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It could have been worse! Academic lessons of 2020

December 20, 2020 3 comments

Well, this year sure was interesting, and not in a good way. Back in 2015, I wrote a blog post discussing how video talks are here to stay, and how we should all agree to start giving them and embrace watching them, whether we like it or not. I was right about that, I suppose. OTOH, I sort of envisioned a gradual acceptance of this practice, not the shock therapy of a phase transition. So, what happened? It’s time to summarize the lessons and roll out some new predictions.

Note: this post is about the academic life which is undergoing some changes. The changes in real life are much more profound, but are well discussed elsewhere.

Teaching

This was probably the bleakest part of the academic life, much commented upon by the media. Good thing there is more to academia than teaching, no matter what the ignorant critics think. I personally haven’t heard anyone saying post-March 2020, that online education is an improvement. If you are like me, you probably spent much more time preparing and delivering your lectures. The quality probably suffered a little. The students probably didn’t learn as much. Neither party probably enjoyed the experience too much. They also probably cheated quite a bit more. Oh, well…

Let’s count the silver linings. First, it will all be over some time next year. At UCLA, not before the end of Summer. Maybe in the Fall… Second, it could’ve been worse. Much worse. Depending on the year, we would have different issues. Back in 1990, we would all be furloughed for a year living off our savings. In 2000, most families had just one personal computer (and no smartphones, obviously). Let the implications of that sink in. But even in 2010 we would have had giant technical issues teaching on Skype (right?) by pointing our laptop cameras on blackboards with dismal effect. The infrastructure which allows good quality streaming was also not widespread (people were still using Redbox, remember?)

Third, the online technology somewhat mitigated the total disaster of studying in the pandemic time. Students who are stuck in faraway countries or busy with family life can watch stored videos of lectures at their convenience. Educational and grading software allows students to submit homeworks and exams online, and instructors to grade them. Many other small things not worth listing, but worth being thankful for.

Fourth, the accelerated embrace of the educational technology could be a good thing long term, even when things go back to normal. No more emails with scanned late homeworks, no more canceled/moved office hours while away at conferences. This can all help us become better at teaching.

Finally, a long declared “death of MOOCs” is no longer controversial. As a long time (closeted) opponent to online education, I am overjoyed that MOOCs are no longer viewed as a positive experience for university students, more like something to suffer through. Here in CA we learned this awhile ago, as the eagerness of the current Gov. Newsom (back then Lt. Gov.) to embrace online courses did not work out well at all. Back in 2013, he said that the whole UC system needs to embrace online education, pronto: “If this doesn’t wake up the U.C. [..] I don’t know what will.” Well, now you know, Governor! I guess, in 2020, I don’t have to hide my feelings on this anymore…

Research

I always thought that mathematicians can work from anywhere with a good WiFi connection. True, but not really – this year was a mixed experience as lonely introverts largely prospered research wise, while busy family people and extraverts clearly suffered. Some day we will know how much has research suffered in 2020, but for me personally it wasn’t bad at all (see e.g. some of my results described in my previous blog post).

Seminars

I am not even sure we should be using the same word to describe research seminars during the pandemic, as the experience of giving and watching math lectures online are so drastically different compared to what we are used to. Let’s count the differences, which are both positive and negative.

  1. The personal interactions suffer. Online people are much more shy to interrupt, follow up with questions after the talk, etc. The usual pre- or post-seminar meals allow the speaker to meet the (often junior) colleagues who might be more open to ask questions in an informal setting. This is all bad.
  2. Being online, the seminar opened to a worldwide audience. This is just terrific as people from remote locations across the globe now have the same access to seminars at leading universities. What arXiv did to math papers, covid did to math seminars.
  3. Again, being online, the seminars are no longer restricting themselves to local speaks or having to make travel arrangements to out of town speakers. Some UCLA seminars this year had many European speakers, something which would be prohibitively expensive just last year.
  4. Many seminars are now recorded with videos and slides posted online, like we do at the UCLA Combinatorics and LA Combinatorics and Complexity seminars I am co-organizing. The viewers can watch them later, can fast forward, come back and re-watch them, etc. All the good features of watching videos I extolled back in 2015. This is all good.
  5. On a minor negative side, the audience is no longer stable as it varies from seminar to seminar, further diminishing personal interactions and making level of the audience somewhat unpredictable and hard to aim for.
  6. As a seminar organizer, I make it a personal quest to encourage people to turn on their cameras at the seminars by saying hello only to those whose faces I see. When the speaker doesn’t see the faces, whether they are nodding or quizzing, they are clueless whether the they are being clear, being too fast or too slow, etc. Stopping to ask for questions no longer works well, especially if the seminar is being recorded. This invariably leads to worse presentations as the speakers can misjudge the audience reactions.
  7. Unfortunately, not everyone is capable of handling technology challenges equally well. I have seen remarkably well presented talks, as well as some of extremely poor quality talks. The ability to mute yourself and hide behind your avatar is the only saving grace in such cases.
  8. Even the true haters of online educations are now at least semi-on-board. Back in May, I wrote to Chris Schaberg dubbed by the insufferable Rebecca Schuman as “vehemently opposed to the practice“. He replied that he is no longer that opposed to teaching online, and that he is now in a “it’s really complicated!” camp. Small miracles…

Conferences

The changes in conferences are largely positive. Unfortunately, some conferences from the Spring and Summer of 2020 were canceled and moved, somewhat optimistically, to 2021. Looking back, they should all have been held in the online format, which opens them to participants from around the world. Let’s count upsides and downsides:

  1. No need for travel, long time commitments and financial expenses. Some conferences continue charging fees for online participation. This seems weird to me. I realize that some conferences are vehicles to support various research centers and societies. Whatever, this is unsustainable as online conferences will likely survive the pandemic. These organizations should figure out some other income sources or die.
  2. The conferences are now truly global, so the emphasis is purely on mathematical areas than on the geographic proximity. This suggests that the (until recently) very popular AMS meetings should probably die, making AMS even more of a publisher than it is now. I am especially looking forward to the death of “joint meetings” in January which in my opinion outlived their usefulness as some kind of math extravaganza events bringing everyone together. In fact, Zoom simply can’t bring five thousand people together, just forget about it…
  3. The conferences are now open to people in other areas. This might seem minor — they were always open. However, given the time/money constraints, a mathematician is likely to go only to conferences in their area. Besides, since they rarely get invited to speak at conferences in other areas, travel to such conferences is even harder to justify. This often leads to groupthink as the same people meet year after year at conferences on narrow subjects. Now that this is no longer an obstacle, we might see more interactions between the fields.
  4. On a negative side, the best kind of conferences are small informal workshops (think of Oberwolfach, AIM, Banff, etc.), where the lectures are advanced and the interactions are intense. I miss those and hope they come back as they are really irreplaceable in the only setting. If all goes well, these are the only conferences which should definitely survive and even expand in numbers perhaps.

Books and journals

A short summary is that in math, everything should be electronic, instantly downloadable and completely free. Cut off from libraries, thousands of mathematicians were instantly left to the perils of their university library’s electronic subscriptions and their personal book collections. Some fared better than others, in part thanks to the arXiv, non-free journals offering old issues free to download, and some ethically dubious foreign websites.

I have been writing about my copyleft views for a long time (see here, there and most recently there). It gets more and more depressing every time. Just when you think there is some hope, the resilience of paid publishing and reluctance to change by the community is keeping the unfortunate status quo. You would think everyone would be screaming about the lack of access to books/journals, but I guess everyone is busy doing something else. Still, there are some lessons worth noting.

  1. You really must have all your papers freely available online. Yes, copyrighted or not, the publishers are ok with authors posting their papers on their personal website. They are not ok when others are posting your papers on their websites, so the free access to your papers is on you and your coauthors (if any). Unless you have already done so, do this asap! Yes, this applies even to papers accessible online by subscription to selected libraries. For example, many libraries including all of UC system no longer have access to Elsevier journals. Please help both us and yourself! How hard is it to put the paper on the arXiv or your personal website? If people like Noga Alon and Richard Stanley found time to put hundreds of their papers online, so can you. I make a point of emailing to people asking them to do that every time I come across a reference which I cannot access. They rarely do, and usually just email me the paper. Oh, well, at least I tried…
  2. Learn to use databases like MathSciNet and Zentralblatt. Maintain your own website by adding the slides, video links as well as all your papers. Make sure to clean up and keep up to date your Google Scholar profile. When left unattended it can get overrun with random papers by other people, random non-research files you authored, separate items for same paper, etc. Deal with all that – it’s easy and takes just a few minutes (also, some people judge them). When people are struggling trying to do research from home, every bit of help counts.
  3. If you are signing a book contract, be nice to online readers. Make sure you keep the right to display a public copy on your website. We all owe a great deal of gratitude to authors who did this. Here is my favorite, now supplemented with high quality free online lectures. Be like that! Don’t be like one author (who will remain unnamed) who refused to email me a copy of a short 5 page section from his recent book. I wanted to teach the section in my graduate class on posets this Fall. Instead, the author suggested I buy a paper copy. His loss — I ended up teaching some other material instead. Later on, I discovered that the book is already available on one of those ethically compromised websites. He was fighting a battle he already lost!

Home computing

Different people can take different conclusions from 2020, but I don’t think anyone would argue the importance of having good home computing. There is a refreshing variety of ways in which people do this, and it’s unclear to me what is the optimal set up. With a vaccine on the horizon, people might be reluctant to further invest into new computing equipment (or video cameras, lights, whiteboard, etc.), but the holiday break is actually a good time to marinate on what worked out well and what didn’t.

Read your evaluations and take them to heart. Make changes when you see there are problems. I know, it’s unfair, your department might never compensate you for all this stuff. Still, it’s a small price to pay for having a safe academic job in the time of widespread anxiety.

Predictions for the future

  1. Very briefly: I think online seminars and conferences are here to stay. Local seminars and small workshops will also survive. The enormous AMS meetings and expensive Theory CS meetings will play with the format, but eventually turn online for good or die untimely death.
  2. Online teaching will remain being offered by every undergraduate math program to reach out to students across the spectrum of personal circumstances. A small minority of courses, but still. Maybe one section of each calculus, linear algebra, intro probability, discrete math, etc. Some faculty might actually prefer this format to stay away from office one semester. Perhaps, in place of a sabbatical, they can ask for permission to spend a semester some other campus, maybe in another state or country, while they continue teaching, holding seminars, supervising students, etc. This could be a perk of academic life to compete with the “remote work” that many businesses are starting to offer on a permanent basis. Universities would have to redefine what they mean by “residence” requirement for both faculty and students.
  3. More university libraries will play hardball and unsubscribe from major for-profit publishers. This would again sound hopeful, but not gain a snowball effect for at least the next 10 years.
  4. There will be some standardization of online teaching requirements across the country. Online cheating will remain widespread. Courts will repeatedly rule that business and institutions can discount or completely ignore all 2020 grades as unreliable in large part because of the cheating scandals.

Final recommendations

  1. Be nice to your junior colleagues. In the winner-take-all no-limits online era, the established and well-known mathematicians get invited over and over, while their junior colleagues get overlooked, just in time when they really need help (job market might be tough this year). So please go out of your way to invite them to give talks at your seminars. Help them with papers and application materials. At least reply to their emails! Yes, even small things count…
  2. Do more organizing if you are in position to do so. In the absence of physical contact, many people are too shy and shell-shocked to reach out. Seminars, conferences, workshops, etc. make academic life seem somewhat normal and the breaks definitely allow for more interactions. Given the apparent abundance of online events one my be forgiven to think that no more is needed. But more locally focused online events are actually important to help your communities. These can prove critical until everything is back to normal.

Good luck everybody! Hope 2021 will be better for us all!

Combinatorial briefs

June 9, 2013 Leave a comment

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 Stanlеy (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.

What do math journals do? What will become of them in the future?

May 28, 2013 4 comments

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.