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All professional mathematicians feel discouraged occasionally due to some issue.

My question is:

How do professional mathematicians deal with discouragement?

In this link , Andrew Wiles say that I would go out for a walk. I'd often walk down by the lake. Walking has a very good effect in that you're in this state of relaxation.

A_S
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jasmine
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2 Answers2

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Pour yourself a beer and reflect on how crazy it is that 1) modern life actually needs knowledge about stuff like "elliptic curves over finite fields" and 2) you are lucky enough to make a living thinking and teaching about them. Works for me every time.

Hailong Dao
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  • I wish I could upvote this twice! – Nik Weaver Apr 05 '21 at 04:39
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    Very well put, I'm still smiling writing this comment. +1 – Alec Rhea Apr 05 '21 at 04:58
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    But I’m a teetotaller! – Alexander Campbell Apr 05 '21 at 04:59
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    what if you don't / barely make a living? – erz Apr 05 '21 at 05:39
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    @erz: sure, mathematicians are not rich. But even graduate students and researchers from many traditionally poor countries can at least support themselves nowadays. How many people can do that 100 years ago? – Hailong Dao Apr 05 '21 at 05:44
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    it's not about being rich, my point is that if your basic needs are met it is not hard to deal with discouragement of not proving the theorem you were aiming at; it's a different thing when every day you don't know if you should continue the struggle or leave mathematics altogether (due to purely career reasons) – erz Apr 05 '21 at 05:52
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    @erz: yes, unfortunately there are still too many talented people who have had to leave research math because getting a decent professional position is not possible. I know quite a few of them. Which is why I think the "survivors" should feel very lucky indeed. On the other hand most of them land on their feet and get very decent work in industry which may still utilize the math skills they have. – Hailong Dao Apr 05 '21 at 06:11
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    @erz If this question occurs to you at all, you should leave immediately. Most of those which continue, they do it because they cannot quit no matter what. This also includes, for example, some very rich people with lots of free time. – მამუკა ჯიბლაძე Apr 05 '21 at 07:20
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    @erz In contrast to მამუკა ჯიბლაძე's comment, I don't think it is necessary to leave mathematics if you have career-related doubts. Some people see mathematics as a "this is absolutely my life's path", others see it as "just a job", and I think both types, and many others, should be welcomed. If circumstances make it too difficult to continue for now, we as a community should try our best to leave doors open for your possible return. – S. Carnahan Apr 06 '21 at 17:20
  • @S.Carnahan i think my comment was misunderstood: I was referring to the case when a mathematician is of the first type, but it is impossible for them to carry on, due to career reasons. I guess "career reasons" is the misleading bit: by this i mean lack of a job or a constant fear of not having a job – erz Apr 06 '21 at 19:17
  • @მამუკაჯიბლაძე but that's the thing: very rich people with lots of free time can afford that – erz Apr 06 '21 at 19:19
  • @erz I just gave an example; there surely are examples of opposite nature, and many in between. – მამუკა ჯიბლაძე Apr 06 '21 at 19:22
  • @მამუკაჯიბლაძე but then i don't understand your point. Mine is that it can be simultaneously impossible to leave and to stay, and not clear what to do with this contradiction. If one is very rich, then this contradiction does not come up. There is also Perelman's way, but it does not apply to lower-mid-tier mathematicians – erz Apr 06 '21 at 19:45
  • @erz No matter whether you are rich or poor, it is by definition impossible to simultaneously do two things that contradict each other. For Perelman, I strongly suspect that he continues to work quite intensely. As well as for Ramanujan, I strongly suspect that if Hardy would just throw out his first letter, he would continue to work as intensely as before (and maybe live much longer and do much more). – მამუკა ჯიბლაძე Apr 08 '21 at 07:24
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It helps me to remember that none of this stuff really matters.

That might sound discouraging at first; why do something if it doesn't matter? Because nothing really matters, and we have to occupy our time!

I was intentionally provocative in the presentation of the above idea, but in a more moderate tone it would probably read something like 'if mathematics makes you happy, do it because it makes you happy and forget the rest', or 'do it because it makes you happy and remember that we are all very small in a very big universe'.

It is somewhat Absurd to pursue challenging tasks in an indifferent universe, but while we're here we should occupy our time with things we find interesting and which bring joy to us and others -- we must imagine Sisyphus happy. Mathematical research is somewhat intrinsically difficult, but for most people who ultimately pursue it the labor is one of love, and a source of limitless wonderment and joy (or wonder and joy with limits if you work in category theory/calculus ;).

All of this is to say, don't sweat the small stuff. Pursue the things you find fascinating, and what will be will be -- que sera sera. (I find that good music helps too.)

After reading this answer before posting, it occurrs to me that none of the content of this message is specific to mathematics in the sense that we could swap out the word 'mathematics' for any other challenging pursuit and the same point would stand. I've flagged the question to be converted to CW (community wiki) by a moderator and would like to wait to post this answer until that happens, but I'm posting it now because I've waited an hour after flagging and would like to post it and go to sleep.

Alec Rhea
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    I fully agree. It is important to understand that 99.9% of mathematics that is today on the arxiv is completely irrelevant to any human being who is not a mathematician. Just go through the list of recent fields medalists and ask yourself whether their work had any impact on human beings outside their respective field and then compare this to https://en.wikipedia.org/wiki/List_of_Nobel_laureates_in_Physiology_or_Medicine So if you get your result into Acta Mathematica or you do not have any result at all, it really does not matter that much in the end. – Landauer Apr 05 '21 at 03:32
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    I fully disagree. Everything that happens, matters. At every moment of our lives, anything we might do, matters. It is like, say, a drummer in an orchestra that sits there for two hours only to contribute three drumbeats somewhere in the middle of the performance. If he becomes bored and walks away, that particular performance will be flawed. Sisyphos matters, each of his steps matters. All those unfortunates hooked on RH, all of their attempts - matter. It is all part of an incredibly enormous and beautiful performance. We cannot enjoy it all the time, after all we have to sleep, but... – მამუკა ჯიბლაძე Apr 05 '21 at 06:36
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    @მამუკაჯიბლაძე Let one thousand flowers bloom! – Alec Rhea Apr 05 '21 at 09:45
  • @მამუკაჯიბლაძე Beautifully said Mamuka! – André Henriques Apr 06 '21 at 21:02