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 on 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.
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.
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.
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 mangers, 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.
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).
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.
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.
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…
I tend to write longish posts, in part for the sake of clarity, and in part because I can – it is easier to express yourself in a long form. However, the brevity has its own benefits, as it forces the author to give succinct summaries of often complex and nuanced views. Similarly, the lack of such summaries can provide plausible deniability of understanding the basic points you are making.
This is the second time I am “inspired” by the Owl blogger who has a Tl;Dr style response to my blog post and rather lengthy list of remarkable quotations that I compiled. So I decided to make the following Readers Digest style summaries of this list and several blog posts.
1) Combinatorics has been sneered at for decades and struggled to get established
In the absence of History of Modern Combinatorics monograph, this is hard to prove. So here are selected quotes, from the above mentioned quotation page. Of course, one should reade them in full to appreciate and understand the context, but for our purposes these will do.
Combinatorics is the slums of topology – Henry Whitehead
Scoffers regard combinatorics as a chaotic realm of binomial coefficients, graphs, and lattices, with a mixed bag of ad hoc tricks and techniques for investigating them. [..] Another criticism of combinatorics is that it “lacks abstraction.” The implication is that combinatorics is lacking in depth and all its results follow from trivial, though possible elaborate, manipulations. This argument is extremely misleading and unfair. – Richard Stanely (1971)
The opinion of many first-class mathematicians about combinatorics is still in the pejorative. While accepting its interest and difficulty, they deny its depth. It is often forcefully stated that combinatorics is a collection of problems which may be interesting in themselves but are not linked and do not constitute a theory. – László Lovász (1979)
Combinatorics [is] a sort of glorified dicethrowing. – Robert Kanigel (1991)
This prejudice, the view that combinatorics is quite different from ‘real mathematics’, was not uncommon in the twentieth century, among popular expositors as well as professionals. – Peter Cameron (2001)
Now that the readers can see where the “traditional sensitivities” come from, the following quote must come as a surprise. Even more remarkable is that it’s become a conventional wisdom:
Like number theory before the 19th century, combinatorics before the 20th century was thought to be an elementary topic without much unity or depth. We now realize that, like number theory, combinatorics is infinitely deep and linked to all parts of mathematics. – John Stillwell (2010)
Of course, the prejudice has never been limited to Combinatorics. Imagine how an expert in Partition Theory and q-series must feel after reading this quote:
[In the context of Partition Theory] Professor Littlewood, when he makes use of an algebraic identity, always saves himself the trouble of proving it; he maintains that an identity, if true, can be verified in a few lines by anybody obtuse enough to feel the need of verification. – Freeman Dyson (1944), see here.
2) Combinatorics papers have been often ostracized and ignored by many top math journals
This is a theme in this post about the Annals, this MO answer, and a smaller theme in this post (see Duke paragraph). This bias against Combinatorics is still ongoing and hardly a secret. I argue that on the one hand, the situation is (slowly) changing for the better. On the other hand, if some journals keep the proud tradition of rejecting the field, that’s ok, really. If only they were honest and clear about it! To those harboring strong feelings on this, listening to some breakup music could be helpful.
3) Despite inherent diversity, Combinatorics is one field
In this post, I discussed how I rewrote Combinatorics Wikipedia article, largely as a collection of links to its subfields. In a more recent post mentioned earlier I argue why it is hard to define the field as a whole. In many ways, Combinatorics resembles a modern nation, united by a language, culture and common history. Although its borders are not easy to define, suggesting that it’s not a separate field of mathematics is an affront to its history and reality (see two sections above). As any political scientist will argue, nation borders can be unhelpful, but are here for a reason. Wishing borders away is a bit like French ”race-ban“ – an imaginary approach to resolve real problems.
Gowers’s “two cultures” essay is an effort to describe and explain cultural differences between Combinatorics and other fields. The author should be praised both for the remarkable essay, and for the bravery of raising the subject. Finally, on the Owl’s attempt to divide Combinatorics into “conceptual” which “has no internal reasons to die in any foreseeable future” and the rest, which “will remain a collection of elementary tricks, [..] will die out and forgotten [sic].” I am assuming the Owl meant here most of the “Hungarian combinatorics”, although to be fair, the blogger leaves some wiggle room there. Either way, “First they came for Hungarian Combinatorics” is all that came to mind.
Recently, there has been plenty of discussions on math journals, their prices, behavior, technology and future. I have been rather reluctant to join the discussion in part due to my own connection to Elsevier, in part because things in Combinatorics are more complicated than in other areas of mathematics (see below), but also because I couldn’t reconcile several somewhat conflicting thoughts that I had. Should all existing editorial boards revolt and all journals be electronic? Or perhaps should we move to “pay-for-publishing” model? Or even “crowd source refereeing”? Well, now that the issue a bit cooled down, I think I figured out exactly what should happen to math journals. Be patient – a long explanation is coming below.
Quick test questions
I would like to argue that the debate over the second question is the general misunderstanding of the first question in the title. In fact, I am pretty sure most mathematicians are quite a bit confused on this, for a good reason. If you think this is easy, quick, answer the following three questions:
1) Published paper has a technical mistake invalidating the main result. Is this a fault of author, referee(s), handling editor, managing editor(s), a publisher, or all of the above? If the reader find such mistake, who she/he is to contact?
2) Published paper proves special case of a known result published 20 years earlier in an obscure paper. Same question. Would the answer change if the author lists the paper in the references?
3) Published paper is written in a really poor English. Sections are disorganized and the introduction is misleading. Same question.
Now that you gave your answers, ask a colleague. Don’t be surprised to hear a different point of view. Or at least don’t be surprised when you hear mine.
What do referees do?
In theory, a lot. In practice, that depends. There are few official journal guides to referees, but there are several well meaning guides (see also here, here, here, here §4.10, and a nice discussion by Don Knuth §15). However, as any editor can tell you, you never know what exactly did the referee do. Some reply within 5 min, some after 2 years. Some write one negative sentence, some 20 detailed pages, some give an advice in the style “yeah, not a bad paper, cites me twice, why not publish it”, while others a brushoff “not sure who this person is, and this problem is indeed strongly related to what I and my collaborators do, but of course our problems are much more interesting/important - rejection would be best”. The anonymity is so relaxing, doing a poor job is just too tempting. The whole system hinges on the shame, sense of responsibility, and personal relationship with the editor.
A slightly better questions is “What do good referees do?” The answer is – they don’t just help the editor make acceptance/rejection decision. They help the authors. They add some background the authors don’t know, look for missing references, improve on the proofs, critique the exposition and even notation. They do their best, kind of what ideal advisors do for their graduate students, who just wrote an early draft of their first ever math paper.
In summary, you can’t blame the referees for anything. They do what they can and as much work as they want. To make a lame comparison, the referees are like wind and the editors are a bit like sailors. While the wind is free, it often changes direction, sometimes completely disappears, and in general quite unreliable. But sometimes it can really take you very far. Of course, crowd sourcing refereeing is like democracy in the army – bad even in theory, and never tried in practice.
First interlude: refereeing war stories
I recall a curious story by Herb Wilf, on how Don Knuth submitted a paper under assumed name with an obscure college address, in order to get full refereeing treatment (the paper was accepted and eventually published under Knuth’s real name). I tried this once, to unexpected outcome (let me not name the journal and the stupendous effort I made to create a fake identity). The referee wrote that the paper was correct, rather interesting but “not quite good enough” for their allegedly excellent journal. The editor was very sympathetic if a bit condescending, asking me not to lose hope, work on my papers harder and submit them again. So I tried submitting to a competing but equal in statue journal, this time under my own name. The paper was accepted in a matter of weeks. You can judge for yourself the moral of this story.
A combinatorialist I know (who shall remain anonymous) had the following story with Duke J. Math. A year and a half after submission, the paper was rejected with three (!) reports mostly describing typos. The authors were dismayed and consulted a CS colleague. That colleague noticed that the three reports were in .pdf but made by cropping from longer files. Turns out, if the cropping is made straightforwardly, the cropped portions are still hidden in the files. Using some hacking software the top portions of the reports were uncovered. The authors discovered that they are extremely positive, giving great praise of the paper. Now the authors believe that the editor despised combinatorics (or their branch of combinatorics) and was fishing for a bad report. After three tries, he gave up and sent them cropped reports lest they think somebody else considers their paper worthy of publishing in the grand old Duke (cf. what Zeilberger wrote about Duke).
Another one of my stories is with the Journal of AMS. A year after submission, one of my papers was rejected with the following remarkable referee report which I quote here in full:
The results are probably well known. The authors should consult with experts.
Needless to say, the results were new, and the paper was quickly published elsewhere. As they say, ”resistance is futile“.
What do associate/handling editors do?
Three little things, really. They choose referees, read their reports and make the decisions. But they are responsible for everything. And I mean for everything, both 1), 2) and 3). If the referee wrote a poorly researched report, they should recognize this and ignore it, request another one. They should ensure they have more than one opinion on the paper, all of them highly informed and from good people. If it seems the authors are not aware of the literature and referee(s) are not helping, they should ensure this is fixed. It the paper is not well written, the editors should ask the authors to rewrite it (or else). At Discrete Mathematics, we use this page by Doug West, as a default style to math grammar. And if the reader finds a mistake, he/she should first contact the editor. Contacting the author(s) is also a good idea, but sometimes the anonymity is helpful – the editor can be trusted to bring bad news and if possible, request a correction.
B.H. Neumann described here how he thinks the journal should operate. I wish his views held widely today. The book by Krantz, §5.5, is a good outline of the ideal editorial experience, and this paper outlines how to select referees. However, this discussion (esp. Rick Durrett’s “rambling”) is more revealing. Now, the reason most people are confused as to who is responsible for 1), 2) and 3), is the fact that while some journals have serious proactive editors, others do not, or their work is largely invisible.
What do managing editors and publishers do?
In theory, managing editors hire associate editors, provide logistical support, distribute paper load, etc. In practice they also serve as handling editors for a large number of papers. The publishers… You know what the publishers do. Most importantly, they either pay editors or they don’t. They either charge libraries a lot, or they don’t. Publishing is a business, after all…
Who wants free universal electronic publishing?
Good mathematicians. Great mathematicians. Mathematicians who write well and see no benefit in their papers being refereed. Mathematicians who have many students and wish the publishing process was speedier and less cumbersome, so their students can get good jobs. Mathematicians who do not value the editorial work and are annoyed when the paper they want to read is “by subscription only” and thus unavailable. In general, these are people who see having to publish as an obstacle, not as a benefit.
Who does not want free universal electronic publishing?
Publishers (of course), libraries, university administrators. These are people and establishments who see value in existing order and don’t want it destroyed. Also: mediocre mathematicians, bad mathematicians, mathematicians from poor countries, mathematicians who don’t have access to good libraries (perhaps, paradoxically). In general, people who need help with their papers. People who don’t want a quick brush-off ”not good enough” or “probably well known”, but those who need advice on the references, on their English, on how the papers are structured and presented, and on what to do next.
So, who is right?
Everyone. For some mathematicians, having all journals to be electronic with virtually no cost is an overall benefit. But at the very least, “pro status quo” crowd have a case, in my view. I don’t mean that Elsevier pricing policy is reasonable, I am talking about the big picture here. In a long run, I think of journals as non-profit NGO‘s, some kind of nerdy versions of Nobel Peace Prize winning Médecins Sans Frontières. While I imagine that in the future many excellent top level journals will be electronic and free, I also think many mid-level journals in specific areas will be run by non-profit publishers, not free at all, and will employ a number of editorial and technical stuff to help the authors, both of papers they accept and reject. This is a public service we should strive to perform, both for the sake of those math papers, and for development of mathematics in other countries.
Right now, the number of mathematicians in the world is already rather large and growing. Free journals can do only so much. Without high quality editors paid by the publishers, with a large influx of papers from the developing world, there is a chance we might loose the traditional high standards for published second tier papers. And I really don’t want to think of a mathematics world once the peer review system is broken. That’s why I am not in the “free publishing camp” – in an effort to save money, we might loose something much more valuable – the system which gives foundation and justification of our work.
Second interlude: journals vis-à-vis combinatorics
I already wrote about the fate of combinatorics papers in the Annals, especially when comparison with Number Theory. My view was gloomy but mildly optimistic. In fact, since that post was written couple more combinatorics papers has been accepted. Good. But let me give you a quiz. Here are two comparable highly selective journals – Duke J. Math. and Composito Math. In the past 10 years Composito published exactly one (!) paper in Combinatorics (defined as primary MSC=05), of the 631 total. In the same period, Duke published 8 combinatorics papers of 681 total.
Q: Which of the two (Composito or Duke) treats combinatorics papers better?
A: Composito, of course.
The reasoning is simple. Forget the anecdotal evidence in the previous interlude. Just look at the “aim and scope” of the journals vs. these numbers. Here is what Compsito website says with a refreshing honesty:
By tradition, the journal published by the foundation focuses on papers in the main stream of pure mathematics. This includes the fields of algebra, number theory, topology, algebraic and analytic geometry and (geometric) analysis. Papers on other topics are welcome if they are of interest not only to specialists.
Translation: combinatorics papers are not welcome (as are papers in many other fields). I think this is totally fair. Nothing wrong with that. Clearly, there are journals which publish mostly in combinatorics, and where papers in none of these fields would be welcome. In fact there is a good historical reason for that. Compare this with what Duke says on its website:
Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world’s leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.
See the difference? They don’t name their favorite areas! How are the authors supposed to guess which are these? Clearly, Combinatorics with its puny 1% proportion of Duke papers is not a subject area that Duke “emphasizes”. Compare it with 104 papers in Number Theory (16%) and 124 papers in Algebraic Geometry (20%) over the same period. Should we conclude that in the past 10 years, Combinatorics was not “the most active and influential”, or perhaps not “mathematics” at all? (yes, some people think so) I have my own answer to this question, and I bet so do you…
Note also, that things used to be different at Duke. For example, exactly 40 years earlier, in the period 1963-1973, Duke published 47 papers in combinatorics out of 972 total, even though the area was only in its first stages of development. How come? The reason is simple: Leonard Carlitz was Managing Editor at the time, and he welcomed papers from a number of prominent combinatorialists active during that time, such as Andrews, Gould, Moon, Riordan, Stanley, Subbarao, etc., as well as a many of his own papers.
So, ideally, what will happen to math journals?
That’s actually easy. Here are my few recommendations and predictions.
1) We should stop with all these geography based journals. That’s enough. I understand the temptation for each country, or university, or geographical entity to have its own math journal, but nowadays this is counterproductive and a cause for humor. This parochial patriotism is perhaps useful in sports (or not), but is nonsense in mathematics. New journals should emphasize new/rapidly growing areas of mathematics underserved by current journals, not new locales where printing presses are available.
2) Existing for profit publishers should realize that with the growth of arXiv and free online competitors, their business model is unsustainable. Eventually all these journals will reorganize into a non-profit institutions or foundations. This does not mean that the journals will become electronic or free. While some probably will, others will remain expensive, have many paid employees (including editors), and will continue to provide services to the authors, all supported by library subscriptions. These extra services are their raison d’être, and will need to be broadly advertised. The authors would learn not to be surprised of a quick one line report from free journals, and expect a serious effort from “expensive journals”.
3) The journals will need to rethink their structure and scope, and try to develop their unique culture and identity. If you have two similar looking free electronic journals, which do not add anything to the papers other than their .sty file, the difference is only the editorial board and history of published papers. This is not enough. All journals, except for the very top few, will have to start limiting their scope to emphasize the areas of their strength, and be honest and clear in advertising these areas. Alternatively, other journals will need to reorganize and split their editorial board into clearly defined fields. Think Proc. LMS, Trans. AMS, or a brand new Sigma, which basically operate as dozens of independent journals, with one to three handling editors in each. While highly efficient, in a long run this strategy is also unsustainable as it leads to general confusion and divergence in the quality of these sub-journals.
4) Even among the top mathematicians, there is plenty of confusion on the quality of existing mathematics journals, some of which go back many decades. See e.g. a section of Tim Gowers’s post about his views of the quality of various Combinatorics journals, since then helpfully updated and corrected. But at least those of us who have been in the area for a while, have the memory of the fortune of previously submitted papers, whether our own, or our students, or colleagues. A circumstantial evidence is better than nothing. For the newcomers or outsiders, such distinctions between journals are a mystery. The occasional rankings (impact factor or this, whatever this is) are more confusing than helpful.
What needs to happen is a new system of awards recognizing achievements of individual journals and/or editors, in their efforts to improve the quality of the journals, attracting top papers in the field, arranging fast refereeing, etc. Think a mixture of Pulitzer Prize and J.D. Power and Associates awards – these would be a great help to understand the quality of the journals. For example, the editors of the Annals clearly hustled to referee within a month in this case (even if motivated by PR purposes). It’s an amazing speed for a technical 50+ page paper, and this effort deserves recognition.
Full disclosure: Of the journals I singled out, I have published once in both JAMS and Duke. Neither paper is in Combinatorics, but both are in Discrete Mathematics, when understood broadly.
Do you think you know the answer? Do you think others have the same answer? Imagine you could go back in time and ask this question to a number of top combinatorialists of the past 50 years. What would they say? Would you agree with them at all?
Turns out, these answers are readily available. I collected them on this page of quotes. The early ones are uncertain, defensive, almost apologetic. The later ones are bolder, prouder of the field and its status. All are enlightening. Take your time, read them all in order.
During my recent MIT visit, Jacob Fox showed me this blog which I found to be rather derogatory in its treatment of combinatorics and notable combinatorialists. This brought me back to my undergraduate days in Moscow, reminded of the long forgotten but back then very common view of combinatorics as “second rate mathematics”. In the US, I always thought, this battle has been won before my time, back in the 1980s. The good guys worked hard and paved the road for all younger combinatorialists to walk on, and be proud of the field. But of course the internet has its own rules, and has room for every prejudice known to men.
While myself uninterested in engaging in conversation, I figured that there got to be some old “war-time” replies which I can show to the Owl blogger. As I see it, only the lack of knowledge can explain these nearsighted generalizations the blogger is showing. And in the age of Google Scholar, there really is no excuse for not knowing the history of the subject, and its traditional sensitivities.
But while compiling the list of quotes linked above, I learned a few things. I learned how tumultuous was the history of combinatorics, with petty fights and random turns into blind alleys. I learned how myopic were some of the people, and how clever and generous were others. I also discovered that there is a good answer to the question in the title (see below), but that answer is not a definition.
What do authorities say?
Not a lot, actually. The AMS MSC (which I love criticizing) lists Combinaorics as 05, on par with about 70 fields, such as Number Theory (11), Geometry (51), Probability (60) and Computer Science (68). It is also on the same level as Nonassociative rings (17), K-theory (19) and Integral equations (51), which are perfectly fine areas, just much smaller. It is one of the 32 categories on the arXiv, but who knows how these came about.
At the level of NSF, it is one of the 11 Disciplinary Research Programs, no longer lumped with “Algebra and Number Theory” (which remain joined at the hip according to NSF). Around the country, Combinatorics is fairly well represented at the top 100 universities, even if breaking “top 10″ barrier remains difficult. Some are firmly in the “algebraic” camp, some in “probabilistic/extremal”, some have a lot of Graph Theory experts, but quite a few have a genuine mix.
This all reminded me of a story how I found out “What is mathematics“. It started with me getting a Master of Arts degree from Harvard. It arrived by mail, and made me unhappy. I thought they made a mistake, that I should have been given Master of Sciences. So I went to the registrar office, asked to see the director and explained the problem. The director was an old lady, who listened carefully, and replied “let me check”. She opened some kind of book, flipped a few pages and declared: “Yes, I see. No mistake made. Mathematics is an Art.” Seeing my disappointed face, she decided to console me “Oh, don’t worry, dear, it’s always been that way at Harvard…”
What the experts are saying.
About the title question, I mean. Let’s review the quotes page. Turns out, a lot of things, often contradicting each other and sometimes themselves. Some are cunning and ingenuous, while others are misleading or plain false. As the management maxim says, “where you stand depends on where you sit”. Naturally, combinatorilists in different areas have a very different view on the question.
Few themes emerge. First, that combinatorics is some kind of discrete universe which deals with discrete “configurations”, their existence and counting. Where to begin? This is “sort of” correct, but largely useless. Should we count logic, rectifiable knots and finite fields in, and things like Borsuk conjecture and algebraic combinatorics out? This is sort of like defining an elephant as a “large animal with a big trunk and big ears”. This “descriptive” definition may work for Webster’s dictionary, but if you have never seen an elephant, you really don’t know how big should be the ears, and have a completely wrong idea about what is a trunk. And if you have seen an elephant, this definition asks you to reject a baby elephant whose trunk and ears are smaller. Not good.
Second theme: combinatorics is defined by its tools and methods, or lack of thereof. This is more of a wishful thinking than a working definition. It is true that practitioners in different parts of combinatorics place a great value on developing new extensions and variations of the available tools, as well as ingenuous ad hoc arguments. But a general attitude, it seems, is basically “when it comes to problem solving, one can use whatever works”. For example, our recent paper proves unimodality results for the classical Gaussian coefficients and their generalizations via technical results for Kronecker coefficients, a tool never been used for that before. Does that make our paper “less combinatorial” somehow? In fact, some experts openly advocate that the more advanced the tools are, the better, while others think that “term ‘combinatorial methods’, has an oxymoronic character”.
Third theme: combinatorics is “special” and cannot be defined. Ugh… This reminds me of an old (1866), but sill politically potent Russian verse (English translation) by Tyutchev. I can certainly understand the unwillingness to define combinatorics, but saying it is not possible is just not true.
Finally, a piecemeal approach. Either going over a long list of topics, or giving detailed and technical rules why something is and something isn’t combinatorics. But this bound to raise controversy, like who decides? For example, take PCM’s “few constraints” rule. Really? Somebody thinks block designs, distance-regular graphs or coding theory have too few constraints? I don’t see it that way. In general, this is an encyclopedia style approach. It can work on Wikipedia which is constantly updated and the controversies are avoided by constant search for a compromise (see also my old post), but it’s not a definition.
My answer, after Gian-Carlo Rota.
After some reading and thinking, I concluded that Gian-Carlo Rota’s 44 y.o. explanation in “Discrete thoughts” is exactly right. Let me illustrate it with my own (lame) metaphor.
Imagine you need to define Russia (not Tyutchev-style). You can say it’s the largest country by land mass, but that’s a description, not a definition. The worst thing you can do is try to define it as a “country in the North” or via its lengthy borders. You see, Russia is huge, spead out and disconnected. It lies to the North of China but has a disconnected common border, it has a 4253 mile border with Kazakhstan (longer than the US-Canada border excluding Alaska), surrounding the country from three sides, it lies North-West of Japan, East of Latvia, South-West of Lithuania (look it up!), etc. It even borders North Korea, not that this tiny border is much in use. Basically, Russian borders are complicated and are a result of numerous wars and population shifts; they have changed many times and might change again.
Now, Rota argues that Combinatorics is similarly formed by the battles, and can only be defined as such. It is a large interconnected field concentrated (but not coinciding!) around basic discrete tools and problems, but with tentacles reaching deep into “foreign territory”. Its current shape is a result of numerous “wars” – the borderline problems are tested on which tools are more successful, and whoever “wins”, gets to absorb a new subfield. For example, in its “war” with topology, combinatorics “won” graph theory and “lost” knot theory (despite a strong combinatorial influence). In other areas, such as computer science and discrete probability, Rota argues there a lot of cooperation, a mutually beneficial “joint governance” (all lame metaphors are mine). But as a consequence, if one is to define Combinatorics (or Russia), the historical-cultural approach would go best. Not all that different from Sheldon’s approach to define Physics ”from the beginning”.
In conclusion, let’s acknowledge that Combinatorics can indeed be defined in the same (lengthy historical) manner as a large diverse country, but such definition would be neither short nor enlightening, more like a short survey. As Danny Kleitman writes, in practice this lack of a clear and meaningful definition of the subject “never bothered him”, and we agree. I think it’s time to stop worrying about that. But if someone makes blank general statements painting all of combinatorics in a certain way, this is just indefensible.
UPDATE (May 29, 2013)
I thought I would add a link to this article by Gian-Carlo Rota, titled “What ‘is’ mathematics?”
This was originally distributed by email on October 7, 1998. For those too young to remember the Fall of 1998, Bill Clinton’s testimony was released on September 21, 1998, with its infamous ”It depends on what the meaning of the word ‘is’ is” quote. Rota’s email never mentions this quote, but is clearly influenced by it.
I became rather interested in the early history of Catalan numbers after reading multiple somewhat contradictory historical accounts. Now that I checked the sources, most of which are available online (see my Catalan Numbers page), I think I understand what happened. While I conclude that Euler deserve most of the credit, as I see it, what really happened is a bit more complicated. Basically, this is a story of research collaboration, only fragments of which are known.
Warning: I am assuming you are familiar with basic results on Catalan numbers, which allows me to concentrate on the story rather than the math.
All sources basically agree that Catalan numbers are named after Eugène Catalan (1814–1894), though they were computed by Leonhard Euler. There are several narratives in the literature, which are variations on the following statements, neither of which is really correct:
1. The problem was introduced by Segner in his 1758 article and solved by Euler in an unsigned article in the same journal volume.
2. The problem was introduced by Euler in his 1758 unsigned article and solved by Segner by a recurrence relation in the same volume.
3. The problem was introduced/solved by Euler in a 1751 letter to Goldbach, but Segner’s paper is the first published solution.
4. Although the problem was raised by Euler and/or Segner, neither of which found a proof. The first proof was given by Lamé in 1838.
Let me delay the explanation of what I think happened. Please be patient!
People and places
There are three heroes in this story: Leonhard Euler (1707–1783), Christian Goldbach (1690–1764), and Johann von Segner (1704–1777). Goldbach was the most senior of the three, he moved to St. Petersburg in 1725, tutored Tsarevich Peter II, and lived in Russia for the rest of his life. When young Euler arrived to St. Petersburg in 1727, Goldbach became his mentor, lifelong friend and a correspondent for over 35 years. Of the numerous letters between them, many were edited and published by Euler’s former assistant, a mathematician and grandson-in-law Nicolas Fuss (1755–1826).
Segner was a physician by trade, but in 1732 became interested in mathematics. In 1735 he was appointed the first mathematics professor at the University of Göttingen (not a big deal at the time). Euler left Russia in 1741 to a position at the Berlin Academy, and joined the court of Frederick the Great of Prussia, at which point he became a frequent correspondent with Segner. Their relationship, perhaps, was closer to a friendly competition than a true friendship between Euler and Goldbach. Although Segner and Euler were contemporaries, Euler rose to prominence very quickly and had a lot of political sway. For example, he slyly engineered Senger’s position at the University of Halle in Saxony, where Segner moved in 1755. Unfortunately, only letters from Segner to Euler survived (159 of them) and these have yet to be digitized.
In 1756, Frederick II overrun the Saxony as a part of initial hostilities of the Seven Year’s War, which put Prussia and Russia on different sides. But Euler continued to publish in Russia, where he was widely respected. When Russian troops marched through Berlin in 1760 (not for the last time), he did not leave the city. Later, when his personal estate was marauded, he was eventually compensated by Catherine the Great (whose court he joined in 1766).
Letter exchange between Euler and Goldbach
* First letter: September 4, 1751 letter, from Euler to Goldbach.
Near the end of the letter, Euler writes matter of factly, that he figured out the numbers of triangulations of the polygons with at most 10 sides. Evidently, he does this by hand, and then takes ratios of successive number to guess the general product formula. He writes:
Die Induction aber, so ich gebraucht, war ziemlich mühsam, doch zweifle ich nicht, dass diese Sach, nicht sollte weit leichter entwickelt werden können.
He continues to guess (correctly) a closed algebraic formula for the g.f. of the Catalan numbers sequence.
* Second letter: October 16, 1751 letter, from Goldbach to Euler.
Here Goldbach suggests there is a way to verify Euler’s g.f. formula by algebraic manipulations. Essentially, he rewrote Euler’s formula for the g.f. for Catalan numbers as a quadratic equation for power series. He the checks the equation for the first few coefficients.
* Third letter: December 4, 1751 letter, from Goldbach to Euler.
Here Euler uses the binomial theorem to show that the generating function formula indeed implies his product formula for the Catalan numbers.
Papers by Euler and Segner
* Segner’s paper in Novi Commentarii, volume 7 (dated 1758/59, but published only in 1761).
Here Segner finds and proves the standard quadratic relation between Catalan numbers. He starts by attributing the problem to Euler and mentioning the first few Catalan numbers that Euler calculated. He then uses this quadratic equation to calculate the first 18 Catalan numbers, but makes an arithmetic mistake, thus miscalculating the last 6.
Euler describes the number of triangulations problem, mentions Segner’s recurrence relation, and then his direct inductive formula for Catalan number, which he rewrites as a conventional product of n-2 fractions. He then uses this formula to correct and extend Segner’s table.
What happened (my speculation) :
This was a collaborative research effort. First, Euler introduced the number of triangulations problem, which perhaps came from his map making work both in Russia and in Berlin (he hints to that in his “summary”). Euler labored to compute by hand the first few Catalan numbers by using ad hoc methods; he correctly calculated them up to 1430 triangulations of a 10-gon. He used these numbers to guess a simple product formula for the Catalan numbers by observing a pattern in successive ratios, and a closed form algebraic formula for the g.f. He clearly realized that the proof of both is needed, but thought this was a difficult problem, at which point he writes to Goldbach. In his reply, Goldbach suggested how to verify the analytic formula, but Euler took a different route and showed that one formula implies the other. From a modern point of view, this was an open exchange of ideas between friends and collaborators, even if dominated by Euler’s genius.
Some years later, Euler evidently suggested this problem to Segner, but never informed him of the product formula which he guessed back then. While Euler’s letters to Segner did not survive, it is clear from Segner’s writing that he knew of some Euler’s calculations, but not the product formula (there is no way he would have made a mistake in the table otherwise), nor even the 1430 value (the largest number reported by Euler to him seemed to be 429). No wonder Segner did not prove Euler’s product formula – he simply did not know what he should be proving, so presented his results as a method for computing Catalan numbers.
Finally, when Euler saw Segner’s work, he immediately realized its value as the last missing piece. Essentially, Segner’s recurrence is exactly what remained in the sequence
combinatorial interpretation → recurrence relation → algebraic equation → closed algebraic formula → product formula,
where the first step is due to Segner, the second and third are easy and closely related to Goldbach’s approach, while the last step is due to Euler himself. Those who teach undergaduates this particular proof, know how much of a pain to teach this last step. As I understand, despite the war and geography, Euler continued editing the volumes of the St. Petersburg based Novi Commentarii. In what should have been the “Summary” of Segner’s article, he included his formula as a way to both gently correct Segner and show the superiority of his product formula. I should mention that Euler’s Latin original sugarcoated this. It is a pity that Euler never published anything else on the subject.
What happened next:
This is much better documented. First, in response to a question by Johann Pfaff, the above mentioned Nicolas Fuss published in 1791 a generalization of Segner’s recurrence relation, and converted it to a higher order algebraic equation for the g.f., thus generalizing Euler’s algebraic formula. This allowed Liouville to give a product formula for this generalization using the Lagrange inversion formula, which was later rediscovered by Kirkman, Cayley and others.
The problem was then studied French mathematician and promoter of Reform Judaism Olry Terquem (1782–1862). As hinted by Liouville in a foonote to Lamé’s article, Terquem knew of both Euler’s and Segner’s articles, but not of the algebraic formulas. He seem to have succeeded in proving that the recurrence relation implies the product formula, thus “achieving it with the help of some properties of factorials”. In in 1838, he suggested the problem to Joseph Liouville (1809–1882), who in turn suggested the problem to a number of people, some of whom became to actively work on the subject. Liouville’s colleague at École Polytechnique, Gabriel Lamé (1795–1870), quickly found an elegant combinatorial solution building on Segner’s approach. Liouville extracted mathematical content from the letter Lamé wrote to him, and quickly published it (English translation), in the Journal de Mathématiques which he started two years earlier. This became the first published complete proof of the product formula for Catalan numbers.
In the following year, other colleagues joint the effort (Binet, Catalan, Rodrigues), and their effort was also published by Liouville. In the following 175 years the problem has been repeatedly rediscovered and generalized (notably, by Bertrand in 1887, in the context of the ballot problem). A small portion of these papers is listed here. Henry Gould’s 2007 count gives 465 publications, surely undercounting the total.
What’s in a name?
Curiously, Catalan’s own contribution was helpful, but not crucial. Netto singled him out in his 1901 monograph, as he favorited Catalan’s language of parenthesized expressions over the less formal discussion of polygon triangulations. Catalan himself called them “Segner numbers“. Given that Euler already has plenty of numbers named after him, it’s too late to change this name. We are stuck with Catalan numbers!
Note: This post is not a piece of research in History of Mathematics, which is a serious field with high standards for quality and rigor. This is merely a speculation, my effort to put together some pieces of the story which do not seem to fit otherwise.
Update (Feb 28, 2013): S. Kotelnikow’s 1766 contribution is removed as he seem to have proved absolutely nothing.
To say that college admissions are overhyped would be an understatement. There are literally many thousands of articles written on the subject each year (GoogleNews counts 2,000 in December 2012 alone), most of which have nothing new to say, except that it is very, very important… In my earlier post I discussed discrimination concerns and crude solutions by universities and the public (read: politicians) to deal with it. But truth of the matter is, these issues are so difficult in part because people value college education so greatly. While I am obviously a strong supporter of college education (also, it pays my bills), college admissions does not have to be that consequential. Here I argue for waiting a year or two, which would decouple the issues, shift decision making from parents to students, and hopefully ease the tension.
The way things are here
When it comes to college admissions, high school students and their parents are anxious and busy with this increasingly costly and time consuming activity. At the end, over 60% of them go to college. Of these, about 76% get into college of their first choice, and of those who don’t, most are happy anyway. Now, all this might seem like a case for “stay the course”, but in fact, lots of people agree on the need for change, but not everyone agrees on what the change should be. Let me present a particular aspect of the problem, which in my view make college admission so hot as an issue.
If you a faculty, you know that many students come to college morally unprepared. Many simply view college as a “high school without parents“. The universities worry about this extended adolescence, but in general are happy to take over this part of parental responsibilities in exchange for higher tuition. No wonder the college bureaucracy is expanding – the need is evident. This is very different from an old model of college as a place of higher learning where either usable skills or arts and letters, are studied by young adults, in preparation of lifetime employment.
It is not a surprise then, that at the end of their college years the students are lost and confused, unprepared for real jobs, and often choose graduate schools as a way to avoid hard decisions.
Why do parents do it?
That is, why are they willing to spend exorbitant amounts of money for a mixture of parenting and education, instead of letting them travel the world or work odd jobs etc., until their children are ready for the education? I it just peer pressure? Probably not. Mostly, because they can. At 18, american high school graduates are not considered adults yet, and with no savings are not in a position to make their own choices. But when parents choose, they are not necessarily governed with what’s best for the children. Paul Graham explains this well in the context of choosing a college major (ht. L. Positselski):
The advice of parents will tend to err on the side of money. It seems safe to say there are more undergrads who want to be novelists and whose parents want them to be doctors than who want to be doctors and whose parents want them to be novelists. The kids think their parents are “materialistic.” Not necessarily. All parents tend to be more conservative for their kids than they would for themselves, simply because, as parents, they share risks more than rewards. If your eight year old son decides to climb a tall tree, or your teenage daughter decides to date the local bad boy, you won’t get a share in the excitement, but if your son falls, or your daughter gets pregnant, you’ll have to deal with the consequences.
So naturally the parents are scared that a year or two outside of the controlled environment will lead to a lifetime of disappointment. They use the tuition money as the last tool they have to control their children, even if this bankrupts them in the meanwhile. This also robs children of potential financial support down the road, whether to start their own business or pursue literary dreams, or house down payment when they start a family.
Why do students do it?
Oh, of course very few children say no to candy (college tuition in this case). Deferred gratification requires a character, an adult quality. The point is not to put the students into position when they have to make a difficult choice between the education they are uncertain about, and the lifestyle they want while contemplating their life goals and risking all this cash their parents saved for college. Only later, some students drop out to pursue their dreams.
How do students fare?
That depends. Sometimes very poorly. They fail basic courses, study for 5 or more years to complete a college degree, drop out, and occasionally commit suicide. The ones who are lucky and realize that their college does not meet their goals, transfer to other schools.
This is not as rare as some people think. For example, Barack Obama transferred from Occidental College to Columbia. Dick Cheney flanked out twice from Yale and eventually graduated from the University of Wyoming. Sarah Palin famously attended 5 colleges before graduating from the University of Idaho. As Tim Noah reports, her grades were good, but she was in constant search of a school which would fit better her ever changing sports and academic interests.
Can things be different?
Of course. And I am not talking about New Guinea lessons. If college was free or nearly free, this would greatly diminish parents’ influence. The knowledge that cheap college will wait while they grow up, would allow many students take a year or two off before they start college. This would allow them to grow up, discover themselves, learn what they really want to do with their life, and become motivated.
Western Europe, of course, has inexpensive education, but is misleading as an example, since most universities are public and tend to be equal in funding and opportunities (within each country). Also, things are slowly changing. But in Eastern Europe, the universities are often very different in quality and offered majors, while still inexpensive enough to allow students to ignore parents’ advice and enjoy several years of travel and self-discovery. Occasionally, a foreign born celebrity laments on the lack of that in America, but is never taken seriously. Too bad.
Really different models
Let us count the ways other societies and subcultures change the above equation to allow 18 year olds to grow up before they join college. While I don’t specifically advocate for either of these, the list does show that a few years away from the studies can be beneficial, or at least does not harm teenagers as much as their parents tend to think.
The most common is the military service, which varies in length may include civil service. It is required even in some of the most developed countries such as Finland, Norway, Switzerland, and South Korea. Until relatively recently it was required in virtually all countries. AmeriCorps (not to be confused with PeaceCorps) is the US civil service pre-college alternative to serving in the military, but with only about 10-15 thousand people joining each year.
In Israel, both men and women are drafted, although at different lengths. At the end of the service it is customary for former soldiers to travel the world for six months to a year, in destinations ranging from Bolivia to Sri Lanka, doing various experiments considered illegal at home. These overseas trips are commonly viewed almost as the rite-of-passage. Virtually all of these former soldiers later come back to Israel and become law obedient productive citizen, many with college degrees.
Religion is another source of lengthy travel and civil commitments, which range from Rumspringa (Amish adolescents’ leaves to explore the world) to Mormon missionary work. Famously, Mitt Romney spent 2.5 years in France, while Jon Huntsman was a missionary in Taiwan.
Both military and civil service tends to make students more mature and goal oriented, if only because they are older. For example, after a 5 year service in the IDF, current Israel Prime Minister Bibi Netanyahu became a freshman at MIT at the age of 23, and earned two degrees (B.S. and M.B.A.) in four years (read why in the article).
Two personal anecdotes
After high school, I did not enroll at the university (not by choice, as I explained earlier), but went to work as a C++ programmer at a bank (no, you don’t need a degree for that). At the end of the year, I learned something about myself. Turns out, I really dislike working all night to meet a deadline, providing mountains of documentation accompanying the code, or dealing with ever more demanding managers who understood little about the actual work. So I promised myself to never ever do any programming again, a pledge that was easy to keep in my current vocation.
In another story, one of my distant relatives (let’s call him Mr. X) asked me what to do about his son suddenly being accepted to an Ivy League school. With a high 5-figure salary he was rich enough not to be eligible for financial aid, and poor enough to afford the tuition. After reading the rules, I told X that things are easier than he thinks. All he had to do is defer enrollment for a year (this is allowed by many schools), send the kid to Russia live with a grandmother, and let him file his own taxes. At the end of the year, X’s son can declare “financial independence” by signing a piece of paper in front of a notary public, that he is “abandoned by parents”. Then, as a pauper, receive all financial aid available in such cases. This trick would undoubtedly have saved Mr. X an upward of 100K. But parental instincts are way too strong – instead he took a second mortgage on the house. (Some minor details are changed to protect the identity of X’s family).
What can be done?
In general, rather little. Changing the culture is hard, and rarely possible top-down without financial incentives. Ideally, after high school the students should travel the world and explore different professions until they settle on what they want to do. But as long as the colleges are expensive, the parents will continue to control the process sending the children to college immediately after high school, without giving them such opportunity.
Fortunately, there is a crisis in university education, with the offering of large scale online courses, and I mean “fortunately” in the same sense as Rahm Emanuel. It has long been suggested by the advocated of inexpensive public education in California that most students should spend the first two years in local community colleges and then transfer to an appropriate UC or CalState school depending on their achievements. Then schools such as Berkeley or UCLA would essentially become 2-year “finishing schools”. The parents tend to revolt at this suggestions due to inherent uncertainty of the outcome. I propose a variation on this approach, essentially bribing all the parties involved.
1. Make available online all standard introductory classes.
2. Allow an off-campus registration for at most 2 years, and charge only a fraction of the tuition for it. Require B- average to maintain it.
3. Encourage more student transfers, both in and out, based on these grades.
Under there conditions with a guaranteed college spot, I believe many more students would choose to save on the tuition and travel the remote parts of the world, perhaps working part-time teaching conversational English, while taking the required few online classes to maintain college eligibility. In a long run, this is also a good deal for the universities, as this would lead to smaller classes and more personalized attention to students who come back and enroll on campus. The students themselves will be more mature and motivated, improving the graduation rate.
Hopefully, with time this will also reduce the temperature of college admission on all sides. As the early online experience is equalizing and there is always a possibility of transfer later on, the potential admission mistakes become much less costly. Baby steps…
Recent reports on alleged discrimination of Asian Americans at Ivy League schools (read a discussion here and view this graph), brought a lot of disgust in me, as well as some ambivalence. Here and in the next post I will try to deconstruct these feelings.
In this post I mention my family and my own history of dealing with discrimination. I then briefly review and make parallels with the current discussion of the issues, and make some recommendations. In the next post, I will explain why the whole issue is overhyped and what does that say about american culture.
Russian Jews go to school
Well, this is a really long story, but when it comes to educational opportunities, things were always pretty bad. By 1880′s most universities and gymnasiums in Imperial Russia instituted a 5 to 10% Jewish quota, which remained in effect until the Russian revolution in 1917. Read more on the history in this book (part III), and in amazing personal memoir (in Russian).
Communists abolished Jewish discrimination replacing it with anti-religious discrimination, often having similar effect. In the 1930s, my grandmother was expelled from college after communist officials discovered that her father (my great-grandfather) was a rabbi. A local newspaper went all schadenfreude about her, and published an anti-clerical article ”The wolf in sheep’s clothing”, apparently missing the irony of the origin of the title.
By the early 1960s, Israel became a super-enemy of USSR, and things were slowly getting hotter for the Jews. For example, despite high exam grades, my father and few dozen Jews was denied admission to Moscow University (МГУ) on account of “lack of dorm space”. Some scandal ensued and he was accepted a month later. By the late 1960s, after the Six-Day War, the Mathematics Department of Мoscow University settled on 0.5% quota (about 2 Jewish students in a class of 450-500), which typically went to children of the university faculty and occasional party officials. When I applied in 1988, I was rejected as the quota remained in effect. In 1989, things were starting to change, and the quota was raised to about 4%. I got in. In the meantime, I became somewhat of an expert on “Jewish problems” (see also here and there), once even holding a seminar on them.
Curiously, the officials had supported the quota very openly, justifying it as follows:
1. We need to maintain proportion of Jews the same as in the country, so as they don’t take space from ethnically Russian students.
2. Jews are already privileged by the virtue of living in large cities, but Russians from small villages need extra help to get quality education. Of course, Jews in Ukrainian, Lithuanian and Belorussian villages were mostly killed in the WWII as part of the Final Solution.
3. Future Russia needs an educated workforce. There is no point of preparing “cadres for Israel“. Thus the “diploma tax“.
My little brush with discrimination in the US
In 1994, already a first year grad student at Harvard, I applied for NSF Graduate Fellowhip, which was highly selective but much less generous back then. I mailed my proposed plan of research, letters of recommendation, transcripts, and the required GRE, both General and Subject. I was rejected. Since I received a more selective Hertz Foundation Fellowship (see my discussion of it here), I wasn’t too upset, but I was curious what did I do wrong. So I filed a FOIA request, and got a reply a few weeks later.
What I learned was remarkable and made me really upset. I discovered that the NSF reviewers rated A all my materials, both the transcript, all the letters, and plan of research. I had a maximal GRE Subject score. But you see, me being Russian and all, I had a mediocre to poor GRE General score on the Verbal Section. The paperwork indicated that the committee then took weighted average of all these grades, made a list of top scorers and I didn’t make the cut. Since I could not fathom why would I need a top GRE Verbal score for Math Ph.D., this seemed clearly discriminatory, on the basis of my native language.
So I found a lawyer (tiny Cambridge, MA is full of them). He patiently explained to me that my Russian native language is not defining me as a member of protected class, and I have no case against NSF. He said that even politically, there is no such thing as “Russian language lobby” (despite our large numbers), and given that there was no harm done (my Hertz), I should go home and learn to be happy. Naturally, I did.
Jews at Harvard and the geographic distribution
The story of Jews at Harvard has been described in great details at a variety of sources. In short, Harvard instituted a 15% quota, which was later softened, substituted with geographic distribution preferences, having same effect on Jewish enrollment. The following quote about the evolution of Harvard President James Conant (1933-1953) is revealing:
Conant’s pro-quote position in the early 1920s, his preference for more students from small towns and cities and the South and West, and his cool response to the plight of the Jewish academic refugees from Hitler suggest that he shared the mild antisemitism common to his social group and time. But his commitment to meritocracy made him more ready to accept able Jews as students and faculty.
While the quotas are both illegal and a thing of the past, the use of geographic distribution in admissions never went away. While not discriminatory in the strict legal sense, they were created with a discriminatory intent, and still have discriminatory effect, as recent immigrants, Jews and other minorities tend to concentrate in large population centers. Not unlike the Russian “village” arguments, this is a slight of hand, which first creates and then heavy-handedly destroys a straw man, all in an effort to deal with other issues which are kept out of sight. We will see this in other cases as well.
All students are somebody’s children
Legacy preferences is another example of misleading practices potentially having discriminatory effect. Universities are claiming that this creates a brand loyalty. But that is misleading of course. Do Ivy League schools really need to develop brand loyalty when they have 10-20 applicants per spot? The truth, of course, is that children of alumni have money and willing to pay a full sticker price of the tuition, and the admission officers aim to have about 20% of such legacy students in each freshmen class.
In fact, the honest market based solution would be to auction this portion of the freshman class to the highest bidder, charging tuition perhaps as much as 100K per year. This auction would raise significant funds which can pay for poor students’ scholarships and stipends, and open up these admission slots to everyone, not just children of alumni. As it is, legacy candidates get preferences in admission and, perhaps counter intuitively, have their tuition subsidized as others may potentially be willing to pay more for their spots. Now, I am NOT advocating for this, just showing how misguided and fundamentally unfair are the current admission policies.
Texas 10% solution
This rule was enacted in response to state losing in Hopwood v. Texas, as a novel legal way to introduce diversity in admissions. An ultimate geographic preference, this rule fills about 75-80% of the freshmen class at the leading Texas universities. Note that the Fisher case is about the affirmative action for the remaining spots.
But it is exactly the kind of rule which makes wrong priorities for the students and the society. In general, it is beneficial for the society when students have a choice which K12 school to attend. It is undoubtedly good when they study in the most challenging environment, work hardest on the most advanced courses available. This rule pushes students to take the easiest courses in the least challenging school, aiming to attain the highest GPA and enter the coveted 10%. And guess what – Texas students do exactly that (this in addition to other rule troubles).
A case for honesty
As it stands, the universities are on the brink of losing another affirmative action case in the Supreme Court. Perhaps this is not immediately apparent, but they are also on the brink of a giant PR disaster when it comes to their hidden quotas for Asian Americans. With good intentions, the admission officers and politician keep coming up with twisted, misleading, uncomfortable and occasionally self-contradictory rationale as to why they do what they do (see above). The problem is – with all the history, we’ve seen this all before, and nobody is buying it. With so much public pressure, they probably have to stop and own up to their choices.
I think it is clear what many top colleges are doing. They have a goal of a freshmen class which would have f(x)% students with property x, for many different x, which can be race, gender, wealth, political connections, geographic location, sexual orientation, sports, music, science and other achievements, etc. So they produce all these policies like the early action, and many rationalizations aimed at reaching that goal. One should have a lot of chutzpah to believe to know exactly the “right mix” function f, but of course they think that…
If it was up to me, I would give the universities a complete freedom to accept whoever they want without fear of lawsuits, in exchange for complete transparency. Education is really not like housing or employment, it is fluid and highly competitive. In exchange, make the universities publish the exact numbers of how many students with every property x have applied and got accepted. For the sake of anonymity, delete all the names and zip codes, and publish on the web the rest of the data from their applications. Let the future applicants, or nonprofits on their behalf, decide their chances of acceptance and make rational choice whether to spend their $75 and endless hours applying to that school. Unfortunately, we don’t live in an ideal world, but you have to let colleges compete with each other, which is the most fair and offers the best model of education.
Finally, when it comes to Asian Americans – Harvard and the rest of the Ivies should just apologize, and starting next year accept twice as many as this year, to compensate for the real or perceived discrimination. Otherwise, a hundred years from now, somebody might still be writing how stupid and morally twisted were these old early 21st century admission policies.
Warning: Here I neither endorse nor reject the affirmative action, but rather advocate for some honesty, clarity and transparency.