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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.

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    $\begingroup$ I think this question may be closed as a duplicate, although I think it is a reasonable question. See here for the previous question along these lines, along with some good answers before it was closed as too opinion-based. $\endgroup$
    – Alec Rhea
    Commented Apr 4, 2021 at 23:28
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    $\begingroup$ you can email your competitors to ask for citations... $\endgroup$
    – AlexArvanitakis
    Commented Apr 5, 2021 at 1:30
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    $\begingroup$ I find this an odd question. Since mathematicians are confronted with discouragement or failure 99.9% of the time, it’s success that many of us are less comfortable with. $\endgroup$
    – Deane Yang
    Commented Apr 5, 2021 at 2:16
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    $\begingroup$ Assuming that this was a personal question, I hope you soon find the motivation you are seeking despite the question being closed. This article might be of interest for you: Emotional Perils of Mathematics. By the way, the question should have been CW (are you familiar with the term?) $\endgroup$
    – polfosol
    Commented Apr 5, 2021 at 8:05
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    $\begingroup$ en.wikipedia.org/wiki/Valery_Fabrikant $\endgroup$
    – Ben McKay
    Commented Apr 5, 2021 at 9:06

2 Answers 2

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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.

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    $\begingroup$ 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 en.wikipedia.org/wiki/… 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. $\endgroup$
    – Landauer
    Commented Apr 5, 2021 at 3:32
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    $\begingroup$ 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... $\endgroup$
    – მამუკა ჯიბლაძე
    Commented Apr 5, 2021 at 6:36
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    $\begingroup$ @მამუკაჯიბლაძე Let one thousand flowers bloom! $\endgroup$
    – Alec Rhea
    Commented Apr 5, 2021 at 9:45
  • $\begingroup$ @მამუკაჯიბლაძე Beautifully said Mamuka! $\endgroup$
    – André Henriques
    Commented Apr 6, 2021 at 21:02
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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.

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    $\begingroup$ Very well put, I'm still smiling writing this comment. +1 $\endgroup$
    – Alec Rhea
    Commented Apr 5, 2021 at 4:58
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    $\begingroup$ But I’m a teetotaller! $\endgroup$
    – Alexander Campbell
    Commented Apr 5, 2021 at 4:59
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    $\begingroup$ what if you don't / barely make a living? $\endgroup$
    – erz
    Commented Apr 5, 2021 at 5:39
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    $\begingroup$ 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) $\endgroup$
    – erz
    Commented Apr 5, 2021 at 5:52
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    $\begingroup$ @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. $\endgroup$
    – Hailong Dao
    Commented Apr 5, 2021 at 6:11

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