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The Covid-19 pandemic has changed our work-lives in ways few of us could have anticipated. These exceptional circumstances have forced each one of us and each one of our institutions to adapt, sometimes in creative ways. I would like to compile a list of those changes and adaptations at all levels of the mathematical ecosystem (all the way from the lives of math undergrads to the working of national funding bodies).

For each entry, please discuss the advantages and disadvantages of the new setup, compared to the previous way of doing things. Be as specific as possible.

Where relevant, please discuss issues of accessibility of events/resources to people who would otherwise have less access to them, and issues of climate change (less traveling means fewer emissions).

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    $\begingroup$ I hope that this will remain open; I have put a question at meta.mathoverflow.net/questions/5047 in case people want to discuss that. $\endgroup$ May 28 at 9:21
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    $\begingroup$ This seems both too broad and subjective and argumentative, unfortunately. "Please discuss" questions usually are not a good fit on a platform like MO. Even though I find the question interesting, I don't think this is the right place for it. $\endgroup$ May 28 at 11:23
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    $\begingroup$ @FrancescoPolizzi "A single return flight from London to New York contributes to almost a quarter of an average UK citizen’s annual carbon emissions": tinyurl.com/yce7aud5 (internet usage is not discussed in the linked article – that very fact is probably an indication that its impact on the climate is significantly smaller) $\endgroup$ May 28 at 15:11
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    $\begingroup$ I agree with the closure: there's not enough specific to research mathematics here -- and asking about "the lives of math undergrads" is outside the scope of MathOverflow. $\endgroup$
    – Matt F.
    May 28 at 16:28
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    $\begingroup$ I really wonder about these theoretical open-close-discussions. Have a look at the answers so far. They are very useful and interesting, not just to mathematicians but to everyone who is interested how mathematics is changing right now. It is a (so far) unique point in history, and here professional mathematicians document what is changing in their area. I think it's great. $\endgroup$ May 31 at 13:31

10 Answers 10

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Online seminars

Research (and other) seminars have gone virtual. The obvious advantage is, that anyone can attend from basically all over the world. The page https://researchseminars.org/ compiles a huge list of talks and you may visit some mathematical talk basically all around the clock. A further advantage is that no travelling is involved, so speakers are much more flexible. Moreover, the virtual format makes it very simple to record the talk and make it available afterwards.

Among the disadvantages is the missing personal contact and possibilities for one-on-one discussion. Also, virtual seminars do not serve as meeting points for groups and departments as much as classical seminars do.

The additional ability to have public and private chats during the talk is at least different to classical talks, but I am not sure if chats provide an advantage or disadvantage.

My personal conclusion is, that virtual seminars are here to stay, but that classical seminars will come back as well and both are going to exist in parallel.

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    $\begingroup$ And now everyone is using Zoom which appeared out of nowhere and originally had very bad security issues. $\endgroup$ May 28 at 9:40
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    $\begingroup$ Well, I don't (most of the time…). Our university provides self-hosted BigBlueButton conference rooms which I find very nice (tbh, superior to Zoom…). But in general, I wanted to keep technology out of the answer - it changes fast and I expect that technical solutions will be quite different in a few years from now. $\endgroup$
    – Dirk
    May 28 at 10:16
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    $\begingroup$ So what will happen? Probably everyone will ensure that their seminar rooms have good cameras and microphones and (perhaps multiple) projectors. All seminars will be streamed and recorded. Live audiences will be smaller but nonzero. Virtual audiences for the best seminars will be larger. Speakers will be invited to visit in person; some will choose to do that, but others will present by video, which will be projected in the seminar room. Very few people will travel to seminars that are not at their home institution. Travel budgets will be partly redirected to equipment. Anything else? $\endgroup$ May 28 at 10:16
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    $\begingroup$ @LSpice I'd be interested to see the distribution of attitudes in different institutions. Certainly in my university there is a strong push from the Vice-Chancellor etc that we should learn as many new lessons as possible and "not let a good crisis go to waste". $\endgroup$ May 28 at 16:04
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    $\begingroup$ I hope virtual seminars continue alongside traditional seminars when this is all over (although I am not a huge fan of Zoom). $\endgroup$ May 28 at 20:02
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Here's something almost trivial:

Writing on a tablet instead of a piece of paper

I think many mathematicians probably acquired a tablet (e.g. something with its own screen like an iPad, or the kind without a screen that plugs into your computer like a Wacom - forgive me for using brand names here) for the first time as a result of the pandemic, in order to simulate the 'chalkboard' teaching experience online.

Now, many of us have the opportunity to continue writing our not-fully-formed mathematical thoughts on a tablet, as opposed to say on a physical notebook that we were using before.

There are pluses and minuses. The pluses are that it's nice to have a systemic and organized record on your computer of various mathematical thoughts you've been exploring, and it's easier to edit notes on the computer. The one big minus I can think of is that I still find it slightly slower to write on a tablet than with a pen and paper.

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  • $\begingroup$ I still cannot write quickly and tidily on a tablet. I was much happier with paper and a visualiser, though I had to write extra software to get the visualiser snapshots on the web in semi-real time and organise them in a structured way. $\endgroup$ May 28 at 15:48
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    $\begingroup$ For me a related change has been learning to make do with pdfs rather than printouts of papers, which after the adjustment period has definitely been a net positive, even ignoring paper waste. $\endgroup$
    – Meow
    May 28 at 21:15
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    $\begingroup$ The latest generation of tablets and styluses (e.g., the iPad Pro + Apple Pencil 2 or the reMarkable 2) really are very good, to the point that someone used to writing with a fountain pen on paper can adjust with surprisingly little frustration. $\endgroup$ May 30 at 13:23
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    $\begingroup$ Yep, this did force me to learn to write on a tablet, and now, reviewing papers / grading is much more convenient. $\endgroup$ May 31 at 7:55
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    $\begingroup$ @NeilStrickland look into matte screen protectors. The bellemond made a world of difference for me. $\endgroup$
    – Andrea
    May 31 at 12:14
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Professional cheating

For me the biggest change in dealing with the pandemic professionally was organized and professional cheating. Of course cheating is nothing new but when I first started in this businesses my impression was that a few bad apples cheated and I could usually detect it because some student had an incredibly silly incoherent answer that is copied word for word by a student sitting next to them.

Over the years it became clear that students could get their homework answered by finding solution keys or by question and answer sites and so I started making homework only worth a token amount of points.

But I honestly had been unaware of the truly professional cheating opportunities now available until online testing began during the pandemic without proctoring. I was also shocked by the percentage of students willing to cheat given the opportunity to do so. All my exam questions would appear and be answered during the exam on sites like Chegg, Course Hero and Slader. A student just has to send a photo of their exam question and they get a photo of a complete solution back in 5-40 minutes. While the solutions are not always correct they are semi-professional. Also I discovered students used group chats like Discord and Whatsapp to share their answers, either obtained from the above websites or via a divide and conquer scheme. In one of my exams a student I caught cheating informed me that 90% of my students were cheating on Discord often with fake names so they could not be identified. This matches 90% of students using an answer identical to Chegg using a different method than we did in class or in the book. Most students register for these sites with fake names and emails or use somebody else's account so even launching an investigation with the site is not very effective at catching people. On timed exams where students got the questions in random order and could not return to a question I found students took 50 minutes to answer the first question and once the solutions became available on Chegg answered the remaining questions in no time flat.

While in person exams will resolve some of this, I now will have to carefully check students do not have phones when they go for bathroom breaks or disallow them and I don't think I will give take-home exams again.

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    $\begingroup$ This resonates with me, for reasons I am not sure I am "allowed" to mention <waves at my university HR and at the whole Student Satisfaction Apparatus in UKHE> but to some extent I wonder if the pandemic merely crystallized a longer-term trend: increasingly students believe that the point of assessment is "pass to the next level of the game" and that the definition of understanding is "knowing how to look up online how to do it" (these are not specific to mathematics education) $\endgroup$
    – Yemon Choi
    May 30 at 15:01
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    $\begingroup$ @YemonChoi, what bothers me is not so much looking something up on Wikipedia. Even MSE usually requires the asker to engage with the answerer and understand something and requires typing the question of you hope to he an answer. But Chegg and it's compatriots that give immediate answers to obvious exam questions (sometimes it the photo the student sends clearly states the time remaining and that they cannot return to the question) and the immediate sharing of answers between students on group chats really irks me. I honestly felt bad for students who did badly honestly. $\endgroup$ May 30 at 15:23
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    $\begingroup$ When I taught a fully online class last fall, I noticed that some of my students were posting my exam questions to Chegg etc. as well. It made a bad year feel even worse. I don't know of any good solution. $\endgroup$ May 30 at 16:23
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    $\begingroup$ Well, there certainly still are some (indeed many!) students who have great academic merit and fully master the material in their courses. If even 5% of students achieve good understanding, this will easily be enough to staff chegg and the like. A single chegg post requires only one answer, but can help hundreds of students cheat. $\endgroup$ May 30 at 20:42
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    $\begingroup$ It's not just universities any more that Chegg is giving trouble now. $\endgroup$ May 31 at 8:23
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Automated assessment

In Sheffield we have increased our use of online automated assessment. We used to use a home-grown system, but have now switched to STACK with some home-grown extensions. Various other systems are available (e.g. WebWork, Numbas) but in my opinion STACK is significantly more intelligent and more able to give meaningful feedback to students based on detailed analysis of mathematical properties of their answers (provided that you put in the work to code that analysis). While the use of such systems is certainly not new, I am aware of a number of places that have significantly increased their engagement in the last year, and my guess is that the momentum will be sustained.

We have a large dataset from the last academic year consisting answers provided by students, feedback given in response, and answers modified in the light of that feedback. I am hoping to do some extensive analysis of this dataset over the summer, and it will be interesting to see what we can learn.

We have also made some initial attempts to assess and provide feedback on student attempts to write proofs. In most cases we provide a pool of phrases, from which they can select a subset and arrange them in appropriate order. I hope to do this much more extensively next year.

(In terms of social justice etc, I also helped a friend at the University of Nairobi to set up STACK there. It's easy to become blasé about working on a server in Kenya by ssh from the UK, but it is quite astonishing when you think about it.)

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Prerecorded lectures

Many universities have been forced to give their lectures online. Some students seem to prefer physical lectures, and some online lectures.

Overwhelmingly the biggest (potential) long-term advantage is that there now exist entire degrees' worth of prerecorded lectures, many times over. This has the possibility to give a meteoric rise to the scale of maths accessibility and outreach.

However, as far as I can tell most of these lectures are currently sitting behind university login pages, and I suspect that the main reason is basically institutional inertia/a prisoners' dilemma situation. If a few universities' lecture recordings were released, this would probably make others less reticent to release theirs, and cause a culture shift. Note that the same thing happened a while ago with lecture notes.

Needless to say if nothing happens and the recordings are just deleted in a couple of years, it will have been a collosal missed opportunity.

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    $\begingroup$ I think that a lot of professors are hesitant to release COVID-19 lecture videos simply because they were put together in an unexpected pandemic crunch, so they aren't up to the standards that the professor feels comfortable having the general public viewing and judging them. Many of us had never recorded, let alone edited, a video a year ago. $\endgroup$ May 28 at 14:30
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    $\begingroup$ Of course, but I feel like the conclusion is the same, except that professors should naturally be allowed to opt out. In Europe there have been 4 or 5 semesters of lockdown by now, so I imagine that a fair number would be happy with the quality of their more recent courses. $\endgroup$
    – Meow
    May 28 at 17:11
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    $\begingroup$ By my count it's the third online semester. On a different note, I have all my (live) lectures freely available online even though they contain errors and glitches. Everybody knows under what circumstances they have been produced... $\endgroup$
    – Dirk
    May 28 at 18:37
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    $\begingroup$ "biggest (potential) long-term advantage" from the viewpoint of the administration and students. From faculty's viewpoint, I've created my replacement. Even if I'm kept around for research and teaching new/non-recorded classes, there is a big loss of leverage. $\endgroup$
    – Hasse1987
    May 28 at 21:15
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    $\begingroup$ Another reason for them to be not published publically is that it can incur significant cost to make such lectures ADA compliant. I believe some number of years ago Berkeley pulled freely available online lectures for this reason. I am of course not trying to bad mouth the ADA, just saying that making the lectures freely available is not as simple as removing a password from some page. $\endgroup$
    – Mark
    May 30 at 22:20
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I am not a mathematics professional or a student, but rather a lay person with a great interest in math. Personally, my available time to consume mathematics literature, lectures, and video content has increased. I suspect this is true for millions of lay mathematicians. If true, that could lead to:

  • An increased interest in the field
  • More math content consumed, which could lead to
  • More advertising dollars spent on math content, which could ultimately bring
  • More funding into the field

And increased funding can change any field.

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Flexible work hours

With a physical workplace, and commuting, work hours are standardized. Now, my work hours are divided into two blocks, one block in the evening after kids are asleep. This allows me to be more flexible when it comes to collaboration with different time zones.

Starting collaborations with people far away is now less of a mental hurdle (this last month, I have discussed research with people from at least 5 different countries on three different continents).

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Lightboard

I build a lightboard at home last summer in order to give my classes (this was inspired by Ivo Vekemans - here's an example of him lecturing). I recorded three whole classes so far, and a bunch of seminar talks. Here's a talk of mine. Overall, I'm very happy with the setup.

Advantage: The result is really beautiful to watch.

Disadvantages: The lightboard + recording equipment uses up a whole room in my house. Also, it's a bit time-consuming to clean the board (if you don't clean it well, it leaves lots of shiny smudges). This makes it essentially impossible to give live talks on it.

This youtube video compares two different types of markers for lightboards, including how they erase. (Btw, to erase, just use a dry cotton cloth – certainly no window-cleaning products.)

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  • $\begingroup$ Looks awesome! Sorry for the stupid question, but does this mean you have to write everything mirrored when recording? Or do you just mirror the recording in the edit? $\endgroup$ May 31 at 13:50
  • $\begingroup$ @MartinBrandenburg. The software does the reflection for me. But some people use a physical mirror to do the reflection. $\endgroup$ May 31 at 15:30
  • $\begingroup$ I bought a Vileda WindoMatic Power Window Vacuum Cleaner. That works quite well to clean the board quickly and effectively - you can use a wet cloth and be quite generous with water and then suck it up with the vacuum cleaner. It doesn't take much longer than cleaning a blackboard in the ordinary way. $\endgroup$ Jun 1 at 8:27
  • $\begingroup$ Hi André, glad to see you've been able to add this answer after all! The videos are great, and this technique (which I hadn't seen before) is certainly worth popularization $\endgroup$ Jun 4 at 5:59
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Lives of undergrads

There's an interesting discussion here which provides some insights into the issues faced by math undergrads: https://old.reddit.com/r/math/comments/nnc1v3/changes_forced_by_the_pandemic/

Here are a couple of excerpts which I found interesting:

For reasons I can't fathom, it was decided that the content should go in pre-recorded lectures the students would have to watch on their own time, but that there would still be the same number of contact hours, which would be given over to either examples, going over the lecture notes that were published and which we were told to read, or just repeating the exact same content as in the videos. This has killed me.

And here's another one:

"The material in the exams will be similar to other years and should only take the participant 3 hours to complete" This is what we were told in our 24 hours exams (last year we had 48 hour exams for exceptionally easy exams). What the board of examiners managed to produce this year is unfathomable. Almost every student in every department ended up taking at a Minimum 18 hours if not more and some even spent the whole 23-24 hours to complete these exams. [...] we had questions never before seen, and extraordinaryily difficult some taking up to 5 pages to write up. Not only did we have to answer these tough questions but we had to make sure it was all neat as well since we had 24 hours so sloppy presentation would not have been acceptable. I was up for hours at end grasping at straws. Out of 500 student who talk a pole 80% spent over 16hours.

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    $\begingroup$ Speaking as someone from the opposite end: 1) the wonderful nature of UKHE means that, erm, the university gets to dictate how you teach and examine 2) in that second excerpt it is claimed that "It would have been impossible to finish that exam in 3 hours even for the lecturers" $\endgroup$
    – Yemon Choi
    May 30 at 14:34
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Interactive virtual poster sessions

In this video, Joel Rosenfeld conpares his experience at two different online conferences.

► He describes the fist conference as disappointing because he wasn't able to establish any of the connections that he had hoped to be able to establish through the workshop. In his words:

Speakers come, give their talk, and then "poof", they're gone.

► He then proceeds to discuss another online conference that he attended, with special attention to a certain poster session that was organised in a particularly creative way. He calls it "that spatial chat thing" (I don't know the official name). It's really hard to describe the setup using words, so I won't describe it here${}^\dagger$ and thus force you to you watch Joel Rosenfeld's video. He says:

I initially thought that this virtual setting was absolutely ludicrous.

But later, he says:

It turned out to be a lot closer to a regular poster session than I had anticipated. Being able to isolate yourself from the rest of the room and talk to somebody made a huge difference as far as having one-on-one conversations.

And finally:

Honestly, it was surprisingly effective. [...] At first, I thought this was a circus. [...] It was better than most of the other conferences I've been to. [...] This added a whole degree of interactivity and engagement that I didn't really think was going to be possible.


${}^\dagger$If someone could edit my answer to include the official name of "that spatial chat thing", it would be great.
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    $\begingroup$ I guess the official name is actually SpatialChat, at least that website seems to have a product very much like what he describes. Another somewhat similar concept is gather.town. $\endgroup$ May 31 at 17:31
  • $\begingroup$ @MartinHairer Haha! That's funny :) Thanks for the clarification. $\endgroup$ May 31 at 18:34
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    $\begingroup$ In the last year or so I have participated in online meetings that used gather.town and wonder.me . I expect there will be other 'spatial chat things' beyond these too. (Of course it's not the same as face to face mingling, but I think it's still much better than the first type of conference mentioned.) $\endgroup$ Jun 4 at 6:07

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