Take an interview!

We all agree that Math is a human endeavor, yet we know so preciously little about mathematicians as humans working in mathematics. Our papers tend to have preciously few quotable sentences outside of the dry mathematical context. In fact, most introductions are filled with passages of the form “X introduced the celebrated tool pqr, which over the next 20 years was refined by A, B and C, and most recently was used by D to prove Z’s conjecture“. It is such a weak tea to convey contributions of six people in one short sentence, yet we all do this nonetheless.

In my “How to write a clear math paper” article accompanying this blog post, I argue that at least the first paragraph or the first subsection of a long paper can be human and aimed at humans. That is the place where one has freedom to be eloquent, inspiring, congratulatory, prescient, revelatory and quotable. I still believe that, but now I have a new suggestion, see the title of this blog post.

The art of autobiographies

These days many great scientists remain active into very old age, and rarely want or have time to write an autobiography. Good for them, bad for us. Psychologically this is understandable — it feels a little epitaphish, so they would much rather have someone else do that. But then their real voice and honest thoughts on life and math are lost, and can never be recorded. There is blogging, of course, but that’s clearly not for everyone.

There are some notable exceptions to this, of course. When I was in High School, reading autobiographies of Richard Feynman, Stan Ulam and Norbert Wiener was a pure joy, a window into a new world. The autobiоgraphy by Sofya Kovalevskaya was short on mathematical stories, but was so well written I think I finished the whole thing in one sitting. G.H. Hardy’s “Apology” is written in different style, but clearly self-revealing; while I personally disagree with much of his general point, I can see why the book continues to be read and inspire passionate debates.

More recently, I read William Tutte, “Graph Theory As I Have Known It“, which is mostly mathematical, but with a lot of personal stories delivered in an authoritative voice. It’s a remarkable book, I can’t praise it enough. Another one of my favorites is Steven Krantz, “Mathematical Apocrypha” and its followup, which are written in the first person, in a pleasant light rumor mill style. Many stories in these near-autobiographies were a common knowledge decades ago (even if some were urban legends), but are often the only way for us to learn now how it was back then.

On the opposite end of the spectrum there is L.S. Pontryagin’s autobiography (in Russian), which is full of wild rumors, vile accusations, and banal antisemitism. The book is a giant self-own, yet I couldn’t stop myself from hate-reading the whole thing just so I could hear all these interesting old stories from horse’s mouth.

Lately, the autobiographies I’ve been reading are getting less and less personal, with little more than background blurbs about each paper. Here are those by George Lusztig and Richard Stanley. It’s an unusual genre, and I applaud the authors for taking time to write these. But these condensed CV-like auto-bios clearly leave a lot of room for stories and details.

Why an interview?

Because a skillful interviewer can help a mathematician reveal personal stories, mathematical and metamathematical beliefs, and even general views (including controversial ones). Basically, reveal the humanity of a person that otherwise remains guarded behind endless Definition-Lemma-Theorem constructions.

Another reason to interview a person is to honor her or his contributions to mathematics. In the aftermath of my previous blog post, I got a lot of contradictory push-back. Some would say “I am shocked, shocked, to find that there is corruption going on. I have submitted to many invited issues, served as a guest editor for others and saw none of that! So you must be wrong, wrong, wrong.” Obviously, I am combining several POVs, satirizing and paraphrasing for the effect.

Others would say “Yes, you are right, some journals are not great so my junior coauthors do suffer, the refereeing is not always rigorous, the invited authors are often not selected very broadly, but what can I do? The only way I can imagine to honor a person is by a math article in an invited issue of a peer review journal, so we must continue this practice” (same disclaimer as above). Yeah, ok the imaginary dude, that’s just self-serving with a pretense of being generous and self-sacrificing. (Yes, my straw man fighting skill are unparalleled).

In fact, there are many ways to honor a person. You can give a talk about that person’s contributions, write a survey or a biographical article, organize a celebratory conference, or if you don’t want to be bothered simply add a dedication in the beginning of the next article you publish. Or, better yet, interview the honoree. Obviously, do this some time soon, while this person is alive, and make sure to put the interview online for everyone to read or hear.

How to do an interview?

Oh, you know, via Zoom, for example. The technical aspects are really trivial these days. With permission, you can record the audio/video by pushing one button. The very same Zoom (or Apple, Google, Amazon, Microsoft, etc.) have good speech-to-text programs which will typeset the whole interview for you, modulo some light editing (especially of math terminology). Again, with a couple of clicks, you can publish the video or the audio on YouTube, the text on your own website or any social media. Done. Really, it’s that easy!

Examples

I have many favorites, in fact. One superb video collection is done by the Simons Institute. I already blogged here about terrific interviews with László Lovász and Endre Szemerédi. The interviewer for both is Avi Wigderson, who is obviously extremely knowledgeable of the subject. He asked many pointed and interesting questions, yet leaving the interviewees plenty of space to develop and expand on their their answers. The videos are then well edited and broken into short watchable pieces.

Another interesting collection of video interviews is made by CIRM (in both English and French). See also general video collections, some of which have rather extensive and professionally made interviews with a number of notable mathematicians and scientists. Let me single out the Web of Stories, which include lengthy fascinating interviews with Michael Atiyah, Freeman Dyson, Don Knuth, Marvin Minsky, and many others.

I already wrote about how to watch a math video talk (some advice may be dated). Here it’s even easier. At the time of the pandemic, when you are Zoom fatigued — put these on your big screen TV and watch them as documentaries with as much or as little attention as you like. I bet you will find them more enlightening than the news, Netflix or other alternatives.

Authorized biography books are less frequent, obviously, but they do exist. One notable recent example is “Genius At Play: The Curious Mind of John Horton Conway” by Siobhan Roberts which is based on many direct conversations. Let me also single out perhaps lesser known “Creative Minds, Charmed Lives” by Yu Kiang Leong, which has a number of interesting interviews with excellent mathematicians, many of the them not on other lists. For example, on my “What is Combinatorics” page, I quote extensively from his interview with Béla Bollobás, but in fact the whole interview is worth reading.

Finally, there is a truly remarkable collection of audio interviews by Eugene Dynkin with leading mathematicians of his era, spanning from 1970s to 2010s (some in English, some in Russian). The collection was digitized using Flash which died about five years ago, rendering the collection unusable. When preparing this post I was going to use this example as a cautionary tale, but to my surprise someone made it possible to download them in .mp3. Enjoy! Listening to these conversations is just delightful.

Final thoughts

Remember, you don’t have to be a professional interviewer to do a good job. Consider two most recent interviews with Noga Alon and Richard Stanley by Toufik Mansour. By employing a simple trick of asking the same well prepared questions, he allows the reader to compare and contrast the answers, and make their own judgement on which ones they like or agree with the most. Some answers are also quite revealing, e.g. Stanley saying he occasionally thinks about the RH (who knew?), or Alon’s strong belief that “mathematics should be considered as one unit” (i.e. without the area divisions). The problems they consider to be important are also rather telling.

Let me mention that in the digital era, even the amateur long forgotten interviews can later be found and proved useful. For example, I concluded my “History of Catalan numbers” with a quote from an obscure Richard Stanley’s interview to the MIT undergraduate newspaper. There, he was discussing the origins of his Catalan numbers exercise which is now a book. Richard later wrote to me in astonishment as he actually completely forgot he gave that interview.

So, happy watching, listening, and reading all the interviews! Hope you take some interviews yourself for all of us to enjoy!

The guest publishing scam

For years, I have been a staunch opponent of “special issues” which proliferate many good journals. As an editor, when asked by the publisher if we should have some particular guest issue I would always say no, only to be outvoted or overruled by the Editor in Chief. While I always believed there is some kind of scam going on, I never really thought about it. In fact, it’s really on the surface for everyone to see…

What is so special about special issues?

Well, let me explain how this works. Imagine you organized an annual conference and you feel it was a success. Or you organized a birthday/memorial conference in honor of a senior colleague in the area and want to do more. You submit a proposal to a journal: please, please, can we become “guest editors” and publish a “special issue” of the journal? Look, our conference had so many terrific people, and the person we are honoring is such a great mathematician, so famous and so kind to everyone, how can you say no?

And the editors/publishers do say yes. Not always. Sometimes. If one journal refuses, the request is made to another journal. Eventually, like with paper submissions, some journal says “sure”. The new guest editors quickly ask all/some conference speakers to submit papers. Some/many do. Most of these papers get accepted. Not a rule, just social contract. As in “how dare you reject this little paper by a favorite student of the honoree?”

The journal publishes them with an introductory article by guest editors lauding the conference. A biographical article with reminiscences is also included, with multiple pictures from earlier conferences or from the family archive, always showing light side of the great person. The paper version of the journal is then sent to all authors, or is presented with a pomp to the honoree at some retirement party as some kind of math version of a gold watch. None of them will ever open the volume. These issues will be recycled at best, as everyone will continue to use online versions.

Sounds like a harmless effort, don’t you see? Nobody is acting dishonorably, and mathematicians get to publish more papers, journals get to have submissions the wouldn’t otherwise, the conference or a person gets honored. So, win-win-win, right? Well, hear me out.

Why do the journal editors do it?

We leave the publishers for last. For a journal editor in chief this is straightforward. If they work for leading for-profit publishers they get paid. For a good reason in fact — it’s a hard work. Now, say some friends ask to do part of your job for free, and the proposal looks good, and the list of potential authors is pretty reasonable perhaps. You get to help yourself, your friends, and the area you favor, without anyone ever holding you responsible for the outcome. Low level corruption issues set aside and ignored, who wouldn’t take this deal?

Why do the guest editors do it?

Well, this is the easiest question. Some want to promote the area, some to honor the honoree, some just want to pad their CVs. It’s all good as far as I am concerned. They are not the problem.

Why do the authors do it?

Well, for multiple reasons. Here are some possible scenarios based on my observations. Some are honorable, some are dishonorable, and some in between.

Some authors care deeply for the subject or the honoree. They send their best work to the invited issue. This is their way to give back. Most likely they could’ve published that paper in a much better journal. Nobody will ever appreciate their “sacrifice”, but they often don’t care, it makes them feel better, and they have a really good excuse anyway. From the journal POV these are the best papers. Grade A.

Other authors think of these special issues completely differently and tailor make the paper to the issue. For example, they write personal memoir style reminiscences, as in “ideas from my conversations with X”, or “the influence of X on my work”. Other times they write nice surveys, as in “how X’s work changed field ABC”, or “recent progress on X’s conjectures”. The former are usually low on math content but mildly entertaining, even if not always appropriate for a traditional math journal (but why be constrained with old conventions?) The latter can be quite useful in a way surveys are often in demand, even if the timing for these particular surveys can be a little forced. Also, both are quite appropriate for these specific issues. Anyway, Grade B.

Some authors are famous, write many papers a year, have published in all good and even not-so-good journals multiple times already, so they don’t care which journal they submit next. Somebody asks them to honor somebody/something, and they want to be nice and send their next paper whether or not it’s good or bad, or even remotely related to the subject. And why not? Their name on the paper is what matters anyway, right? Or at least that’s what they think. Grade C.

Some authors have problematic papers which they desperately want to publish. Look, doing research, writing papers and publishing is hard, I get it. Sometimes you aim to prove a big deal and just almost nothing comes out, but you still want to report on your findings just as a tribute to the time you spent on the problem. Or a paper was rejected from a couple of journals and you are close to typing up a stronger result, so want to find a home for the paper asap before it becomes unpublishable at your own hand! Or you haven’t published for years, you’re worried your department may refuse you a promotion, so you want to publish anything, anywhere, just to get a new line on your CV. So given a chance you submit, with an understanding that whatever you submit will likely get published. The temptation is just too strong to look away. I don’t approve, if you can’t tell… Grade D/F.

Why do the publishers do it?

That’s where the scam is. Let me give you a short version before you quit reading, and expound on it below. Roughly — publisher’s contracts with libraries require them to deliver a certain number of pages each year. But the editorial boards are somewhat unruly, unpredictable and partly dysfunctional, like many math departments I suppose. Sometimes they over-accept papers by creating large backlogs and lowering standards. Other times, they are on a quest to raise standards and start to reject a lot of submissions. The journals are skittish about increasing and especially about decreasing the page numbers which would lead to their loss of income, creating a desperate need for more pages, any pages they can publish and mail to the libraries. This vacuum is then happily filled with all those special issues.

What made me so upset that I decided to blog on this?

Look, there is always something that’s a last drop. In this case it was a reference to my paper, and not a good kind. At some point Google Scholar informed me about a paper with a curious title citing a rather technical paper of mine. So I clicked. Here is the citation, in its full glory:

“Therefore, people need to think about the principles and methods of knowledge storage, management and application from a new perspective, and transform human knowledge into a form that can be understood and applied by machines at a higher level—the knowledge map, which is realized on the basis of information interconnection to change knowledge interconnection possible [27].”  

Visualization Analysis of Knowledge Network Research Based on Mapping Knowledge, by Hong Liu, Ying Jiang, Hua Fan, Xin Wang & Kang Zhao, Journal of Signal Processing Systems (2020)

And here is [27]: Pak, I., & Panova, G. (2017). On the complexity of computing Kronecker coefficients, Computational Complexity, 26, 1–36.

Now, I reread the above quote three times and understood nothing. Naturally, I know my paper [27] rather well. It is a technical result on computational complexity of of computing certain numbers which naturally arise in Algebraic Combinatorics, and our approach uses symmetric functions, Young tableau combinatorics and Barvinok’s algorithm. We definitely say nothing about the “knowledge storage” or “interconnection” or “management” of any of that.

Confused, I let it go, but an unrelated Google search brought up the paper again. So I reread the quote three more times. Finally convinced this is pure nonsense, I googled the journal to see if it’s one of the numerous spam journals I hear about.

Turns out, the Journal of Signal Processing Systems (JSPS) is a serious journal in the area, with impact factor around 1, and H-index of 49. For comparison, the European Journal of Combinatorics has impact factor around 0.9 and H-index of 45.

Now, JSPS has three main editors — Sun-Yuan Kung from Princeton, Shuvra S. Bhattacharyya from University of Maryland College Park, and Jarmo Takala from Tampere University in Helsinki. All reputable people. For example, Kung has over 30K citations on Google Scholar, while Takala has over 400 published papers.

So, in my usual shy and unassuming way, I wrote to them a short email on Sep 25, 2020, inquiring about the fateful citation:

Dear Editors,
I want to bring to your attention the following article recently published in the Journal of Signal Processing Systems.  I personally have neither knowledge nor expertise in your field, so I can’t tell you whether this is indeed a spam article.  However, I can tell when I see a bogus citation to my own work, which is used to justify some empty verbosity.  Please do keep me posted as to what actions you intend to take on the matter (if any). 
Best,  —  Igor Pak

Here is the reply that I got:

Dear Prof. Pak,
thank you for providing feedback about the citation in this article. The article is published in a special issue, where the papers have been selected by guest editors. We will have a discussion with the guest editors on this matter. Sincerely,
Jarmo Takala
Co-Editor-inChief J. Signal Processing Systems

Now you see what I mean? It’s been over a month since my email. The paper is still there. Clearly going nowhere. The editors basically take no responsibility as they did not oversee the guest issue. They have every incentive to blame someone else and drop the discussion, because this whole thing can only lead to embarrassment and bad rep. This trick is called “blame shifting”.

Meanwhile, the guest editors have no incentives to actually do anything because they are not affiliated with the journal. In fact, you can’t even tell from the Editors’ email or from the paper who they are. So I still don’t know who they are and have no way to reach out to them. The three Editors above never replied to my later email, so I guess we are stuck. All right then, maybe the time will tell….

Explaining the trick in basic terms

I am not sure what the business term for this type of predatory behavior, but let me give you some familiar examples so you get the idea.

(1) Say, you are a large very old liberal arts university located in Cambridge, MA. Yes, like Harvard. Almost exactly like Harvard. You have a fancy very expensive college with very low admission rate of less than 1 in 20. But you know you are a good brand, and every time you make some rich kid go away, your treasurer’s heart is bleeding. So how do you make more money off the brand?

Well, you start an Extension School which even gives Bachelor and Master’s degrees. And it’s a moneymaker! It brings over $500 million each year, about the same as the undergraduate and graduate tuitions combined! But wait, careful! You do give them “Harvard degrees“, just not “Harvard College degrees“. And, naturally, they would never include the Extension School students in the “average SAT score” or “income one year after graduation” stats they report to US News, because it’s not Harvard College, don’t you understand?

Occasionally this leads to confusion and even minor scandals, but who cares, right? We are talking a lot of money! A lot of people have afterhours adjunct jobs, rooms have higher occupancy rate aiming to recoup building repairs (well, pre-pandemic), and a lot of people get educated and feel good about getting an education at Harvard, win-win-win…

But you see where I am going — same brand is split into two under one roof, selling two different, highly unequal, almost unrelated products, all for the benefit of a very rich private corporation.

(2) Now, here is a sweet completely made up example. You are a large corporation selling luxury dark chocolate candies made of very expensive cocoa beans. A new CEO comes up with a request. Cut candy weight to save on the beans without lowering candy box prices, and make it a PR campaign so that everyone feels great and rushes to buy these. You say impossible? Not at all!

Here is what you do. Say, your luxury box of dark chocolate candies weights 200 grams, so each is 20 grams. You make each candy a little bit smaller, so the total weight is now 175 gram — for each candy the difference of 2.5 grams is barely noticeable. You make the candy box bigger and put two more rather large 25 gram candies made out of cheap white chocolate, wrapped into a visually different wrap. You sell them in one box. The new weight is 225 grams, i.e. larger than before. You advertise “now with two bonus candies at the same price!”, and customers feel happy to get some “free stuff”. At the end, they might not like the cheap candies, but who cares – they get to have the same old 10 expensive candies, right?

Again, you see where I am going. They created an artificial confusion by selling a superior and an inferior product in the same box without an honest breakdown, so the customers are completely duped.

Back to publishers

They are playing just as unfair as the second example above. The librarians can’t tell the difference between quality of “special issues”, they only negotiate on the number of pages. The journal’s reputation doesn’t suffer from those. Indeed, it is understood that they are not always but often enough of lower quality, but you can’t really submit there unless you are in the loop. I don’t know how the impact factor and H index are calculated, but I bet the publishers work with Web Of Science to exclude these special issues and report only the usual issues akin to the Harvard example. Or not. Nobody cares for these indices anymore, right?

Some examples

Let me just show how chaotic is the publishing of special issues. Take Discrete Mathematics, an Elsevier journal where I was an editor for 8 years (and whose Wikipedia page I made myself). Here is a page with Special Issues. There is no order to any of these conferences. There are 8th French Combinatorial Conference, Seventh Czech-Slovak International Symposium, 23rd British Combinatorics Conference, huh? What happened to the previous 7, 6 and 22 proceedings, respectively? You notice a lot of special issues from before the journal was overhauled and very few in recent years. Clearly the journal is on the right track. Good for them!

Here are three special issues in JCTA, and here are two in JCTB (both Elsevier). Why these? Are the editors sure these have the same quality as the rest of these top rated journals? Well, hopefully no longer top rated for JCTA. The Annals of Combinatorics (Springer) has literally “Ten Years of BAD Math” special issue (yes, I know what BAD Math means, but the name is awful even if the papers are great). The European Journal of Combinatorics (Elsevier again), publishes usually 1-2 special issue per year. Why?? Not enough submissions? Same for Advances Applied Math (also Elsevier), although very few special issues in recent years (good!). I think one of my papers (of grade B) is in one of the older special issues. Ooops!

Now compare these with the Electronic Journal of Combinatorics which stopped publishing special issues back in 2012. This journal is free online, has no page limitation, so it cares more about its reputation than filling the pages. Or take the extreme case of the Annals of Mathematics which would laugh at the idea of a “special issue”. Now you get it!

What gives?

It’s simple, really. STOP publishing special issues! If you are an Editor in Chief, just refuse! Who really knows what kind of scam the guest editors or the publishers are running? But you know your journal, all papers go through you, and you are responsible for all accepted papers. Really, the journal editors are the only ones responsible for journal reputation and for the peer review!

Expensive for profit publishers enjoying side special issue scam — I’ve been looking forward to your demise for a long while. Even more recently I felt optimistic since a lot of papers are now freely accessible. Now that we are all cut off from the libraries during pandemic — can we all agree that these publishers bring virtually no added value??

If you are a potential guest editor who really wants to organize a special issue based on your conference, or to honor somebody, ask publishers to make a special book deal. They might. They do it all the time, even if this is a bit less lucrative business than journal publishing. Individual mathematicians don’t, but the libraries do buy these volumes. And they should.

If you are a potential contributor to a special issue — do what is listed above in Grade B (write a special topic survey or personal reminiscences), which will be published in a book as a chapter. No serious peer review research. These go to journals.

And if you are one of those scam journal publishers who keep emailing me every week to become a special issue editor because you are so enthralled with my latest arXiv preprint — you go die in a ditch!

Final Disclaimer: All these bad opinions are not at all about any particular journal or special issue. There are numerous good papers published in special issues, and these issues are often dedicated to just wonderful mathematicians. I myself admit of publishing papers in a several such special issues. Here I am making a general point which is hopefully clear.

How Combinatorics became legitimate (according to László Lovász and Endre Szemerédi)

Simons Foundation has a series of fantastic interviews with leading mathematicians (ht Federico Ardila).  Let me single out the interviews with László Lovász and Endre Szemerédi.  Avi Wigderson asked both of them about the history of combinatorics and how it came into prominence.  Watch parts 8-9 in Lovász’s interview and 10-11 in Szemerédi’s interview to hear their fascinating answers.

P.S.  See also my old blog posts on what is combinatorics, how it became legitimate and how to watch math videos.

Some good news

Two of my former Ph.D. students won major prizes recently — Matjaž Konvalinka and Danny Nguyen.  Matjaž is an Associate Professor at University of Ljubljana, Danny is a Lewis Research Assistant Professor at University of Michigan, Ann Arbor.  Congratulations to both of them!

(1) The 2019 Robbins Prize is awarded to Roger Behrend, Ilse Fischer and Matjaž Konvalinka for their paper “Diagonally and antidiagonally symmetric alternating sign matrices of odd order”.  The Robbins Prize is given in Combinatorics and related areas of interest is named after the late David P. Robbins and is given once every 3 years by AMS and MAA.

In many ways, this paper completes the long project of enumerating alternating sign matrices (ASMs) initiated by William Mills, David Robbins, and Howard Rumsey in the early 1980s.  The original #ASM(n)=#TSSCPP(n) conjecture follows from Andrews’s proof of the conjectured product formula for #TSSCPP(n), and Zeilberger’s 84 page computer assisted proof of the the same conjectured product formula for #ASM(n).  This led to a long series of remarkable developments which include Kuperberg’s proof using the Izergin-Korepin determinant for the six vertex model, the Cantini–Sportiello proof of the Razumov-Stroganov conjecture, and a recent self-contained determinantal proof for the number of ASMs by Fischer.  Bressoud’s book (and this talk, slides) is a good introduction.  But the full story is yet to be written.

(2)  The 2018 Sacks Prize is awarded to Danny Nguyen for his UCLA Ph.D. dissertation on the complexity of short formulas in Presburger Arithmetic (PA) and many related works (some joint with me, some with others).  See also the UCLA announcement.  The Sacks Prize is given by the international Association for Symbolic Logic for “the most outstanding doctoral dissertation in mathematical logic“.  It is sometimes shared between two awardees, and sometimes not given at all.  This year Danny is the sole winner of the prize.

Danny’s dissertation is a compilation of eight (!) papers Danny wrote during his graduate studies, all on the same or closely related subject.  These papers advance and mostly finish off the long program of understanding the boundary of what’s feasible in PA. The most important of these is our joint FOCS paper which basically says that Integer Programming and Parametric Integer Programming is all that’s left in P, while all longer formulas are NP-hard.  See Featured MathSciNet Review by Sasha Barvinok and an overlapping blog post by Gil Kalai discussing these results.  See also Danny’s FOCS talk video and my MSRI talk video presenting this work.

 

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.

Just combinatorics matters

I would really like everyone to know that every time you say or write that something is “just combinatorics” somebody rolls his eyes.  Guess who?

Here is a short collection of “just combinatorics” quotes.  It’s a followup on my “What is Combinatorics?” quotes page inspired by the “What is Combinatorics?” blog post.

The status quo of math publishing

We all like the status quo.  It’s one of my favorite statuses…  The status quo is usually excellent or at least good enough.  It’s just so tempting to do nothing at all that we tend to just keep it.  For years and years which turn into decades.  Until finally the time has come to debate it…

Some say the status quo on math publishing is unsustainable.  That the publishers are much too greedy, that we do all the work and pay twice, that we should boycott the most outrageous of these publishers, that the University of California, German, Hungary, Norway and Swedish library systems recent decisions are a watershed moment calling for action, etc.  My own institution (UCLA) is actually the leader in the movement.  While I totally agree with the sentiment, I mostly disagree with the boycott(s) as currently practiced and other proposed measures.  It comes from a position of weakness and requires major changes to the status quo.

Having been thinking about this all for awhile, I am now very optimistic.  In fact, there is a way we can use our natural position of strength to achieve all the goals we want while keeping the status quo.  It may seem hard to believe, but with a few simple measures we can get there in a span of a few years.  This post is a long explanation of how and why we do this.

What IS the current status quo?

In mathematics, it’s pretty simple.  We, the mathematicians, do most of the work:  produce a decent looking .pdf file, perform a peer review on a largely volunteer basis (some editors do get paid occasionally), disseminate the results as best as we can, and lobby our libraries to buy the journal subscriptions.  The journals collect the copyright forms, make minor edits to the paper to conform to their favorite style, print papers on paper, mail them to the libraries, post the .pdf files on the internet accessible via library website, and charge libraries outrageous fees for these services.  They also have armies of managers, lawyers, shareholders, etc. to protect the status quo.

Is it all good or bad?  It’s mostly good, really.  We want all these basic services, just disagree on the price.  There is an old Russian Jewish proverb, that if a problem can be solved with money — it’s not a real problem but a business expense (here is a modern version).  So we should deal with predatory pricing as a business issue and not get emotional by boycotting selective journals or publishers.  We can argue for price decreases completely rationally, by showing that their product lost 90%, but not all its value, and that it’s in our common interest to devalue it, but not kill it.

Why keep the status quo?

This is easy.  We as a community tend to like our journals more than we hate them.  They compete for our papers.  We compete with each other to get published in best places.  This means we as a community know which journals are good, better or best in every area, or in the whole field of mathematics.  This means that each journal has composed the best editorial board it could.  It would be a waste to let this naturally formed structures go.

Now, in the past I strongly criticized top journals, the whole publishing industry, made fun of it, and more recently presented an ethical code of conduct for all journals.   Yet it’s clear that the cost of complete destruction of existing journal nomenclature is too high to pay and thus unlikely to happen.

Why changing the status quo is impractical?

Consider the alternatives.  Yes, the editorial board resignations do happen, most recently in the Journal of Algebraic Combinatorics (JACO) which resigned in mass to form a journal named Algebraic Combinatorics (ALCO).  But despite laudations, the original journal exists and doing fine or at least ok.  To my dismay and mild disbelief, the new Editorial Board of JACO has some well-known and wildly respected people.  Arguably, this is not the outcome the resigners aimed for (for the record, I published twice in JACO and recently had a paper accepted by ALCO).

Now, at first, starting new journals may seems like a great idea.  Unfortunately, by the conservative nature of academia they always struggle to get off the ground.  Some survive, such as EJC or EJP, have been pioneers in the area, but others are not doing so well.  The fine print is also an issue — the much hyped Pi and Sigma charge $1000 per article for “processing”, whatever that entails.   Terry Tao wrote that these journals suggest “alternatives to the status quo”.  Maybe.  But how exactly is that an improvement?  (Again, for the record, I published in both EJC, EJP, and recently in Sigma.  No, I didn’t pay, but let me stay on point here — that story can wait for another time.)

Other alternatives are even less effective.  Boycotting selective publishers gives a free reign to others to charge a lot, at the time when we need a systemic change.  I believe that it gives all but the worst publishers the cover they need to survive, while the worst already have enough power to survive and remain in the lead.  There is a long argument here I am trying to avoid.  Having had it with Mark Wilson, I know it would overwhelm this post.  Let me not rebut it thoroughly point-by-point, but present my own vision.

What can we do?

Boycott them all!  I mean all non-free journals, at all times, at all cost.  By that I don’t mean everyone should avoid submission, refereeing, being on the editorial board.  Not at all, rather opposite.  Please do NOT boycott anyone specifically, proceed with your work, keep the status quo.

What I mean is this.  Boycott all non-free journals as a consumer!  Do NOT download papers from journal websites.  I will give detailed suggestions below, after I explained my rationale.  In short, every time you download a paper from the journal website it gives publishers leverage to claim they are indispensable, and gives libraries the fear of faculty revolt if they unsubscribe.  They (both the publishers and the libraries) have no idea how little we need the paid journal websites.

Detailed advice on how to boycott all math journal publishers

Follow the following simple rules.  On your side as an author, make every(!) paper you ever wrote freely accessible.  Not just the latest – all of them!  Put them on the arXiv, viXra, your own website, or anywhere you like as long as the search engines can find them.  If you don’t know how, ask for help.  If you can read this WP blog post, you can also post your papers on some WP site.  If you are afraid of the copyright, snap out of it!  I do this routinely, of course.  Many greats have also done this for all their papers, e.g. Noga Alon and Richard Stanley.  Famously, all papers by Paul Erdős are online.  So my message for all of you reading this: if you don’t have all your papers free online, go ahead, just post them all!  Yes, that means right now!  Stop reading and come back when you are done.

Now, for reading papers the rules are more complicated.   Every time you need to download an article, don’t go to MathSciNet.  Instead, google it first.  Google Scholar usually gives you multiple options on the download location.  Choose the one in the arXiv or author’s website.  Done.

If you fail, but feel the paper could be available from some nefarious copyright violating websites, consider using Yandex, DuckDuckGo, or other search engines which are less concerned about the copyright.

Now, suppose the only location is the journal website.  Often, this happens when the paper is old or old-ish, i.e. outside the 4 year sliding window for Elsevier.  As far as I am concerned, this part of the publisher is “free” since anyone in the world can download it without charge.  Make sure you download the paper without informing your campus library.  This is easy off campus — use any browser without remote access (VPN).  On campus, use a browser masking your ip address, i.e. the Opera.

Now, suppose nothing works.  Say, the paper is recent but inaccessible for free.  Then email to the authors and request the file of paper.  Shame them into putting the paper online while you are at it.   Forward them this blog post, perhaps.

Suppose now the paper is inaccessible for free, but the authors are non-responsive and unlikely to ever make the paper available.  Well, ok — download it from the journal website then via your library.  But then be a mensch.  Post the paper online.  Yes, in violation of copyright.  Yes, other people already do it.  Yes, everyone is downloading them and would be grateful.  No, they won’t fight us all.

Finally, suppose you create a course website.  Make sure all or at least most of your links are to free version of the articles.  Download them all and repost them on your course website so the students can bypass the library redirect.  Every bit helps.

Why would this work?  I.  Shaming is powerful.

Well, in mathematics shaming is widespread and actually works except in some extreme cases.  It’s routine, in fact, to shame authors for not filling gaps in their proofs, for not acknowledging priority, or for not retracting incorrect papers (when the authors refuse to do it, the journals can also be shamed).  Sometimes the shaming doesn’t work.  Here is my own example of shaming fail (rather extreme, unfortunately), turned shaming success on pages of this blog.

More broadly, public shaming is one of the key instruments in the 21st century.  Mathbabe (who is writing a book about shaming) notably shamed Mochizuki for not traveling around to defend his papers.   Harron famously shamed white cis men for working in academia.  Again, maybe not in all cases, but in general public shaming works rather well, and there is a lot of shaming happening everywhere.  

So think about it — what if we can shame every working mathematician into posting all their papers online?  We can then convince libraries that we don’t need to renew all our math journal subscriptions since we can function perfectly well without them.  Now, we would still want the journal to function, but are prepared to spend maybe 10-15% of the prices that Springer and Elsevier currently charge.  Just don’t renew the contract otherwise.  Use the savings to hire more postdocs, new faculty, give students more scholarships to travel to conferences, make new Summer research opportunities, etc.

Why would this work?  II.  Personal perspective.

About a year ago I bought a new laptop and decided to follow some of the rules above as an experiment.  The results were surprisingly good.  I had to download some old non-free papers from  publisher sites maybe about 4-5 times a month.  I went to the library about once every couple of months.  For new papers, I emailed the authors maybe the total of about once every three months, getting the paper every time.  I feel I could have emailed more often, asking for old papers as well.

Only occasionally (maybe once a month) I had to resort to overseas paper depositaries, all out of laziness — it’s faster than walking to the library.  In summary — it’s already easy to be a research mathematician without paying for journals.  In the future, it will get even easier.

Why would this work?  III.  Librarian perspective.

Imagine you are a head librarian responsible for journal contracts and purchasing.   You have access to the download data and you realize that many math journals continue to be useful and even popular.  The publishers bring you a similar or possibly more inflated date showing their products in best light.  Right now you have no evidence the journals are largely useless are worried about backslash which would happen if you accidentally cut down on popular journals.  So you renew just about everything that your library has always been subscribing and skip on subscribing to new journals unless you get special requests for the faculty that you should.

Now imagine that in 2-3 years your data suggests rapidly decreasing popularity of the journals.  You make a projection that the downloads will decrease by a factor of 10 within a few more years.  That frees you from worrying about cancelling subscriptions and gives you strong leverage in negotiating.  Ironically that also helps you keeps the status quo — the publishers slash their price but you can keep most of the subscriptions.

Why would this work?  IV.  Historical perspective.

The history is full of hard fought battles which were made obsolete by cultural and technological changes.  The examples include the “war of the currents“, the “war” of three competing NYC subway systems, same with multiple US railroads, the “long-distance price war“, the “browser war” and the “search engine war“.  They were all very different and resolved in many different ways, but have two things in common — they were ruthless at the time, and nobody cares anymore.  Even the airlines keep slashing prices, making services indistinguishably awful to the point of becoming near-utilities like electric and gas companies.

The same will happen to the journal publishing empires.  In fact, the necessary technology has been available for awhile — it’s the culture that needs to change.  Eventually all existing print journals will become glorified versions of arXiv overlay publications with substantially scaled down stuff and technical production.  Not by choice, of course — there is just no money in it.  Just like the airline travel — service will get worse, but much cheaper.

The publishers will continue to send print copies of journals to a few dozen libraries worldwide which will be immediately put into off-campus underground bunker-like storages as an anti-apocalyptic measure, and since the reader’s demand will be close to nonexistent.  They will remain profitable by cutting cost everywhere since apparently this is all we really care about.

The publishers already know that they are doomed, they just want to prolong the agony and extract as much rent as they can before turning into public utilities.  This is why the Elsevier refuses to budge with the UC and other systems.  They realize that publicly slashing prices for one customer today will lead to an avalanche of similar demands tomorrow, so they would rather forgo a few customers than start a revolution which would decimate their journal value in 5 years (duration of the Elsevier contract).

None of this is new, of course.  Odlyzko described it all back in 1997, in a remarkably prescient yet depressing article.  Unfortunately, we have been moving in the wrong direction.  Gowers is right that publishers cannot be shamed, but his efforts to shame people into boycotting Elsevier may be misplaced as it continues going strong.  The shaming did lead to the continuing conversation and the above mentioned four year sliding window which is the key to my proposal.

What’s happening now?  Why is Elsevier not budging?

As everyone who ever asked for a discount knows, you should do this privately, not publicly.  Very quietly slashing the prices by a factor of 2, then trying to play the same trick again in 5 years would have been smarter and satisfied everybody.  To further help Elsevier hide the losses from shareholders and general public, the library could have used some bureaucratic gimmicks like paying the same for many journals but getting new books for free or something like that.  This would further confuse everybody except professional negotiators on behalf of other library systems, thus still helping to push the prices down.

But the UC system wanted to lead a revolution with their public demands, so here we are, breaking the status quo for no real reason.  There are no winners here.  Even my aunt Bella from Odessa who used to take me regularly to Privoz Market to watch her bargain, could have told you that’s exactly what’s going to happen…

Again, the result is bad for everybody — the Elsevier would have been happier to get some money — less than the usual amount, but better than nothing given the trivial marginal costs.  At the same time, we at UCLA still need the occasional journal access while in the difficult transition period.

AMS, please step up!

There is one more bad actor in the whole publishing drama whose role needs to change.  I am speaking about the AMS, which is essentially a giant publishing house with an army of volunteers and a side business of organizing professional meetings.  Let’s looks at the numbers, the 2016 annual report (for some reason the last one available).  On p.12 we read: of the $31.8 mil operating revenue dues make up about 8%, meetings 4%, while publishing a whopping 68%.  No wonder the AMS is not pushing for changes in current journal pay structure — they are conflicted to the point of being complicit in preserving existing prices.

But let’s dig a little deeper.  On p.16 we see that the journals are fantastically profitable!  They raise $5.2 mil with $1.5 mil in operating expenses, a 247% profit margin.  With margins like that who wants to rock the boat?  Compare this with next item — books.  The AMS made $4.1 mil while spent $3.6 mil.  That’s a healthy 14% profit margin.  Nice, but nothing to write home about.  By its nature, the book market is highly competitive as libraries and individuals have option to buy them or not on a per title basis.  Thus, the competition.

If you think the AMS prices are lower than of other publishers, that’s probably right.  This very dated page by Kirby is helpful.  For example, in 1996, the PTRF (Springer) charged $2100, the Advances (Academic Press, now Elsevier) $1326, the Annals (Princeton Univ. Press) $200, while JAMS only $174.  Still…

What should be done?  Ideally, the AMS should sell its journal business to some university press and invest long-term the sale profits.  That would free it to pursue the widely popular efforts towards free publishing.  In reality that’s unlikely to happen, so perhaps some sort of “Chinese wall” separating journal publishing and the AMS political activities.  This “wall” might already exist, I wouldn’t know.  I am open to suggestions.  Either way, I think the AMS members should brace themselves for the future where the AMS has a little less money.  But since the MathSciNet alone brings 1/3 of the revenue, and other successful products like MathJobs are also money makers, I think the AMS will be fine.

I do have one pet peeve.  The MathSciNet, which is a good product otherwise, should have a “web search” button next to the “article” button.  The latter automatically takes you to the journal website, while the former would search the article on Google Scholar (or Microsoft Academic, I suppose, let the people choose a default).  This would help people circumvent the publishers by cutting down on clicks.

What gives?

I have always been a non-believer in boycotts of specific publishers, and I feel the history proved me more right than wrong.  People tend to avoid boycotts when they have significant cost, and without the overwhelming participation boycotts simply don’t work.  Asking people not to submit or referee for the leading journals in their fields is like asking to voluntarily pay higher taxes.  Some do this, of course, but most don’t, even those who generally agree with higher taxes as a good public policy.

In fact, I always thought we need some kind of one-line bill by the US Congress requiring all research made at every publicly funded university being available for free online.  In my conspiratorial imagination, the AMS being a large publisher refused to bring this up in its lobbying efforts, thus nothing ever happened.  While I still think this bill is a good idea, I no longer think it’s a necessary step.

Now I am finally optimistic that the boycott I am proposing is going to succeed.  The (nearly) free publishing is coming!  Please spread the word, everybody!

UPDATE (March 19, 2019):  Mark Wilson has a blog post commenting and clarifying ALCO vs. JACO situation.

What we’ve got here is failure to communicate

Here is a lengthy and somewhat detached followup discussion on the very unfortunate Hill’s affair, which is much commented by Tim Gowers, Terry Tao and many others (see e.g. links and comments on their blog posts).  While many seem to be universally distraught by the story and there are some clear disagreements on what happened, there are even deeper disagreements on what should have happened.  The latter question is the subject of this blog post.

Note:  Below we discuss both the ethical and moral aspects of the issue.  Be patient before commenting your disagreements until you finish the reading — there is a lengthy disclaimer at the end.

Review process:

1. When the paper is submitted there is a very important email acknowledging receipt of the submission.  Large publishers have systems send such emails automatically.  Until this email is received, the paper is not considered submitted.  For example, it is not unethical for the author to get tired of waiting to hear from the journal and submit elsewhere instead.  If the journal later comes back and says “sorry for the wait, here are the reports”, the author should just inform the journal that the paper is under consideration elsewhere and should be considered withdrawn (this happens sometimes).
2. Similarly, there is a very important email acknowledging acceptance of the submission.  Until this point the editors ethically can do as they please, even reject the paper with multiple positive reports.  Morality of the latter is in the eye of the beholder (cf. here), but there are absolutely no ethical issues here unless the editor violated the rules set up by the journal.  In principle, editors can and do make decisions based on informal discussions with others, this is totally fine.
3. If a journal withdraws acceptance after the formal acceptance email is sent, this is potentially a serious violation of ethical standards.  Major exception: this is not unethical if the journal follows a certain procedural steps (see the section below).  This should not be done except for some extreme circumstances, such as last minute discovery of a counterexample to the main result which the author refuses to recognize and thus voluntarily withdraw the paper.   It is not immoral since until the actual publication no actual harm is done to the author.
4. The next key event is publication of the article, whether online of in print, usually/often coupled with the transfer of copyright.  If the journal officially “withdraws acceptance” after the paper is published without deleting the paper, this is not immoral, but depends on the procedural steps as in the previous item.
5. If a journal deletes the paper after the publication, online or otherwise, this is a gross violation of both moral and ethical standards.  The journals which do that should be ostracized regardless their reasoning for this act.  Major exception: the journal has legal reasoning, e.g. the author violated copyright laws by lifting from another published article as in the Dănuț Marcu case (see below).

Withdrawal process:

1.  As we mentioned earlier, the withdrawal of accepted or published article should be extremely rare, only in extreme circumstances such as a major math error for a not-yet-published article or a gross ethical violation by the author or by the handling editor of a published article.
2. For a published article with a major math error or which was later discovered to be known, the journal should not withdraw the article but instead work with the author to publish an erratum or an acknowledgement of priority.  Here an erratum can be either fixing/modifying the results, or a complete withdrawal of the main claim.  An example of the latter is an erratum by Daniel Biss.  Note that the journal can in principle publish a note authored by someone else (e.g. this note by Mnёv in the case of Biss), but this should be treated as a separate article and not a substitute for an erratum by the author.  A good example of acknowledgement of priority is this one by Lagarias and Moews.
3. To withdraw the disputed article the journal’s editorial board should either follow the procedure set up by the publisher or set up a procedure for an ad hoc committee which would look into the paper and the submission circumstances.  Again, if the paper is already published, only non-math issues such as ethical violations by the author, referee(s) and/or handling editor can be taken into consideration.
4. Typically, a decision to form an ad hoc committee or call for a full editorial vote should me made by the editor in chief, at the request of (usually at least two) members of the editorial board.  It is totally fine to have a vote by the whole editorial board, even immediately after the issue was raised, but the threshold for successful withdrawal motion should be set by the publisher or agreed by the editorial board before the particular issue arises.  Otherwise, the decision needs to be made by consensus with both the handling editor and the editor in chief abstaining from the committee discussion and the vote.
5. Examples of the various ways the journals act on withdrawing/retracting published papers can be found in the case of notorious plagiarist Dănuț Marcu.  For example, Geometria Dedicata decided not to remove Marcu’s paper but simply issued a statement, which I personally find insufficient as it is not a retraction in any formal sense.  Alternatively, SUBBI‘s apology is very radical yet the reasoning is completely unexplained. Finally, Soifer’s statement on behalf of Geombinatorics is very thorough, well narrated and quite decisive, but suffers from authoritarian decision making.
6. In summary, if the process is set up in advance and is carefully followed, the withdrawal/retraction of accepted or published papers can be both appropriate and even desirable.  But when the process is not followed, such action can be considered unethical and should be avoided whenever possible.

Author’s rights and obligations:

1. The author can withdraw the paper at any moment until publication.  It is also author’s right not to agree to any discussion or rejoinder.  The journal, of course, is under no obligation to ask the author’s permission to publish a refutation of the article.
2. If the acceptance is issued, the author has every right not go along with the proposed quiet withdrawal of the article.  In this case the author might want to consider complaining to the editor in chief or the publisher making the case that the editors are acting inappropriately.
3. Until acceptance is issued, the author should not publicly disclose the journal where the paper is submitted, since doing so constitutes a (very minor) moral violation.  Many would disagree on this point, so let me elaborate.  Informing the public of the journal submission is tempting people in who are competition or who have a negative opinion of the paper to interfere with the peer review process.  While virtually all people virtually all the time will act honorably and not contact the journal, such temptation is undesirable and easily avoidable.
4. As soon as the acceptance or publication is issued, the author should make this public immediately, by the similar reasoning of avoiding temptation by the third parties (of different kind).

Third party outreach:

1.  If the paper is accepted but not yet published, reaching out to the editor in chief by a third party requesting to publish a rebuttal of some kind is totally fine.  Asking to withdraw the paper for mathematical reasons is also fine, but should provide a clear formal math reasoning as in “Lemma 3 is false because…”  The editor then has a choice but not an obligation to trigger the withdrawal process.
2. Asking to withdraw the not-yet-published paper without providing math reasoning, but saying something like “this author is a crank” or “publishing this paper will do bad for your reputation” is akin to bullying and thus a minor ethical violation.  The reason it’s minor is because it is journal’s obligations to ignore such emails.  Journal acting on such an email with rumors or unverified facts is an ethical violation on its own.
3. If a third party learns about a publicly available paper which may or may not be an accepted submission with which they disagree for math or other reason, it it ethical to contact the author directly.  In fact, in case of math issues this is highly desirable.
4. If a third party learns about a paper submission to a journal without being contacted to review it, and the paper is not yet accepted, then contacting the journal is a strong ethical violation.  Typically, the journal where the paper is submitted it not known to public, so the third party is acting on the information it should not have.  Every such email can be considered as an act of bullying no matter the content.
5. In an unlikely case everything is as above but the journal’s name where the paper is submitted is publicly available, the third party can contact the journal.  Whether this is ethical or not depends on the wording of the email.  I can imagine some plausible circumstances when e.g. the third party knows that the author is Dănuț Marcu mentioned earlier.  In these rare cases the third party should make every effort to CC the email to everyone even remotely involved, such as all authors of the paper, the publisher, the editor in chief, and perhaps all members of the editorial board.  If the third party feels constrained by the necessity of this broad outreach then the case is not egregious enough, and such email is still bullying and thus unethical.
6. Once the paper is published anyone can contact the journal for any reason since there is little can be done by the journal beyond what’s described above.  For example, on two different occasions I wrote to journals pointing out that their recently published results are not new and asking them to inform the authors while keeping my anonymity.  Both editors said they would.  One of the journals later published an acknowledgement of retribution.  The other did not.

Editor’s rights and obligations:

1. Editors have every right to encourage submissions of papers to the journal, and in fact it’s part of their job.  It is absolutely ethical to encourage submissions from colleagues, close relatives, political friends, etc.  The publisher should set up a clear and unobtrusive conflict of interest directive, so if the editor is too close to the author or the subject he or she should transfer the paper to the editor in chief who will chose a different handling editor.
2. The journal should have a clear scope worked out by the publisher in cooperation with the editorial board.  If the paper is outside of the scope it should be rejected regardless of its mathematical merit.  When I was an editor of Discrete Mathematics, I would reject some “proofs” of the Goldbach conjecture and similar results based on that reasoning.  If the paper prompts the journal to re-evaluate its scope, it’s fine, but the discussion should involve the whole editorial board and irrespective of the paper in question.  Presumably, some editors would not want to continue being on the board if the journal starts changing direction.
3. If the accepted but not yet published paper seems to fall outside of the journal’s scope, other editors can request the editor in chief to initiate the withdrawal process discussed above.  The wording of request is crucial here – if the issue is neither the the scope nor the major math errors, but rather the weakness of results, then this is inappropriate.
4. If the issue is the possibly unethical behavior of the handling editor, then the withdrawal may or may not be appropriate depending on the behavior, I suppose.  But if the author was acting ethically and the unethical behavior is solely by the handling editor, I say proceed to publish the paper and then issue a formal retraction while keeping the paper published, of course.

Complaining to universities:

1. While perfectly ethical, contacting the university administration to initiate a formal investigation of a faculty member is an extremely serious step which should be avoided if at all possible.  Except for the egregious cases of verifiable formal violations of the university code of conduct (such as academic dishonesty), this action in itself is akin to bullying and thus immoral.
2. The code of conduct is usually available on the university website – the complainer would do well to consult it before filing a complaint.  In particular, the complaint would typically be addressed to the university senate committee on faculty affairs, the office of academic integrity and/or dean of the faculty.  Whether the university president is in math or even the same area is completely irrelevant as the president plays no role in the working of the committee.  In fact, when this is the case, the president is likely to recuse herself or himself from any part of the investigation and severe any contacts with the complainer to avoid appearance of impropriety.
3. When a formal complaint is received, the university is usually compelled to initiate an investigation and set up an ad hoc subcommittee of the faculty senate which thoroughly examines the issue.  Faculty’s tenure and life being is on the line.  They can be asked to retain legal representation and can be prohibited from discussing the matters of the case with outsiders without university lawyers and/or PR people signing on every communication.  Once the investigation is complete the findings are kept private except for administrative decisions such as firing, suspension, etc.  In summary, if the author seeks information rather than punishment, this is counterproductive.

Complaining to institutions:

1. I don’t know what to make of the alleged NSF request, which could be ethical and appropriate, or even common.   Then so would be complaining to the NSF on a publicly available research product supported by the agency.  The issue is the opposite to that of the journals — the NSF is a part of the the Federal Government and is thus subject to a large number of regulations and code of conduct rules.  These can explain its request.  We in mathematics are rather fortunate that our theorems tend to lack any political implications in the real world.  But perhaps researchers in Political Science and Sociology have different experiences with granting agencies, I wouldn’t know.
2. Contacting the AMS can in fact be rather useful, even though it currently has no way to conduct an appropriate investigation.  Put bluntly, all parties in the conflict can simply ignore AMS’s request for documents.  But maybe this should change in the future.  I am not a member of the AMS so have no standing in telling it what to do, but I do have some thoughts on the subject.  I will try to write them up at some point.

Public discourse:

1. Many commenters on the case opined that while deleting a published paper is bad (I am paraphrasing), but the paper is also bad for whatever reason (politics, lack of strong math, editor’s behavior, being out of scope, etc.)  This is very unfortunate.  Let me explain.
2. Of course, discussing math in the paper is perfectly ethical: academics can discuss any paper they like, this can be considered as part of the job.  Same with discussing the scope of the paper and the verifiable journal and other party actions.
3. Publicly discussing personalities and motivation of the editors publishing or non-publishing, third parties contacting editors in chief, etc. is arguably unethical and can be perceived as borderline bullying.  It is also of questionable morality as no complete set of facts are known.
4. So while making a judgement on the journal conduct next to the judgement on the math in the paper is ethical, it seems somewhat immoral to me.  When you write “yes, the journals’ actions are disturbing, but the math in the paper is poor” we all understand that while formally these are two separate discussions, the negative judgement in the second part can provide an excuse for misbehavior in the first part.  So here is my new rule:  If you would not be discussing the math in the paper without the pretext of its submission history, you should not be discussing it at all. 

In summary:

I argue that for all issues related to submissions, withdrawal, etc. there is a well understood ethical code of conduct.  Decisions on who behaved unethically hinge on formal details of each case.  Until these formalities are clarified, making judgements is both premature and unhelpful.

Part of the problem is the lack of clarity about procedural rules by the journals, as discussed above.  While large institutions such as major universities and long established journal publishers do have such rules set up, most journals tend not to disclose them, unfortunately.  Even worse, many new, independent and/or electronic journals have no such rules at all.  In such environment we are reduced to saying that this is all a failure to communicate.

Lengthy disclaimer:

1. I have no special knowledge of what actually happened to Hill’s submission.  I outlined what I think should have happened in different scenarios if all participants acted morally and ethically (there are no legal issues here that I am aware of).  I am not trying to blame anyone and in fact, it is possible that none of these theoretical scenarios are applicable.  Yet I do think such a general discussion is useful as it distills the arguments.
2. I have not read Hill’s paper as I think its content is irrelevant to the discussion and since I am deeply uninterested in the subject.  I am, however, interested in mathematical publishing and all academia related matters.
3. What’s ethical and what’s moral are not exactly the same.  As far as this post is concerned, ethical issues cover all math research/university/academic related stuff.  Moral issues are more personal and community related, thus less universal perhaps.  In other words, I am presenting my own POV everywhere here.
4. To give specific examples of the difference, if you stole your officemate’s lunch you acted immorally.  If you submitted your paper to two journals simultaneously you acted unethically.  And if you published a paper based on your officemate’s ideas she told you in secret, you acted both immorally and unethically.  Note that in the last example I am making a moral judgement since I equate this with stealing, while others might think it’s just unethical but morally ok.
5. There is very little black & white about immoral/unethical acts, and one always needs to assign a relative measure of the perceived violation.  This is similar to criminal acts, which can be a misdemeanor, a gross misdemeanor, a felony, etc.

 

ICM Paper

Well, I finally finished my ICM paper. It’s only 30 pp, but it took many sleepless nights to write and maybe about 10 years to understand what exactly do I want to say. The published version will be a bit shorter – I had to cut section 4 to satisfy their page limitations.

Basically, I give a survey of various recent and not-so-recent results in Enumerative Combinatorics around three major questions:

(1) What is a formula?
(2) What is a good bijection?
(3) What is a combinatorial interpretation?

Not that I answer these questions, but rather explain how one could answer them from computational complexity point of view. I tried to cover as much ground as I could without overwhelming the reader. Clearly, I had to make a lot of choices, and a great deal of beautiful mathematics had to be omitted, sometimes in favor of the Computational Combinatorics approach. Also, much of the survey surely reflects my own POV on the subject. I sincerely apologize to everyone I slighted and who disagrees with my opinion! Hope you still enjoy the reading.

Let me mention that I will wait for a bit before posting the paper on the arXiv. I very much welcome all comments and suggestions! Post them here or email privately.

P.S. In thinking of how approach this paper, I read a large number of papers in previous ICM proceedings, e.g. papers by Noga Alon, Mireille Bousquet-Mélou, Paul Erdős, Philippe Flajolet, Marc Noy, János Pach, Richard Stanley, Benny Sudakov, and many others. They are all terrific and worth reading even if just to see how the field has been changing over the years. I also greatly benefited from a short introductory article by Doron Zeilberger, which I strongly recommend.

How to write math papers clearly

Writing a mathematical paper is both an act of recording mathematical content and a means of communication of one’s work.  In contrast with other types of writing, the style of math papers is incredibly rigid and resistant to even modest innovation.  As a result, both goals suffer, sometimes immeasurably.  The clarity suffers the most, which affects everyone in the field.

Over the years, I have been giving advice to my students and postdocs on how to write clearly.  I collected them all in these notes.  Please consider reading them and passing them to your students and colleagues.  

Below I include one subsection dealing with different reference styles and what each version really means.  This is somewhat subjective, of course. Enjoy!

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4.2. How to cite a single paper. The citation rules are almost as complicated as Chinese honorifics, with an added disadvantage of never being discussed anywhere. Below we go through the (incomplete) list of possible ways in the decreasing level of citation importance and/or proof reliability.

(1) “Roth proved Murakami’s conjecture in [Roth].” Clear.

(2) “Roth proved Murakami’s conjecture [Roth].” Roth proved the conjecture, possibly in a different paper, but this is likely a definitive version of the proof.

(3) “Roth proved Murakami’s conjecture, see [Roth].” Roth proved the conjecture, but [Roth] can be anything from the original paper to the followup, to some kind of survey Roth wrote. Very occasionally you have “see [Melville]”, but that usually means that Roth’s proof is unpublished or otherwise unavailable (say, it was given at a lecture, and Roth can’t be bothered to write it up), and Melville was the first to publish Roth’s proof, possibly without permission, but with attribution and perhaps filling some minor gaps.

(4) “Roth proved Murakami’s conjecture [Roth], see also [Woolf].” Apparently Woolf also made an important contribution, perhaps extending it to greater generality, or fixing some major gaps or errors in [Roth].

(5) “Roth proved Murakami’s conjecture in [Roth] (see also [Woolf]).” Looks like [Woolf] has a complete proof of Roth, possibly fixing some minor errors in [Roth].

(6) “Roth proved Murakami’s conjecture (see [Woolf]).” Here [Woolf] is a definitive version of the proof, e.g. the standard monograph on the subject.

(7) “Roth proved Murakami’s conjecture, see e.g. [Faulkner, Fitzgerald, Frost].” The result is important enough to be cited and its validity confirmed in several books/surveys. If there ever was a controversy whether Roth’s argument is an actual proof, it was resolved in Roth’s favor. Still, the original proof may have been too long, incomplete or simply presented in an old fashioned way, or published in an inaccessible conference proceedings, so here are sources with a better or more recent exposition. Or, more likely, the author was too lazy to look for the right reference, so overcompensated with three random textbooks on the subject.

(8) “Roth proved Murakami’s conjecture (see e.g. [Faulkner, Fitzgerald, Frost]).” The result is probably classical or at least very well known. Here are books/surveys which all probably have statements and/or proofs. Neither the author nor the reader will ever bother to check.

(9) “Roth proved Murakami’s conjecture.⁷ Footnote 7: See [Mailer].” Most likely, the author never actually read [Mailer], nor has access to that paper. Or, perhaps, [Mailer] states that Roth proved the conjecture, but includes neither a proof nor a reference. The author cannot
verify the claim independently and is visibly annoyed by the ambiguity, but felt obliged to credit Roth for the benefit of the reader, or to avoid the wrath of Roth.

(10) “Roth proved Murakami’s conjecture.⁷ Footnote 7: Love letter from H. Fielding to J. Austen, dated December 16, 1975.” This means that the letter likely exists and contains the whole proof or at least an outline of the proof. The author may or may not have seen it. Googling will probably either turn up the letter or a public discussion about what’s in it, and why it is not available.

(11) “Roth proved Murakami’s conjecture.⁷ Footnote 7: Personal communication.” This means Roth has sent the author an email (or said over beer), claiming to have a proof. Or perhaps Roth’s student accidentally mentioned this while answering a question after the talk. The proof
may or may not be correct and the paper may or may not be forthcoming.

(12) “Roth claims to have proved Murakami’s conjecture in [Roth].” Paper [Roth] has a well known gap which was never fixed even though Roth insists on it to be fixable; the author would rather avoid going on record about this, but anything is possible after some wine at a banquet. Another possibility is that [Roth] is completely erroneous as explained elsewhere, but Roth’s
work is too famous not to be mentioned; in that case there is often a followup sentence clarifying the matter, sometimes in parentheses as in “(see, however, [Atwood])”. Or, perhaps, [Roth] is a 3 page note published in Doklady Acad. Sci. USSR back in the 1970s, containing a very brief outline of the proof, and despite considerable effort nobody has yet to give a complete proof of its Lemma 2; there wouldn’t be any followup to this sentence then, but the author would be happy to clarify things by email.

UPDATE 1. (Nov 1, 2017): There is now a video of the MSRI talk I gave based on the article.

UPDATE 2. (Mar 13, 2018): The paper was published in the Journal of Humanistic Mathematics. Apparently it’s now number 5 on “Most Popular Papers” list. Number 1 is “My Sets and Sexuality”, of course.