a very poor predictor of success in math graduate programs, at least when it comes to GPA and graduation rate.

So how do grad schools use the GRE Math scores? That’s very much unclear. Of course, all schools gather the statistics like averages of those applied, admitted and/or accepted (reported to the dean, external department reviewers, the NRC study, the US News, etc.), but very few make it publicly available.  In a rare moment of openness, Penn State admits what amounts to not much use of GRE scores: their average scores vary widely over the years, swinging from 650 to 890, with a positive trend in recent years.  In a general MO discussion on this, Pete Clark writes that University of Georgia does  not require GRE Subject, so he looks for high GRE General scores.  UCLA is a bit evasive: “those we offer admission to have GRE subject scores in or above the 80th percentile” which according to GRE chart amounts to minimum of about 790, suggesting relevance.   MIT is blunt but imprecise: “There is no minimum GRE test score required, but if the score on the math subject GRE is not very high, evidence of excellence must be present elsewhere in the application or in the letters of recommendation.” UPenn is actually helpful: “[GRE Math score] should be at least 750, though applicants with somewhat lower scores may be admitted if the rest of their application is sufficiently strong,” and that the recent average score is 820.  This all makes a very foggy picture.

3. Putnam competition in numbers

The premise is simple: first Saturday in December, 6 hours (in two sittings) to solve 12 problems in all areas of mathematics, maximum of 10 points per problem.  Joe Gallian wrote a nice summary. The problems are difficult: the maximal score 120 is achieved only very occasionally, once in about 10-15 years.  The median score is often either 0, 1 or 2 (out of 120!), and the mean is between 5 and 10 points.  I bet it must be depressing to spend 6 hours and get no or almost no points.

The top 5 scorers are “Putnam Fellows”, another 18-20 are “in the money”, and about 50-60 get “honorable mention”.  In 2011, there were “4,440 students from 572 colleges and universities in Canada and the United States”.  The historical data shows that there is a clear correlation between doing well on Putnam and doing well in mathematics, which is even more pronounced for the top 25, and especially Putnam fellows.

Of course, the competition is not aimed at helping graduate admissions, as emphasized by the mid-March results date (way after the applications are due and the admission decisions are made).  It does not even make the scores available in any official format.  In fact, historically, it is primarily a team competition, a nerdy alternative to college athletics.  Finally, a competition is not necessarily similar to do research.  As Kedlaya said, “A contest problem is meant to be solved in the space of minutes or hours, whereas in research, one sometimes works on the same problem for days, months, occasionally even years.”

4. A bissel of analysis

(a)  GRE Math.  While useful to some extend, mostly for the middle and bottom scoring students, it is largely useless for most of the better prepared students.  Indeed, in the “upper middle range” of 75 to 90 percentile, the test scores range between 770 and 850, comprising about 500 students every year.  By the rules of GRE, many of these students cannot be even compared.  Those who can, it is unclear whether they really are better candidates for doing research and teaching in mathematics.  Indeed, the excessive emphasis on calculus, real analysis and linear algebra shows the student’s ability to memorize concepts and quickly perform routine tasks.  This does not test problem solving.  Neither do “other topics” which are heavily testing definitions of a group, ring, metric space, etc.  I bet the performance in this part strongly correlates with the quality of the undergraduate institution: better colleges offer more serious math classes, and GRE Math preparation classes, which cover these basic topics; others do not.

For the top 10%, the GRE Math scores does distinguish between them, but that’s hardly necessary.  Of the top 250-300 students over half of them are international and often come with accolades like “the best student in N years from the XYZ university.” Last year I recall even one European student described as “the best student since World War II from … country”.  Those 100-150 that are from the US, are well served with numerous REU programs both national and at their home universities, by the Budapest and Moscow semesters, Putnam, IMO and other competitions, etc.  Their GRE scores seem irrelevant in retrospect.

Now, using AMS Classification, Group I of 48 top math graduate programs graduates about 550 Ph.D’s.  All are research oriented.  I am guesstimating that they must be accepting c. 800 students in total.  So after the top 300 are accepted, how are they suppose to choose the next 500 if GRE is irrelevant?

(b) Putnam.  Even though a majority receive only single digit score, there is a clear benefit for the top programs to know who the winners are.  The top 25 individuals, clearly possess excellent problem solving abilities, which is useful in a number of areas of mathematics.  The are multiple problems with this.  First, it would be nice to have the list of winners available by December.  Second, it would be nice if Putnam is offered overseas.  But even for the US/Canada based students, as it stands, the senior’s performance is not counted in admissions due calendar issues.  Since students often are encouraged to take their junior year abroad, the best performance they can include in their applications is from their sophomore year, which is often inferior to their senior year performance.  So with exception of the truly top students, Putnam results are not used in the admissions.

5. A modest proposal, Russian style

(a) GRE Math.  Split the GRE Mathematics into two parts.  Keep Calculus/Linear Algebra in the first half, more or less in the same multiple choice form as you have now.  It is clearly helpful for middle and bottom tier students and programs.  For the second part, make it a no-hard-math-required problem solving style.  Make many relatively simple problems, much much simpler than IMO problems, more like Moscow olympiads for the freshman-sophomore HS years (8-9th year out of 11).  This would allow relatively unbiased testing of problem solving, extremely useful to mathematics programs.  Both scores would need to be reported (kind of like 4 GRE General scores).

As revenue figures suggest, ETS is essentially a large utility company which does not want to rock the boat.  But it has made changes before, and this particular change would be relatively painless and have the added advantage that no “other fields” need to be argued about – all students will know exactly what is the scope of the test.

(b) Putnam.  Ugh.  It’s true that “if it ain’t broke, don’t fix it“, so I don’t want to propose major changes.  Just three minor tweaks, which will not change the core competition, but hopefully will make it more democratic and helpful for graduate admissions.

* First, move the competition to late September, so the scores can be revealed before Jan 1.  I really don’t see what exactly is hard about that.  Perhaps, some Putnam prep classes will have to be moved to the Spring.  So what?

* Second, open it for international students.  I know, I know, time difference, language issues, etc.  Whatever, keep it on the US time and only in English, as it is now.  If the overseas students want to participate, they might have to do this at night perhaps (simply allow unlimited tea, coffee and Red Bull).  This is still better than not giving them an opportunity at all.  Another issue is trust (in foreign faculty supervisors).  For that, use the technology.  Reveal the problem on some website for all at once.  Videotape what’s happening in all rooms where the competition is taking place.  Have all solutions uploaded as .pdf files to the main server within minutes after the end of the competition (they should still be graded locally, with top scores re-graded at a central location).  While some of this might be an obstacle for some universities in poor countries, the majority of foreign universities already have all the necessary technology to make this happen.

* Third, and most controversially, at least for the US/Canadian students allow an easy “parallel track”.  That is, come up with substantially easier problems which can be administered at the same time in parallel.  The students should be given a choice – either real problems which are hard, or easier problems which do not count.  This would be good for students’ morale as a means to prevent the annual 40% of 0 scores, and the scores can be useful for admission.  I am modelling this based on the widely successful Tournament of Towns, which has two levels and two tracks (harder and easier), see this problem archive.

P.S.  Full disclosure: I took GRE Math in 1994 and received maximal score available at that time. I recall finishing early, but missing a couple of problems possibly due to some English language difficulties.  I did not participate in the Putnam – was busy in Moscow.  More recently, I also participated in graduate admissions, but everywhere above made sure I use only open sources and no “inside information”.

What’s the Matter with Hertz Foundation?

Imagine you have plenty of money and dozens of volunteers.  You decide to award one or two fellowships a year to the best of the best of the best in math sciences.  Easy, right?  Then how do you repeatedly fail at this, without anyone notice?  Let me tell you how.  It’s an interesting story, so bear with me.

A small warning.  Although it may seem I am criticizing Hertz Foundation, my intention is to show its weakness so it can improve.

What is the Hertz Foundation?

Yesterday I wrote a recommendation letter to the Hertz Foundation.  Although a Fellow myself, I never particularly cared for the foundation, mostly because it changed so little in my life (I received it only for two out of five years of eligibility).  But I became rather curious as to what usually happens to Hertz Fellows.  I compiled the data, and found the results quite disheartening.  While perhaps excellent in other fields, I came to believe that Hertz does barely a mediocre job awarding fellowships in mathematics.  And now that I think about it, this was all completely predictable.

First, a bit of history.  John Hertz was the Yellow Cab founder and car rental entrepreneur (thus the namesake company), and he left a lot of money dedicated for education in “applied physical sciences”, now understood to include applied mathematics.  What exactly is “applied mathematics” is rather contentious, so the foundation wisely decided that “it is up to each fellowship applicant to advocate to us his or her specific field of interest as an ‘applied physical science’.”

In practice, according to the website, about 600 applicants in all areas of science and engineering apply for a fellowship.  Applications are allowed only either in the senior year of college or 1st year of grad school.  The fellowships are generous and include both the stipend and the tuition; between 15 and 20 students are awarded every year.  Only US citizen and permanent residents are eligible, and the fellowship can be used only in one of the 47 “tenable schools” (more on this below).  The Foundation sorts the applications, and volunteers interview some of them in the first round.  In the second round, pretty much only one person interviews all that advanced, and the decision is made.  Historically, only one or two fellowships in mathematical sciences are awarded each year (this includes pure math, applied math, and occasionally theoretical CS or statistics).

Forty years of Math Hertz Fellowships in numbers

The Hertz Foundation website has a data on all past fellows.  I compiled the data in Hertz-list which spanned 40 years (1971-2010), listed by the year the fellowship ended, which usually but not always coincided with graduation.  There were 67 awardees in mathematics, which makes it about 1.7 fellowships a year.  The Foundation states that it awarded “over 1000 fellowships” so I guess about 5-6% went into maths (perhaps, fewer in recent years).  Here is who gets them.

1) Which schools are awarded?  Well, only 44 US graduate programs are allowed to administer the fellowships.  The reasons (other than logistical) are unclear to me.  Of those programs that are “in”, you have University of Rochester (which nearly lost its graduate program), and UC Santa Cruz (where rumors say a similar move had been considered).  Those which are “out” include graduate programs at Brown, UPenn, Rutgers, UNC Chapel Hill, etc.  The real distribution is much more skewed, of course. Here is a complete list of awards per institution:

MIT – 14
Harvard, Princeton – 8
Caltech, NYU – 7
Berkeley, Stanford – 5
UCLA – 3
CMU, Cornell, U Chicago – 2
GA Tech, JHU, RPI, Rice – 1

In summary, only 15 universities had at least one award (34%), and just 7 universities were awarded 54 fellowships (i.e. 16% of universities received 81% of all fellowships).  There is nothing wrong with this per se, just a variation on the 80-20 rule you might argue.  But wait!  Hertz Foundation is a non-profit institution and the fellowship itself comes with a “moral commitment“.  Even if you need to interfere with “free marketplace” of acceptance decisions (see P.S. below), wouldn’t it be in the spirit of John Hertz’s original goal, to make a special effort to distribute the awards more widely?  For example, Simons Foundation is not shy about awarding fellowship to institutions many of which are not even on Hertz’s list.

2)  Where are they now?  After two hours of googling, I located almost all former fellows and determined their current affiliations (see the Hertz-list).  I found that of the 67 fellows:

University mathematicians – 27 (40%)
Of these, work at Hertz eligible universities – 14, or about 21% of the total (excluding 3 overseas)
At least 10 who did not receive a Ph.D. – 15%
At least 13 are in non-academic research – 19% (probably more)
At least 8 in Software Development and Finance – 12% (probably more)

Now, there is certainly nothing wrong with directing corporate research, writing software, selling derivatives, designing museum exhibits, and even playing symphony orchestra or heading real estate company, as some of the awardees do now.  Many of these are highly desirable vocations.  But really, was this what Hertz had in mind when dedicating the money?  In the foundation’s language, “benefit us all” they don’t.

I should mention that the list of Hertz Fellows in Mathematics does include a number of great academic success stories, but that’s not actually surprising.  Every US cohort has dozens of excellent mathematicians.  But the 60% drop out rate from academia is very unfortunate, only 21% working in “tenable universities” is dismaying, and the 15% drop out rate from graduate programs is simply miserable.  Couldn’t they have done better?

A bit of analysis

Every year, US universities award over 1,600 Ph.D.’s in mathematical sciences, of which over a half go to US citizen (more if you include permanent residents, but stats is not easily available).  So they are choosing 1.7 out of over 800 eligible students.  Ok, because of their “tenable schools” restriction this is probably more like 300-400.   Therefore, less than half of one percent of potential applicants are awarded!  For comparison, Harvard college acceptance rate is 10 times that.

Let me repeat: in mathematics, Hertz fellows drop out from their Ph.D. programs at a rate of 15%.  If you look into the raw 2006 NRC data for graduation rates, you will see that many of the top universities have over 90% graduation rate in the math programs (say, Harvard has over 91%).  Does that mean that Harvard on average does a better job selecting 10-15 grad students every year, while Hertz can’t choose one?

Yes, I think it does.  And the gap is further considering that Hertz has virtually no competition (NSF Fellowships are less generous in every respect).  You see, people at Harvard (or Princeton, MIT, UCLA, etc.) who read graduate applications, know what they are doing.  They are professionals who are looking for the most talented mathematicians from a large pool of applicants.  They know which letters need to be taken seriously, and which with a grain of salt.  They know which undergraduate research experience is solid and which is worthless.  They just know how things are done.

Now, a vast majority of Hertz interviewers are themselves former fellows, and thus about 95% of them have no idea about the mathematics research (they just assume it’s no different from the research they are accustomed to).  Nor does the one final interviewer, who is an applied physicist.  As a result, they are to some extend, flipping coins and rolling dies, in hope things will work out.  You can’t really blame them – they simply don’t know how to choose.  I still remember my own two interviews.  Both interviewers were nice, professional, highly experienced and well intentioned, but looking back I can see that neither had much experience with mathematical research.

You can also see this lack of understanding of mathematics culture is creeping up in other activities of the foundation, such as the thesis prize award (where are mathematicians?), etc.   Of course a private foundation can award anyone it pleases, but it seems to me it would do much more good if only some special care is applied.

A modest proposal

There is of course, a radical way to change the review of mathematics applicants – subcontract it to the AMS (or IMA, MSRI, IPAM – all have the required infrastructure).  For a modest fee, the AMS will organize a panel of mathematicians who will review and rank the applicants without interviewing them.  The panel will be taking into consideration only students’ research potential, not the university prestige, etc.  The Hertz people can then interview the top ranked and make a decision at the last stage, but the first round will be by far superior to current methods.  Even the NSA trusts AMS, so shouldn’t you?

Hertz might even save some money it currently spends on travel and lodging reimbursements.  The 13% operating budget is about average, but there is some room for improvement.  Subcontracting will probably lead to an increase in applications, as AMS really knows how to advertise to its members (I bet you currently receive only about 40 mathematics applications, out of a potential 400+ pool).  To summarize: really, Hertz Foundation, think about doing that!

P.S.  It is not surprising that the 7 top universities get a large number of the fellowships.  One might be tempted to assume that clueless interviewers are perhaps somewhat biased towards famous school names in the hope that these schools already made a good decision accepting these applicants, but this is not the whole story.  The described bias can only work for the 1st year grad applicants, but for undergraduate applicants a different process seems to hold.  Once a graduate school learns that an applicant received Hertz Fellowship (or NSF for that matter), it has every incentive to accept the student, as the tuition and the stipend are paid by the outside sources now.

P.P.S.  Of course, mathematicians’ review can also fail.  Even the super prestigious AIM Fellowship has at least one recipient who left academia for bigger and better things.

UPDATE (April 15, 2019).  Over the years since this blog post, I have been contacted by people from the Hertz Foundation board.  I have also followed up on the story and the recent fellowship recipients.  I am happy to say that the foundation implemented various important changes vis-à-vis math interviews, to the visible effect.  At the moment, the numbers are too small to report statistics and the changes I know are not a public information.   I concluded that my criticism no longer applies, a happy ending to the story.  I encourage now everyone to support the foundation financially as well as recommend your best students to apply.