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It could have been worse! Academic lessons of 2020

December 20, 2020 4 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!

What if math dies?

April 7, 2019 2 comments

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

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

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

The worst idea I’ve heard in a while

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

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

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

The inanity of it all

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

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

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

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

Economics matters

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

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

Can’t we just ignore these people?

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

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

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

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

Predictable apocalypse

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

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

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

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

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

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

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

Final message:

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

You should watch combinatorics videos!

May 2, 2015 4 comments

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! 

Grading Gian-Carlo Rota’s predictions

November 27, 2014 4 comments

In this post I will try to evaluate Gian-Carlo Rota‘s predictions on the future of Combinatorics that he made in this 1969 article.  He did surprisingly well, but I am a tough grader and possibly biased about some of the predictions.  Judge for yourself…

It’s tough to make predictions, especially about the future

It is a truth universally acknowledged that humans are very interested in predicting the future. They do this incessantly, compiling the lists of the best and the worst, and in general can’t get enough of them. People tend to forget wrong predictions (unless they are outrageously wrong).  This allows a person to make the same improbable predictions over and over and over and over again, making news every time.  There are even professional prognosticators who make a living writing about the future of life and technology.  Sometimes these predictions are rather interesting (see here and there), but even the best ones are more often wrong than right…

Although rarely done, analyzing past predictions is a useful exercise, for example as a clue to the truthiness of the modern day oracles.  Of course, one can argue that many of the political or technology predictions linked above are either random or self-serving, and thus not worth careful investigation. On the other hand, as we will see below, Rota’s predictions are remarkably earnest and sometimes even brave.  And the fact that they were made so long ago makes them uniquely attractive, practically begging to be studied.

Now, it has been 45 years since Rota’s article, basically an eternity in the life span of Combinatorics. There, Rota describes Combinatorics as “the least developed branches of mathematics“. A quick review of the last few quotes on this list I assembled shows how much things have changed. Basically, the area moved from an ad hoc collection of problems to a 360-degree panorama of rapidly growing subareas, each of which with its own deep theoretical results, classical benchmarks, advanced tools and exciting open problems. This makes grading rather difficult, as it suggests that even random old predictions are likely to be true – just about anything people worked on back in the 1960 has been advanced by now. Thus, before turning to Rota, let’s agree on the grading scale.

Grading on a curve

To give you the feel for my curve, I will use the celebrated example of the 1899-1901 postcards in the En L’An 2000 French series, which range from insightful to utter nonsense (click on the titles to view the postcards, all available from Wikimedia).

Electric train.  Absolutely.  These were introduced only in 1940s and have been further developed in France among other countries.  Note the aerodynamic shape of the engine.  Grade:  A.

Correspondance cinema.  Both the (silent) cinema and phonograph were invented by 1900; the sound came to movie theaters only in 1927.  So the invention here is of a home theater for movies with sound.  Great prediction although not overly ambitious. Grade:  A-.

  Military cyclists.  While bicycle infantry was already introduced in France by 1900, military use of motorcycles came much later.  The idea is natural, but some designs of bikes from WW2 are remarkably similar.  Some points are lost due to the lack of widespread popularity in 2000.  Grade: B+.

  Electric scrubbing.  This is an electric appliance for floor cleaning.  Well, they do exist, sort of, obviously based on different principles.  In part due to the modern day popularity, this is solid prediction anyway.  Grade:  B.

 Auto-rollers.  Roller skates have been invented in 18th century and by 1900 became popular.  So no credit for the design, but extra credit for believing in the future of the mean of transportation now dominated by rollerblades. Thus the author’s invention is in the category of “motorized personal footwear”. In that case the corresponding modern invention is of the electric skateboard which has only recently become available, post-2000 and yet to become very popular. Grade: B-.

Barber.  The author imagines a barber operating machinery which shaves and cuts customer’s hair.   The design is so ridiculous (and awfully dangerous), it’s a good thing this never came about.  There are however electric shavers and hair cutters which are designed very differently.  Grade:  C.

•  Air cup.  The Wright brothers’ planes had similar designs, so no credit again.  The author assumes that personal air travel will become commonplace, and at low speeds and heights.  This is almost completely false.  However, unfortunately, and hopefully only very occasionally, some pilots do enjoy one for the road.  Grade:  D.

 Race in Pacific.  The author imagines that the public spectacle of horse racing will move underwater and become some kind of fish racing.  Ridiculous.  Also a complete failure to envision modern popularity of auto racing which already began in Paris in 1887.  Grade:  F.

Rota’s predictions on combinatorial problems:

In his paper, Rota writes:

Fortunately, most combinatorial problems can be stated in everyday language. To give an idea of the present state of the field, we have selected a few of the many problems that are now being actively worked upon.

We take each of these “problems” as a kind of predictions of where the field is going.  Here are my (biased and possibly uninformed) grades for each problem he mentions.

1)  The Ising Problem.  I think it is fair to say that since 1969 combinatorics made no contribution in this direction.  While physicists and probabilists continue studying this problem, there is no exact solution in dimension 3 and higher.  Grade: F.

2)  Percolation Theory.  The study of percolation completely exploded since 1969 and is now a subject of numerous articles in both probability, statistical physics and combinatorics, as well as several research monographs.  One connection is given by an observation that p-percolation on a complete graph Kn gives the Erdős–Rényi random graph model. Even I accidentally wrote a few papers on the subject some years ago (see one, two and three).  Grade: A.

3)  The Number of Necklaces, and Polya’s Problem.  Taken literally, the necklaces do come up in combinatorics of words and free Lie algebra, but this context was mentioned by Rota already. As far as I can tell, there are various natural (and interesting) generalizations of necklaces, but none surprising.  Of course, if the cyclic/dihedral group action here is replaced by other actions, e.g. the symmetric group, then modern developments are abundant.  But I think it’s a reach too far, since Rota knew the works of Young, MacMahon, Schur and others but does not mention any of it.  Similarly, Polya’s theorem used to be included in all major combinatorics textbooks (and is included now, occasionally), but is rarely taught these days.  Simply put, the g.f. implications haven’t proved useful.  Grade: D.

4)  Self-avoiding Walk. Despite strong interest, until recently there were very few results in the two-dimensional case (some remarkable results were obtained in higher dimensions). While the recent breakthrough results (see here and there) do use some interesting combinatorics, the authors’ motivation comes from probability. Combinatorialists did of course contribute to the study of somewhat related questions on enumeration of various classes of polyomino (which can be viewed as self-avoiding cycles in the grid, see e.g. here).  Grade: C.

5)  The Traveling Salesman Problem. This is a fundamental problem in optimization theory, connected to the study of Hamiltonian cycles in Graph Theory and numerous other areas. It is also one of the earliest NP-hard problems still playing a benchmark role in Theoretical Computer Science. No quick of summary of the progress in the past 45 years would give it justice. Note that Rota’s paper was written before the notions of NP-completeness. In this light, his emphasis on algorithmic complexity and allusions to Computability Theory (e.g. unsolvable problems) are most prescient.  So are his briefly mentioned connections to topology which are currently a popular topic.  Well done!  Grade: A+.

6)  The Coloring Problem.  This was a popular topic way before Rota’s article (inspired by the Four Color Theorem, the chromatic polynomial, etc.), and continues to be even more so, with truly remarkable advances in multiple directions.  Note Rota’s mentioning of matroids which may seem extraneous here at first, but in fact absolutely relevant indeed (in part due to Rota’s then-ongoing effort).  Very good but unsurprising prediction.  Grade: A-.

7)  The Pigeonhole Principle and Ramsey’s Theorem. The Extremal Graph Theory was about to explode in many directions, with the the Erdős-Stone-Simonovits theorem proved just a few years earlier and the Szemerédi regularity lemma a few years later.  Still, Rota never mentions Paul Erdős and his collaborators, nor any of these results, nor potential directions.  What a missed opportunity!  Grade: B+.

Rota’s predictions on combinatorial areas:

In the concluding section “The Coming Explosion”, Rota sets this up as follows:

Before concluding this brief survey, we shall list the main subjects in which current work in combinatorial theory is being done.

Here is a list and more of my comments.

1)  Enumerative Analysis.  Sure.  But this was an easy prediction to make given the ongoing effort by Carlitz, Polya, Riordan, Rota himself and many other peope.  Grade: A-.

2)  Finite Geometries and Block Designs.  The subject was already popular and it did continue to develop but perhaps at a different pace and directions than Rota anticipated (Hadamard matrices, tools from Number Theory).  In fact, a lot of later work was connection with with Group Theory (including some applications of CFSG which was an ongoing project) and in Coding Theory (as Rota predicted).  Grade: B-.

3)  Applications to Logic.  Rota gives a one-sentence desctiption:

The development of decision theory has forced logicians to make wide use of combinatorial methods.

There are various important connections between Logic and Combinatorics, for example in Descriptive Set Theory (see e.g. here or more recent work by my future UCLA colleague there).  Note however, that Infinitary Combinatorics was already under development, after the Erdős-Rado theorem (1956).  Another very interesting and more recent connection is to Model Theory (see e.g. here).  But the best interpretation here I can think of here are the numerous applications to Game Theory, which already existed (Nash’s equilibrium theorem is from 1950) and was under rapid development.  Either way, Rota was too vague in this case to be given much credit.  Grade: C.

4)  Statistical Mechanics.   He mentions the Ising model again and insists on “close connections with number theory”.  One can argue this all to be too vague or misdirected, but the area does indeed explode in part in the directions of problems Rota mentions earlier. So I am inclined to give him benefit of the doubt on this one. Grade: A-.

The final grade

In total, Rota clearly got more things right than wrong.  He displayed an occasional clairvoyance, had some very clever insights into the future, but also a few flops.  Note also the near complete lack of self-serving predictions, such as the Umbral Calculus that Rota was very fond of.  Since predictions are hard, successes have a great weight than failures.  I would give a final grade somewhere between A- and B+ depending on how far into the future do we think he was making the predictions.  Overall, good job, Gian-Carlo!

P.S.  Full disclosure:  I took a few advanced classes with Gian-Carlo Rota as a graduate student cross registering from Harvard to MIT, and he may have graded my homeworks (this was in 1994-1996 academic years).  I don’t recall the final grades, but I think they were good.  Eventually Rota wrote me a letter of recommendation for a postdoc position.

UPDATE (October 16, 2019)

I would still give a failing grade for Race in Pacific.   But having seen The Aquaman, the similarities are too eerie to ignore, so this prediction needs an upgrade.  Say, D-.