Innovation anxiety

I am on record of liking the status quo of math publishing. It’s very far from ideal as I repeatedly discuss on this blog, see e.g. my posts on the elitism, the invited issues, the non-free aspect of it in the electronic era, and especially the pay-to-publish corruption. But overall it’s ok. I give it a B+. It took us about two centuries to get where we are now. It may take us awhile to get to an A.

Given that there is room for improvement, it’s unsurprising that some people make an effort. The problem is that their efforts be moving us in the wrong direction. I am talking specifically about two ideas that frequently come up by people with best intensions: abolishing peer review and anonymizing the author’s name at the review stage. The former is radical, detrimental to our well being and unlikely to take hold in the near future. The second is already here and is simply misguided.

Before I take on both issues, let me take a bit of a rhetorical detour to make a rather obvious point. I will be quick, I promise!

Don’t steal!

Well, this is obvious, right? But why not? Let’s set all moral and legal issues aside and discuss it as adults. Why should a person X be upset if Y stole an object A from Z? Especially if X doesn’t know either Y or Z, and doesn’t really care who A should belong to. Ah, I see you really don’t want to engage with the issue — just like me you already know that this is appalling (and criminal, obviously).

However, if you look objectively at the society we live in, there is clearly some gray area. Indeed, some people think that taxation is a form of theft (“taking money by force”, you see). Millions of people think that illegally downloading movies is not stealing. My university administration thinks stealing my time making me fill all kinds of forms is totally kosher. The country where I grew up in was very proud about the many ways it stole my parents’ rights for liberty and the pursuit of happiness (so that they could keep their lives). The very same country thinks it’s ok to invade and steal territory from a neighboring country. Apparently many people in the world are ok with this (as in “not my problem”). Not comparing any of these, just challenging the “isn’t it obvious” premise.

Let me give a purely American answer to the “why not” question. Not the most interesting or innovative argument perhaps, but most relevant to the peer review discussion. Back in September 1789, Thomas Jefferson was worried about the constitutional precommitment. Why not, he wondered, have a revolution every 19 years, as a way not to burden future generations with rigid ideas from the past?

In February 1790, James Madison painted a grim picture of what would happen: “most of the rights of property would become absolutely defunct and the most violent struggles be generated” between property haves and have-nots, making remedy worse than the disease. In particular, allowing theft would be detrimental to continuing peaceful existence of the community (duh!).

In summary: a fairly minor change in the core part of the moral code can lead to drastic consequences.

Everyone hates peer review!

Indeed, I don’t know anyone who succeeded in academia without a great deal of frustration over the referee reports, many baseless rejections from the journals, or without having to spend many hours (days, weeks) writing their own referee reports. It’s all part of the job. Not the best part. The part well hidden from outside observers who think that professors mostly teach or emulate a drug cartel otherwise.

Well, the help is on the way! Every now and then somebody notably comes along and proposes to abolish the whole thing. Here is one, two, three just in the last few years. Enough? I guess not. Here is the most recent one, by Adam Mastroianni, twitted by Marc Andreessen to his 1.1 million followers.

This is all laughable, right? Well, hold on. Over the past two weeks I spoke to several well known people who think that abolishing peer review would make the community more equitable and would likely foster the innovation. So let’s address these objections seriously, point by point, straight from Mastroianni’s article.

(1) “If scientists cared a lot about peer review, when their papers got reviewed and rejected, they would listen to the feedback, do more experiments, rewrite the paper, etc. Instead, they usually just submit the same paper to another journal.” Huh? The same level journal? I wish…

(2) “Nobody cares to find out what the reviewers said or how the authors edited their paper in response” Oh yes, they do! Thus multiple rounds of review, sometimes over several years. Thus a lot of frustration. Thus occasional rejections after many rounds if the issue turns out non-fixable. That’s the point.

(3) “Scientists take unreviewed work seriously without thinking twice.” Sure, why not? Especially if they can understand the details. Occasionally they give well known people benefit of the doubt, at least for awhile. But then they email you and ask “Is this paper ok? Why isn’t it published yet? Are there any problems with the proof?” Or sometimes some real scrutiny happens outside of the peer review.

(4) “A little bit of vetting is better than none at all, right? I say: no way.” Huh? In math this is plainly ridiculous, but the author is moving in another direction. He supports this outrageous claim by saying that in biomedical sciences the peer review “fools people into thinking they’re safe when they’re not. That’s what our current system of peer review does, and it’s dangerous.” Uhm. So apparently Adam Mastroianni thinks if you can’t get 100% certainty, it’s better to have none. I feel like I’ve heard the same sentiment form my anti-masking relatives.

Obviously, I wouldn’t know and honestly couldn’t care less about how biomedical academics do research. Simply put, I trust experts in other fields and don’t think I know better than them what they do, should do or shouldn’t do. Mastroianni uses “nobody” 11 times in his blog post — must be great to have such a vast knowledge of everyone’s behavior. In any event, I do know that modern medical advances are nothing short of spectacular overall. Sounds like their system works really well, so maybe let them be…

The author concludes by arguing that it’s so much better to just post papers on the arXiv. He did that with one paper, put some jokes in it and people wrote him nice emails. We are all so happy for you, Adam! But wait, who says you can’t do this with all your papers in parallel with journal submissions? That’s what everyone in math does, at least the arXiv part. And if the journals where you publish don’t allow you to do that, that’s a problem with these specific journals, not with the whole peer review.

As for the jokes — I guess I am a mini-expert. Many of my papers have at least one joke. Some are obscure. Some are not funny. Some are both. After all, “what’s life without whimsy“? The journals tend to be ok with them, although some make me work for it. For example, in this recent paper, the referee asked me to specifically explain in the acknowledgements why am I thankful to Jane Austen. So I did as requested — it was an inspiration behind the first sentence (it’s on my long list of starters in my previous blog post). Anyway, you can do this, Adam! I believe in you!

Everyone needs peer review!

Let’s try to imagine now what would happen if the peer review is abolished. I know, this is obvious. But let’s game it out, post-apocaliptic style.

(1) All papers will be posted on the arXiv. In a few curious cases an informal discussion will emerge, like this one about this recent proof of the four color theorem. Most paper will be ignored just like they are ignored now.

(2) Without a neutral vetting process the journals will turn to publishing “who you know”, meaning the best known and best connected people in the area as “safe bets” whose work was repeatedly peer reviewed in the past. Junior mathematicians will have no other way to get published in leading journals without collaboration (i.e. writing “joint papers”) with top people in the area.

(3) Knowing that their papers won’t be refereed, people will start making shortcuts in their arguments. Soon enough some fraction will turn up unsalvageable incorrect. Embarrassments like the ones discussed in this page will become a common occurrence. Eventually the Atiyah-style proofs of famous theorems will become widespread confusing anyone and everyone.

(4) Granting agencies will start giving grants only to the best known people in the area who have most papers in best known journals (if you can peer review papers, you can’t expect to peer review grant proposals, right?) Eventually they will just stop, opting to give more money to best universities and institutions, in effect outsourcing their work.

(5) Universities will eventually abolish tenure as we know it, because if anyone is free to work on whatever they want without real rewards or accountability, what’s the point of tenure protection? When there are no objective standards, in the university hiring the letters will play the ultimate role along with many biases and random preferences by the hiring committees.

(6) People who work in deeper areas will be spending an extraordinary amount of time reading and verifying earlier papers in the area. Faced with these difficulties graduate students will stay away from such areas opting for more shallow areas. Eventually these areas will diminish to the point of near-extinsion. If you think this is unlikely, look into post-1980 history of finite group theory.

(7) In shallow areas, junior mathematicians will become increasingly more innovative to avoid reading older literature, but rather try to come up with a completely new question or a new theory which can be at least partially resolved on 10 pages. They will start running unrefereed competitive conferences where they will exhibit their little papers as works of modern art. The whole of math will become subjective and susceptible to fashion trends, not unlike some parts of theoretical computer science (TCS).

(8) Eventually people in other fields will start saying that math is trivial and useless, that everything they do can be done by an advanced high schooler in 15 min. We’ve seen this all before, think candid comments by Richard Feynman, or these uneducated proclamations by this blog’s old villain Amy Wax. In regards to combinatorics, such views were prevalent until relatively recently, see my “What is combinatorics” with some truly disparaging quotations, and this interview by László Lovász. Soon after, everyone (physics, economics, engineering, etc.) will start developing their own kind of math, which will be the end of the whole field as we know it.

…

(100) In the distant future, after the human civilization dies and rises up again, historians will look at the ruins of this civilization and wonder what happened? They will never learn that’s it’s all started with Adam Mastroianni when he proclaimed that “science must be free“.

Less catastrophic scenarios

If abolishing peer review does seem a little farfetched, consider the following less drastic measures to change or “improve” peer review.

(i) Say, you allow simultaneous submissions to multiple journals, whichever accepts first gets the paper. Currently, the waiting time is terribly long, so one can argue this would be an improvement. In support of this idea, one can argue that in journalism pitching a story to multiple editors is routine, that job applications are concurrent to all universities, etc. In fact, there is even an algorithm to resolve these kind of situations successfully. Let’s game this out this fantasy.

The first thing that would happen is that journals would be overwhelmed with submissions. The referees are already hard to find. After the change, they would start refusing all requests since they would also be overwhelmed with them and it’s unclear if the report would even be useful. The editors would refuse all but a few selected papers from leading mathematicians. Chat rooms would emerge in the style “who is refereeing which paper” (cf. PubPeer) to either collaborate or at least not make redundant effort. But since it’s hard to trust anonymous claims “I checked and there are no issues with Lemma 2 in that paper” (could that be the author?), these chats will either show real names thus leading to other complications (see below), or cease to exist.

Eventually the publishers will start asking for a signed official copyright transfer “conditional on acceptance” (some already do that), and those in violation will be hit with lawsuits. Universities will change their faculty code of conduct to include such copyright violations as a cause for dismissal, including tenure removal. That’s when the practice will stop and be back to normal, at great cost obviously.

(ii) Non-anonymizing referees is another perennial idea. Wouldn’t it be great if the referees get some credit for all the work that they do (so they can list it on their CVs). Even better if their referee report is available to the general public to read and scrutinize, etc. Win-win-win, right?

No, of course not. Many specialized sub-areas are small so it is hard to find a referee. For the authors, it’s relatively easy to guess who the referees are, at least if you have some experience. But there is still this crucial ambiguity as in “you have a guess but you don’t know for sure” which helps maintain friendship or at least collegiality with those who have written a negative referee report. You take away this ambiguity, and everyone will start refusing refereeing requests. Refereeing is hard already, there is really no need to risk collegial relationships as a result, especially in you are both going to be working the area for years or even decades to come.

(iii) Let’s pay the referees! This is similar but different from (ii). Think about it — the referees are hard to find, so we need to reward them. Everyone know that when you pay for something, everyone takes this more seriously, right? Ugh. I guess I have some new for you…

Think it over. You got a technical 30 page paper to referee. How much would you want to get paid? You start doing a mental calculation. Say, at a very modest $100/hr it would take you maybe 10-20 hours to write a thorough referee report. That’s $1-2K. Some people suggest $50/hr but that was before the current inflation. While I do my own share of refereeing, personally, I would charge more per hour as I can get paid better doing something else (say, teach our Summer school). For a traditional journal to pay this kind of money per paper is simply insane. Their budgets are are relatively small, let me spare you the details.

Now, who can afford that kind of money? Right — we are back to the open access journals who would pass the cost to the authors in the form of an APC. That’s when the story turn from bad to awful. For that kind of money the journals would want a positive referee report since rejected authors don’t pay. If you are not willing to play ball and give them a positive report, they will stop inviting you to referee, leading to more even corruption these journals have in the form of pay-to-publish.

You can probably imagine that this won’t end well. Just talk to medical or biological scientists who grudgingly pays to Nature or Science about 3K from their grants (which are much larger than ours). The pay because they have to, of course, and if they bulk they might not get a new grant setting back their career.

Double blind refereeing

In math, this means that the authors’ names are hidden from referees to avoid biases. The names are visible to the editors, obviously, to prevent “please referee your own paper” requests. The authors are allowed to post their papers on their websites or the arXiv, where it could be easily found by the title, so they don’t suffer from anxieties about their career or competitive pressures.

Now, in contrast with other “let’s improve the peer review” ideas, this is already happening. In other fields this has been happening for years. Closer to home, conferences in TCS have long resisted going double blind, but recently FOCS 2022, SODA 2023 and STOC 2023 all made the switch. Apparently they found Boaz Barak’s arguments unpersuasive. Well, good to know.

Even closer to home, a leading journal in my own area, Combinatorial Theory, turned double blind. This is not a happy turn of event, at least not from my perspective. I published 11 papers in JCTA, before the editorial board broke off and started CT. I have one paper accepted at CT which had to undergo the new double blind process. In total, this is 3 times as many as any other journal where I published. This was by far my favorite math journal.

Let’s hear from the journal why they did it (original emphasis):

The philosophy behind doubly anonymous refereeing is to reduce the effect of initial impressions and biases that may come from knowing the identity of authors. Our goal is to work together as a combinatorics community to select the most impactful, interesting, and well written mathematical papers within the scope of Combinatorial Theory.

Oh, sure. Terrific goal. I did not know my area has a bias problem (especially compared to many other areas), but of course how would I know?

Now, surely the journal didn’t think this change would be free? The editors must have compared pluses and minuses, and decided that on balance the benefits outweigh the cost, right? The journal is mum on that. If any serious discussion was conducted (as I was told), there is no public record of it. Here is what the journal says how the change is implemented:

As a referee, you are not disqualified to evaluate a paper if you think you know an author’s identity (unless you have a conflict of interest, such as being the author’s advisor or student). The journal asks you not to do additional research to identify the authors.

Right. So let me try to understand this. The referee is asked to make a decision whether to spend upwards of 10-20 hours on the basis of the first impression of the paper and without knowledge of the authors’ identity. They are asked not to google the authors’ names, but are ok if you do because they can’t enforce this ethical guideline anyway. So let’s think this over.

Double take on double blind

(1) The idea is so old in other sciences, there is plenty of research on its relative benefits. See e.g. here, there or there. From my cursory reading, it seems, there is a clear evidence of a persistent bias based on the reputation of educational institution. Other biases as well, to a lesser degree. This is beyond unfortunate. Collectively, we have to do better.

(2) Peer reviews have very different forms in different sciences. What works in some would not necessarily would work in others. For example, TCS conferences never really had a proper refereeing process. The referees are given 3 weeks to write an opinion of the paper based on the first 10 pages. They can read the proofs beyond the 10 pages, but don’t have to. They write “honest” opinions to the program committee (invisible to the authors) and whatever they think is “helpful” to the authors. Those of you outside of TCS can’t even imagine the quality and biases of these fully anonymous opinions. In recent years, the top conferences introduced the rebuttal stage which is probably helpful to avoid random superficial nitpicking at lengthy technical arguments.

In this large scale superficial setting with rapid turnover, the double blind refereeing is probably doing more good than bad by helping avoid biases. The authors who want to remain anonymous can simply not make their papers available for about three months between the submission and the decision dates. The conference submission date is a solid date stamp for them to stake the result, and three months are unlikely to make major change to their career prospects. OTOH, the authors who want to stake their reputation on the validity of their technical arguments (which are unlikely to be fully read by the referees) can put their papers on the arXiv. All in all, this seems reasonable and workable.

(3) The journal process is quite a bit longer than the conference, naturally. For example, our forthcoming CT paper was submitted on July 2, 2021 and accepted on November 3, 2022. That’s 16 months, exactly 490 days, or about 20 days per page, including the references. This is all completely normal and is nobody’s fault (definitely not the handling editor’s). In the meantime my junior coauthor applied for a job, was interviewed, got an offer, accepted and started a TT job. For this alone, it never crossed our mind not to put the paper on the arXiv right away.

Now, I have no doubt that the referee googled our paper simply because in our arguments we frequently refer our previous papers on the subject for which this was a sequel (er… actually we refer to some [CPP21a] and [CPP21b] papers). In such cases, if the referee knows that the paper under review is written by the same authors there is clearly more confidence that we are aware of the intricate parts of our own technical details from the previous paper. That’s a good thing.

Another good thing to have is the knowledge that our paper is surviving public scrutiny. Whenever issues arise we fix them, whenever some conjecture are proved or refuted, we update the paper. That’s a normal academic behavior no matter what Adam Mastroianni says. Our reputation and integrity is all we have, and one should make every effort to maintain it. But then the referee who has been procrastinating for a year can (and probably should) compare with the updated version. It’s the right thing to do.

Who wants to hide their name?

Now that I offered you some reasons why looking for paper authors is a good thing (at least in some cases), let’s look for negatives. Under what circumstances might the authors prefer to stay anonymous and not make their paper public on the arXiv?

(a) Junior researchers who are afraid their low status can reduce their chances to get accepted. Right, like graduate students. This will hurt them both mathematically and job wise. This is probably my biggest worry that CT is encouraging more such cases.

(b) Serial submitters and self-plagiarists. Some people write many hundreds of papers. They will definitely benefit from anonymity. The editors know who they are and that their “average paper” has few if any citations outside of self-citations. But they are in a bind — they have to be neutral arbiters and judge each new paper independently of the past. Who knows, maybe this new submission is really good? The referees have no such obligation. On the contrary, they are explicitly asked to make a judgement. But if they have no name to judge the paper by, what are they supposed to do?

Now, this whole anonymity thing is unlikely to help serial submitters at CT, assuming that the journal standards remain high. Their papers will be rejected and they will move on, submitting down the line until they find an obscure enough journal that will bite. If other, somewhat less selective journals adopt the double blind review practice, this could improve their chances, however.

For CT, the difference is that in the anonymous case the referees (and the editors) will spend quite a bit more time per paper. For example, when I know that the author is a junior researcher from a university with limited access to modern literature and senior experts, I go out of my way to write a detailed referee report to help the authors, suggest some literature they are missing or potential directions for their study. If this is a serial submitter, I don’t. What’s the point? I’ve tried this a few times, and got the very same paper from another journal next week. They wouldn’t even fix the typos that I pointed out, as if saying “who has the time for that?” This is where Mastroianni is right: why would their 234-th paper be any different from 233-rd?

(c) Cranks, fraudsters and scammers. The anonymity is their defense mechanism. Say, you google the author and it’s Dănuț Marcu, a serial plagiarist of 400+ math papers. Then you look for a paper he is plagiarizing from and if successful making efforts to ban him from your journal. But if the author is anonymous, you try to referee. There is a very good chance you will accept since he used to plagiarize good but old and somewhat obscure papers. So you see — the author’s identity matters!

Same with the occasional zero-knowledge (ZK) aspirational provers whom I profiled at the end of this blog post. If you are an expert in the area and know of somebody who has tried for years to solve a major conjecture producing one false or incomplete solution after another, what do you do when you see a new attempt? Now compare with what you do if this paper is by anonymous? Are you going to spend the same effort effort working out details of both papers? Wouldn’t in the case of a ZK prover you stop when you find a mistake in the proof of Lemma 2, while in the case of a genuine new effort try to work it out?

In summary: as I explained in my post above, it’s the right thing to do to judge people by their past work and their academic integrity. When authors are anonymous and cannot be found, the losers are the most vulnerable, while the winners are the nefarious characters. Those who do post their work on the arXiv come out about even.

Small changes can make a major difference

If you are still reading, you probably think I am completely 100% opposed to changes in peer review. That’s not true. I am only opposed to large changes. The stakes are just too high. We’ve been doing peer review for a long time. Over the decades we found a workable model. As I tried to explain above, even modest changes can be detrimental.

On the other hand, very small changes can be helpful if implemented gradually and slowly. This is what TCS did with their double blind review and their rebuttal process. They started experimenting with lesser known and low stakes conferences, and improved the process over the years. Eventually they worked out the kinks like COI and implemented the changes at top conferences. If you had to make changes, why would you start with a top journal in the area??

Let me give one more example of a well meaning but ultimately misguided effort to make a change. My former Lt. Governor Gavin Newsom once decided that MOOCs are the answer to education foes and is a way for CA to start giving $10K Bachelor’s degrees. The thinking was — let’s make a major change (a disruption!) to the old technology (teaching) in the style of Google, Uber and Theranos!

Lo and behold, California spent millions and went nowhere. Our collective teaching experience during COVID shows that this was not an accident or mismanagement. My current Governor, the very same Gavin Newsom, dropped this idea like a rock, limiting it to cosmetic changes. Note that this isn’t to say that online education is hopeless. In fact, see this old blog post where I offer some suggestions.

My modest proposal

The following suggestions are limited to pure math. Other fields and sciences are much too foreign for me to judge.

(i) Introduce a very clearly defined quick opinion window of about 3-4 weeks. The referees asked for quick opinions can either decline or agree within 48 hours. It will only take them about 10-20 minutes to make an opinion based on the introduction, so give them a week to respond with 1-2 paragraphs. Collect 2-3 quick opinions. If as an editor you feel you need more, you are probably biased against the paper or the area, and are fishing for a negative opinion to have “quick reject“. This is a bit similar to the way Nature, Science, etc. deal with their submissions.

(ii) Make quick opinion requests anonymous. Request the reviewers to assess how the paper fits the journal (better, worse, on point, best submitted to another area to journals X, Y or Z, etc.) Adopt the practice of returning these opinions to the authors. Proceed to the second stage by mutual agreement. This is a bit similar to TCS which has authors use the feedback from the conference makes decisions about the journal or other conference submissions.

(iii) If the paper is rejected or withdrawn after the quick opinion stage, adopt the practice to send quick opinions to another journal where the paper is resubmitted. Don’t communicate the names of the reviewers — if the new editor has no trust in the first editor’s qualifications, let them collect their own quick opinions. This would protect the reviewers from their names going to multiple journals thus making their names semi-public.

(iv) The most selective journals should require that the paper not be available on the web during the quick opinion stage, and violators be rejected without review. Anonymous for one — anonymous for all! The three week long delay is unlikely to hurt anybody, and the journal submission email confirmation should serve as a solid certificate of a priority if necessary. Some people will try to game the system like give a talk with the same title as the paper or write a blog post. Then it’s on editor’s discretion what to do.

(v) In the second (actual review) stage, the referees should get papers with authors’ names and proceed per usual practice.

Happy New Year everyone!

Are we united in anything?

Unity here, unity there, unity shmunity is everywhere. You just can’t avoid hearing about it. Every day, no matter the subject, somebody is going to call for it. Be it in Ukraine or Canada, Taiwan or Haiti, everyone is calling for unity. President Biden in his Inaugural Address called for it eight times by my count. So did former President Bush on every recent societal issue: here, there, everywhere. So did Obama and Reagan. I am sure just about every major US politician made the same call at some point. And why not? Like the “world peace“, the unity is assumed to be a universal good, or at least an inspirational if quickly forgettable goal.

Take the Beijing Olympic Games, which proudly claims that their motto “demonstrates unity and a collective effort” towards “the goal of pursuing world unity, peace and progress”. Come again? While The New York Times isn’t buying the whole “world unity” thing and calls the games “divisive” it still thinks that “Opening Ceremony [is] in Search of Unity.” Vox is also going there, claiming that the ceremony “emphasized peace, world unity, and the people around the world who have battled the pandemic.” So it sounds to me that despite all the politics, both Vox and the Times think that this mythical unity is something valuable, right? Well, ok, good to know…

Closer to home, you see the same themes said about the International Congress of Mathematicians to be held in St. Petersburg later this year. Here is Arkady Dvorkovich, co-chair of the Executive Organizing Committee and former Deputy Prime Minister of Russia: “It seems to us that Russia will be able to truly unite mathematicians from all over the world“. Huh? Are you sure? Unite in what exactly? Because even many Russian mathematicians are not on board with having the ICM in St. Petersburg. And among those from “all over the world”, quite a few are very openly boycotting the congress, so much that even the IMU started to worry. Doesn’t “unity” mean “for all”, as in ∀?

Unity of mathematics

Frequent readers of this blog can probably guess where I stand on the “unity”. Even in my own area of Combinatorics, I couldn’t find much of it at all. I openly mocked “the feeling of unity of mathematics” argument in favor of some conjectures. I tried but could never understand Noga Alon’s claim that “mathematics should be considered as one unit” other than a political statement by a former PC Chair of the 2006 ICM.

So, about this “unity of mathematics”. Like, really? All of mathematics? Quick, tell me what exactly do the Stochastic PDEs, Algebraic Number Theory, Enumerative Combinatorics and Biostatistics have in common? Anything comes to mind? Anything at all? Ugh. Let’s make another experiment. Say, I tell you that only two of these four areas have Fields medals. Can you guess which ones? Oh, you can? Really, it was that easy?? Doesn’t this cut against all of this alleged “unity”?

Anyway, let’s be serious. Mathematics is not a unit. It’s not even a “patterned tapestry” of connected threads. It’s a human endeavor. It’s an assorted collection of scientific pursuits unconstrained by physical experiments. Some of them are deep, some shallow, some are connected to others, and some are motivated by real world applications. You check the MSC 2020 classification, and there is everything under the sun, 224 pages in total. It’s preposterous to look for and expect to find some unity there. There is none to be found.

Let me put it differently. Take poetry. Like math, it’s a artistic endeavor. Poems are written by the people and for the people. To enjoy. To recall when in need or when in a mood. Like math papers. Now, can anyone keep a straight face and say “unity of poetry“? Of course not. If anything, it’s the opposite. In poetry, having a distinctive voice is celebrated. Diverse styles are lauded. New forms are created. Strong emotions are evoked. That’s the point. Why would math be any different then?

What exactly unites us?

Mathematicians, I mean. Not much, I suppose, to the contrary of math politicians’ claims:

I like to think that increasing breadth in research will help the mathematical sciences to recognize our essential unity. (Margaret Wright, SIAM President, 1996)

Huh? Isn’t this like saying that space exploration will help foster cross-cultural understanding? Sounds reasonable until you actually think about what is being said…

Even the style of doing research is completely different. Some prove theorems, some make heavy computer computations, some make physical experiments, etc. At the end, some write papers and put them on the arXiv, some write long books full of words (e.g. mathematical historians), some submit to competitive conferences (e.g. in theoretical computer science), some upload software packages and experimental evidence to some data depositary. It’s all different. Don’t be alarmed, this is normal.

In truth, very little unites us. Some mathematicians work at large state universities, others at small private liberal arts colleges with a completely different approach to teaching. Some have a great commitment to math education, some spend every waking hour doing research, while others enjoy frequent fishing trips thanks to tenure. Some go into university administration or math politics, while others become journal editors.

In truth, only two things unites us — giant math societies like the AMS and giant conferences like ICMs and joint AMS/MAA/SIAM meetings. Let’s treat them separately, but before we go there, let’s take a detour just to see what an honest unrestricted public discourse sounds like:

What to do about the Olympics

The answer depends on who you ask, obviously. And opinions are abound. I personally don’t care other than the unfortunate fact that 2028 Olympics will be hosted on my campus. But we in math should learn how to be critical, so here is a range of voices that I googled. Do with them as you please.

Some are sort of in favor:

I still believe the Olympics contribute a net benefit to humanity. (Beth Daley, The Conversation, Feb. 2018)

Some are positive if a little ambivalent:

The Games aren’t dead. Not by a longshot. But it’s worth noting that the reason they are alive has strikingly little to do with games, athletes or medals. (L. Jon Wertheim, Time, June 2021)

Some like The New York Times are highly critical, calling it “absurdity”. Some are blunt:

More and more, the international spectacle has become synonymous with overspending, corruption, and autocratic regimes. (Yasmeen Serhan, The Atlantic, Aug. 2021)

yet unwilling to make the leap and call it quits. Others are less shy:

You can’t reform the Olympics. The Olympics are showing us what they are, and what they’ve always been. (Gia Lappe and Jonny Coleman, Jacobin, July 2021)

and

Boil down all the sanctimonious drivel about how edifying the games are, and you’re left with the unavoidable truth: The Olympics wreck lives. (Natalie Shure, The New Republic, July 2021)

What is the ICM

Well, it’s a giant collective effort. A very old tradition. Medals are distributed. Lots of talks. Speakers are told that it’s an honor to be chosen. Universities issue press releases. Yes, like this one. Rich countries set up and give away travel grants. Poor countries scramble to pay for participants. The host country gets dubious PR benefits. A week after it’s over everyone forgets it ever happened. Life goes on.

I went to just one ICM, in Rio in 2018. It was an honor to be invited. But the experience was decidedly mixed. The speakers were terrific mathematicians, all of them. Many were good speakers. A few were dreadful in both content and style. Some figured they are giving talks in their research seminar rather than to a general audience, so I left a couple of such talks in middle. Many talks in parallel sections were not even recorded. What a shame!

The crowds were stupefying. I saw a lot of faces. Some were friendly, of people I hadn’t seen in years, sometimes 20 years. Some were people I knew only by name. It was nice to say hello, to shake their hand. But there were thousands more. Literally. An ocean of people. I was drowning. This was the worst place for an introvert.

While there, I asked a lot of people how did they like the ICM. Some were electrified by the experience and had a decent enough time. Some looked like fish out of the water — when asked they just stared at me incomprehensively silently saying “What are you, an idiot?” Some told me they just went to the opening ceremony and left for the beach for the rest of the ICM. Assaf Naor said that he loved everything. I was so amused by that, I asked if I could quote him. “Yes,” he said, “you can quote me: I loved absolutely every bit of the ICM”. Here we go — not everyone is an introvert.

Whatever happened at the ICM

Unlike the Olympics, math people tend to be shy in their ICM criticism. In his somewhat unfortunately titled but otherwise useful historical book “Mathematicians of the World, Unite!” the author, Guillermo Curbera, largely stays exuberant about the subject. He does mention some critical stories, like this one:

Charlotte Angas Scott reported bluntly on the presentation of papers in the congress, which in her opinion were “usually shockingly bad” since “instead of speaking to the audience, [the lecturer] reads his paper to himself in a monotone that is sometimes hurried, sometimes hesitating, and frequently bored . . . so that he is often tedious and incomprehensible.” (Paris 1900 Chapter, p. 24)

Curbera does mention in passing that the were some controversies: Grothendieck refused to attend ICM Moscow in 1966 for political reasons, Margulis and Novikov were not allowed by the Soviet Union to leave the country to receive their Fields medals. Well, nobody’s perfect, right?

Most reports I found on the web are highly positive. Read, for example, Gil Kalai’s blog posts on the ICM 2018. Everything was great, right? Even Doron Zeilberger, not known for holding his tongue, is mostly positive (about the ICM Beijing in 2002). He does suggest that the invited speakers “should go to a ‘training camp‘” for some sort of teacher training re-education, apparently not seeing the irony, or simply under impression of all those great things in Beijing.

The only (highly controversial) criticism that I found was from Ulf Persson who starts with:

The congresses are by now considered to be monstrous affairs very different from the original intimate gatherings where group pictures could be taken.

He then continues to talk about various personal inconveniences, his misimpressions about the ICM setting, the culture, the city, etc., all in a somewhat insensitive and rather disparaging manner. Apparently, this criticism and misimpressions earned a major smackdown from Marcelo Viana, the ICM 2018 Organizing Committee Chair, who wrote that this was a “piece of bigotry” by somebody who is “poorly informed”. Fair enough. I agree with that and with the EMS President Volker Mehrmann who wrote in the same EMS newsletter that the article was “very counterproductive”. Sure. But an oversized 4 page reaction to an opinion article in a math newsletter from another continent seem indicative that the big boss hates criticism. Because we need all that “unity”, right?

Anyway, don’t hold your breath to see anything critical about the ICM St. Petersburg later this year. Clearly, everything is going to be just fantastic, nothing controversial about it. Right…

What to do about the ICM

Stop having them in the current form. It’s the 21st century, and we are starting the third year of the pandemic. All talks can be moved online so that everyone can watch them either as they happen, or later on YouTube. Let me note that I’ve sat in the bleachers of these makeshift 1000+ people convention center auditoriums where the LaTeX formulas are barely visible. This is what the view is like:

Note that the ICM is not like a sports event — there is literally nothing at stake. Also, there are usually no questions afterwards anyway. You are all better off watching the talks later on your laptop, perhaps even on a x1.5 speed. To get the idea, imagine watching this talk in a huge room full of people…. Even better, we can also spread out these online lectures across the time zones so that people from different countries can participate. Something like this World Relay in Combinatorics.

Really, all that CO₂ burned to get humans halfway across the world to seat in a crowded space is not doing anyone any good. If the Nobel Prizes can be awarded remotely, so can the Fields medals. Tourism value aside, the amount of meaningful person-to-person interaction is so minimal in a large crowd, I am struggling to find a single good reason at all to have these extravaganzas in-person.

What to do about the AMS

I am not a member of any math societies so it’s not my place to tell them what to do. As a frequent contributor to AMS journals and a former editor of one of them, I did call on the AMS to separate its society business form the publishing, but given that their business model hinges on the books and journals they sell, this is unlikely. Still, let me make some quick observations which might be helpful.

The AMS is clearly getting less and less popular. I couldn’t find the exact membership numbers, but their “dues and outreach” earnings have been flat for a while. Things are clearly not going in the right direction, so much that the current AMS President Ruth Charney sent out a survey earlier this week asking people like me why do we not want to join.

People seem to realize that they have many different views on all thing math related and are seeking associations which are a better fit. One notable example is the Just Mathematics Collective which has several notable boycott initiatives. Another is the Association for Mathematical Research formed following various controversies. Note that there is a great deal of disagreements between these two, see e.g. here, there and there.

I feel these are very good developments. It’s healthy to express disagreements on issues you consider important. And while I disagree with other things in the article below, I do agree with this basic premise:

Totalitarian countries have unity. Democratic republics have disagreement. (Kevin Williamson, Against Unity, National Review, Jan. 2021)

So everyone just chill. Enjoy diverse views and opinions. Disagree with the others. And think twice before you call for “unity” of anything, or praise the ephemeral “unity of mathematics”. There is none.

It could have been worse! Academic lessons of 2020

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!

Take an interview!

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

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

The art of autobiographies

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

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

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

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

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

Why an interview?

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

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

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

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

How to do an interview?

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

Examples

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

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

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

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

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

Final thoughts

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

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

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

P.S. (Added Dec 3, 2020) At my urging, Bruce Rothschild has typed up a brief “History of Combinatorics at UCLA“. I only added hyperlinks to it, to clarify the personalities Bruce is talking about (thus, all link mistakes are mine).

P.P.S. (Added Feb 6, 2021) At my request, the editors of ECA clarified their interview process (as of today, they have posted nine of them). Their interviews are conducted over email and are essentially replies to the nearly identical sets of questions. The responses are edited for clarity and undergo several rounds of approval by the interviewee. This practice is short of what one would traditionally describe as a journalistic interview (e.g., there are no uncomfortable questions), and is more akin to writing a puff piece. Still, we strongly support this initiative by the ECA as the first systematic effort to put combinatorialists on record. Hopefully, with passage of time others types of interviews will also emerge from various sources.

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

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

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

You should watch combinatorics videos!

Here is my collection of links to Combinatorics videos, which I assembled over the years, and recently decided to publish.  In the past few years the number of videos just exploded.  We clearly live in a new era.  This post is about how to handle the transition.

What is this new collection?

I selected over 400 videos of lectures and seminars in Combinatorics, which I thought might be of interest to a general audience.  I tried to cover a large number of areas both within Combinatorics and related fields.  I have seen many (but not all!) of the talks, and think highly of them.  Sometimes I haven’t seen the video, but have heard this talk “live” at the same or a different venue, or read the paper, etc.  I tried to be impartial in my selection, but I am sure there is some bias towards some of my favorite speakers.

The collection includes multiple lectures by Noga Alon, Persi Diaconis, Gil Kalai, Don Knuth, László Lovász, János Pach, Vic Reiner, Paul Seymour, Richard Stanley, Terry Tao, Xavier Viennot, Avi Wigderson, Doron Zeilberger, and many many others. Occasionally the speakers were filmed giving similar talks at different institutions, so I included quick links to those as well so the viewer can choose.

Typically, these videos are from some workshops or public lecture series.  Most are hosted on the institution websites, but a few are on YouTube or Vimeo (some of these are broken into several parts).  The earliest video is from 1992 and the most recent video was made a few days ago.   Almost all videos are from the US or Canada, with a few recent additions from Europe.  I also added links to a few introductory lectures and graduate courses on the bottom of the page.

Why now?

Until a couple of years ago, the videos were made only at a few conference centers such as Banff, MSRI and IAS.  The choice was sparse and the videos were easy to find.  The opposite is true now, on both counts.  The number of recorded lectures in all areas is in tens of thousands, they are spread across the globe, and navigating is near impossible unless you know exactly what you are looking for.  In fact, there are so many videos I really struggled with the choice of which to include (and also with which of them qualify as Combinatorics).  I am not sure I can maintain the collection in the future – it’s already getting too big.  Hopefully, some new technology will come along (see below), but for now this will do.

Why Combinatorics?

That’s what I do.  I try to think of the area as broad as possible, and apologize in advance if I omitted a few things.  For the subarea division, I used as a basis my own Wikipedia entry for Combinatorics (weirdly, you can listen to it now in a robotic voice).  The content and the historical approach within sub-areas is motivated by my views here on what exactly is Combinatorics.

Why should you start watching videos now?

First, because you can.  One of the best things about being in academia is the ability (in fact, necessity) to learn.  You can’t possibly follow everything what happens in all fields of mathematics and even all areas of combinatorics.  Many conferences are specialized and the same people tend to meet a year after year, with few opportunities for outsiders to learn what’s new over there.  Well, now you can.  Just scroll down the list and (hopefully) be amazed at the number of classical works (i.e. over 5 y.o.) you never heard of, the variety of recent developments and connections to other fields.  So don’t just watch people in your area from workshops you missed for some reason.  Explore other areas!  You might be surprised to see some new ideas even on your favorite combinatorial objects.  And if you like what you see, you can follow the links to see other videos from the same workshops, or search for more videos by the same speaker…

Second, you should start watching because it’s a very different experience.  You already know this, of course.  One can pause videos, go back and forward, save the video to watch it again, or stop watching it right in the beginning.  This ability is to popular, Adam Sandler even made an awful movie about it…  On the other hand, the traditional model of lecture attendance is where you either listen intently trying to understand in real time and take notes, or are bored out your mind but can’t really leave.  It still has its advantages, but clearly is not always superior.  Let me elaborate on this below.

How to watch videos?

This might seem like a silly question, but give me a chance to suggest a few ideas…

0) Prepare for the lecture.  Make sure to have enough uninterrupted time.  Lock the door.  Turn off the cell phone.  Download and save the video (see below).  Download and save the slides.  Search for them if they are not on the lecture website (some people put them on their home pages).  Never delete anything – store the video on an external hard drive if you are running out of space.  Trust me, you never know when you might need it again, and the space is cheap anyway…

Some years ago I made a mistake by not saving Gil Kalai’s video of a talk titled “Results and Problems around Borsuk’s Conjecture”.  I found it very inspiring — it’s the only talk I referenced it in my book.  Well, apparently, in its infinite wisdom, PIMS lost the video and now only the audio is available, which is nearly useless for a blackboard talk.  What a shame!

1) Use 2 devices.  Have the video on a big screen, say, a large laptop or a TV hooked to your  laptop.  If the TV is too far, use a wireless mouse to operate a laptop from across the room or something like a Google stick to project from a far.  Then, have the slides of the talk opened on your tablet if you like taking computer notes or just like scrolling by hand gestures, or on your other laptop if you don’t.  The slides are almost universally in .pdf and most software including the Adobe Reader allows to take notes straight in the file.

Another reason to have slides opened is the inability for some camera people to understand what needs to be filmed.  This is especially severe if they just love to show the unusual academic personalities, or are used to filming humanities lectures where people read at the podium.  As a result, occasionally, you see them pointing a camera to a slide full of formulas for 2 seconds (and out of focus), and then going back for 2 minutes filming a speaker who is animatedly pointing to the screen (now invisible), explaining the math.  Ugh…

2) If the subject is familiar and you feel bored with the lengthy introduction, scroll the slides until you see something new.  This will give you a hint to where you should go forward in the video.  And if you did miss some definition you can pause the video and scroll the slides to read it.

3) If there are no slides, or you want to know some details which the speaker is purposefully omitting, pause the video and download the paper.  I do this routinely while listening to talks, but many people are too shy to do this out of misplaced fear that others might think they are not paying attention.  Well, there is no one to judge you now.

4) If you are the kind of person who likes to ask questions to clarify things, you still can.  Pause the video and search the web for the answer.  If you don’t find it, ask a colleague by skype, sms, chat, email, whatever.  If everything fails – write to the speaker.  She or he might just tell you, but don’t be surprised if they also ignore your email…

5) If you know others who might be interested in the video lecture, just make it happen.  For example, you can organize a weekly seminar where you and your graduate students watch the lectures you choose (when you have no other speakers).  If students have questions, pause the video and try to answer them.  In principle, if you have a good audience the speaker may agree to answer the questions for 5-10 min over skype, after you are done watching.  Obviously, I’ve never seen this happen (too much coordination?).  But why not try this – I bet if you ask nicely many speakers would agree to this.

6) If you already know a lot about the subject, haven’t been following it recently but want to get an update, consider binge watching.  Pick the most recent lecture series and just let it run when you do house shores or ride a subway.  When things get interesting, you will know to drop everything and start paying attention.

Why should you agree to be videotaped?

Because the audience is ready to see your talks now.  Think of this as another way of reaching out with your math to a suddenly much broader mathematical community (remember the “broad impact” section on your NSF grant proposal?).  Let me just say that there is nothing to fear – nobody is expecting you to have acting skills, or cares that you have a terrible haircut.  But if you make a little effort towards giving a good talk, your math will get across and you might make new friends.

Personally, I am extremely uncomfortable being videotaped – the mere knowledge of the camera filming makes me very nervous.  However I gradually (and grudgingly) concluded that this is now a part of the job, and I have to learn how to do this well.  Unfortunately, I am not there yet…

Yes, I realize that many traditionalists will object that “something will be missing” when you start aiming at giving good video talks at the expense of local audience.  But the world is changing if hasn’t changed already and you can’t stop the tide.  This happened before, many times.  For example, at some point all the big Hollywood studios have discovered that they can make movies simpler and make a great deal more money overseas to compensate for the loss in the US market.  They are completely hooked now, and no matter what critics say this global strategy is likely irreversible.  Of course, this leaves a room for a niche market (say, low budget art-house movies), but let’s not continue with this analogy.

How to give video lectures?

Most people do nothing special.  Just business as usual, hook up the mike and hope it doesn’t distort your voice too bad.  That’s a mistake.  Let me give a number of suggestions based mostly on watching many bad talks.  Of course, the advice for giving regular talks apply here as well.

0) Find out ahead of time if you get filmed and where the camera is.  During the lecture, don’t run around; try to stand still in full view of the camera and point to the screen with your hands.  Be animated, but without sudden moves.  Don’t use a laser pointer.  Don’t suddenly raise your voice.  Don’t appeal to the previous talks at the same workshop.  Don’t appeal to people in the audience – the camera can rarely capture what they say or do.  If you are asked a question, quickly summarize it so the viewer knows what question you are answering.  Don’t make silly off-the-cuff jokes (this is a hard one).

1) Think carefully whether you want to give a blackboard or a computer talk.  This is crucial.  If it’s a blackboard talk, make sure your handwriting is clear and most importantly BIG.  The cameras are usually in the very back and your handwriting won’t be legible otherwise.  Unless you are speaking the Fields Institute whose technology allows one to zoom into the high resolution video, nobody might be able to see what you write.  Same goes for handwritten slides unless they are very neat, done on a laptop, and the program allows you to increase their size.  Also, the blackboard management becomes a difficult issue.  You should think through what results/definitions should stay on the blackboard visible to the camera at all times and what can be safely deleted or lifted up if the blackboard allows that.

2) If it’s a computer talk, stick to your decision and make a lot of effort to have the slides look good.  Remember, people will be downloading them…  Also, make every effort NOT to answer questions on a blackboard next to the screen.  The lightning never works – the rooms are usually dimmed for a computer talk and no one ever thinks of turning the lights on just for 30 seconds when you explain something.  So make sure to include all your definition, examples, etc, in the slides.  If you don’t want to show some of them – in PowerPoint there is a way to hide them and pull them up only if someone asks to clarify something.  I often prepare the answers to some standard questions in the invisible part of my slides (such as “What happens for other root systems?” or “Do your results generalize to higher dimensions?”), sometimes to unintended comedic effect.  Anyhow, think this through.

3) Don’t give the same videotaped talk twice.  If you do give two or more talks on the same paper, make some substantial changes.  Take Rota’s advice: “Relate to your audience”…  If it’s a colloquium talk, make a broad accessible survey and include your results at the end.  Or, if it’s a workshop talk, try to make an effort to explain most proof ideas, etc.  Make sure to have long self-explanatory talk titles to indicate which talk is which.  Follow the book industry lead for creating subtitles.  For example use “My most recent solution of the Riemann hypothesis, an introduction for graduate students” or “The Pythagorean theorem: How to apply it to the Langlands Program and Quantum Field Theory”.

4) Download and host your own videos on your website alongside your slides and your relevant paper(s), or at least make clear links to them from your website.  You can’s trust anyone to keep your files.  Some would argue that re-posting them on YouTube will then suffice.  There are two issues here.  First, this is rarely legal (see below).  Second, as I mentioned above, many viewers would want to have a copy of the file.  Hopefully, in the future there will be a copyright-free arXiv-style video hosting site for academics (see my predictions below).

5) In the future, we would probably need to consider having a general rule about adding a file with errata and clarifications to your talk, especially if something you said is not exactly correct, or even just to indicate, post-factum, whether all these conjectures you mentioned have been resolved and which way.  The viewers would want to know.

For example, my student pointed out to me that in my recent Banff talk, one of my lemmas is imprecise.  Since the paper is already available, this is not a problem, but if it wasn’t this could lead to a serious confusion.

6) Watch other people’s videos.  Pay attention to what they do best.  Then watch your own videos.  I know, it’s painful.  Turn off the sound perhaps.  Still, this might help you to correct the worst errors.

7) For advanced lecturers – try to play with the format.  Of course, the videos allow you to do things you couldn’t do before (like embedding links to papers and other talks, inserting some Java demonstration clips, etc.), but I am talking about something different.  You can turn the lecture into an artistic performance, like this amazing lecture by Xavier Viennot.  Not everyone has the ability or can afford to do this, but having it recorded can make it worthwhile, perhaps.

Know your rights

There are some delicate legal issues when dealing with videos, with laws varying in different states in the US (and in other countries, of course).  I am not an expert on any of this and will write only as I understand them in the US.  Please add a comment on this post if you think I got any of this wrong.

1) Some YouTube videos of math lectures look like they have been shut by a phone.  I usually don’t link to those.  As I understand the law on this, anyone can film a public event for his/her own consumption.  However, you and the institution own the copyright so the YouTube posting is illegal without both of yours explicit permission (written and signed).  You can fight this by sending a “cease and desist” letter to the person who posted the video, but contacting YouTube directly might be more efficient – they have a large legal department to sort these issues.

2) You are typically asked to sign away your rights before your talk.  If an institution forgot to do this, you can ask to take your talk down for whatever reason.  However, even if you did sign the paper you can still do this – I doubt the institution will fight you on this just to avoid bad publicity.  A single email to the IT department should suffice.

3) If the file with your talk is posted, it is (obviously) legal for you to download it, but not to post it on your website or repost elsewhere such as YouTube or WordPress.  As far as I am concerned, you should go ahead and post it on your university website anyway (but not on YT or WP!).  Many authors typically post all their papers on their website even if they don’t own a copyright on them (which is the case or virtually all papers before 2000).  I am one of them.  The publishers just concluded that this is the cost of doing business – if they start going after people like us, the authors can revolt.  The same with math videos.  The institutions probably won’t have a problem with your university website posting as long as you acknowledge the source.  But involving a third party creates a host of legal problems since these internet companies are making money out of the videos they don’t own a copyright for.  Stay away from this.

4)  You can the edit the video by using numerous software, some of which is free to download.  Your can remove the outside noise, make the slides sharper, everything brighter, etc.  I wouldn’t post a heavily edited video when someone else owns a copyright, but a minor editing as above is ok I think.

5) If the institution’s website does not allow to download the video but has a streaming option (typically, the Adobe Flash or HTML5), you can still legally save it on your computer, but this depends on what software you choose.  There are plenty of software which capture the video being played on your computer and save it in a file.  These are 100% legal.  Other websites play the videos on their computers and allow you to download afterwards.  This is probably legal at the institutions, but a gray area at YouTube or Vimeo which have terms of service these companies may be violating.  Just remember – such videos can only be legal for personal consumption.  Also, the quality of such recording is typically poor – having the original file is much better.

What will happen in the future?

Yes, I will be making some predictions.  Not anything interesting like Gian-Carlo Rota’s effort I recently analyzed, but still…

1) Watching and giving video lectures will become a norm for everyone.  The ethical standards will develop that everyone gets to have the files of videos they made.  Soon enough there will be established some large well organized searchable (and not-for-profit!) math video depositories arXiv-style where you can submit your video and link to it from your website and where others can download from.  Right now companies like DropBox allow you to do this, but it’s for-profit (your have to pay extra for space), and it obviously needs a front like the arXiv.  This would quickly make my collection a thing of the past.

2) Good math videos will become a “work product”, just like papers and books.  It is just another venue to communicate your results and ideas.  People will start working harder on them.  They will become a standard item on CVs, grant applications, job promotions, etc.  More and more people will start referencing them just like I’ve done with Kalai’s talk.  Hopefully part 1) will happen soon enough so all talks get standard and stable links.

3) The video services will become ubiquitous.  First, all conference centers will acquire advanced equipment in the style of the Banff Center which is voice directed and requires no professional involvement except perhaps at the editing stage.  Yes, I am thinking of you, MFO.  A new library is great, but the talks you could have recorded there are priceless – it’s time to embrace the 21st century….

Second, more and more university rooms will be equipped with the cameras, etc.  UCLA already has a few large rooms like that (which is how we make the lamely named BruinCasts), but in time many department will have several such rooms to hold seminars.  The storage space is not an issue, but the labor cost, equipment and the broadband are.  Still, I give it a decade or two…

4) Watching and showing math videos will become a standard part of the research and graduate education.  Ignore the doomsayers who proclaim that this will supplant the traditional teaching (hopefully, not in our lifetime), but it’s clear already there are unexplored educational benefits from this.  This should be of great benefit especially to people in remote locations who don’t have access to such lectures otherwise.  Just like the Wikipedia has done before, this will even the playing field and help the talent to emerge from unlikely places.  If all goes well, maybe the mathematics will survive after all…

Happy watching everyone!