I think it would be appropriate to make this question CW...

It is likely that this question will not survive here on MO for long, but I do hope that the community gives it a chance. I also hope to get answers that might help others feeling unmotivated, but in general not discouraged.

Among mathematicians, especially the young bunch (postdocs and beginning tenure track), among many causes for lack of productivity, two seem to stand out most often: discouragement and lack of motivation, or the combination of both. I in particular fix attention on those mathematicians who otherwise are (would be) very productive -- an assertion made plausible perhaps by their previous contributions. I would go as far as to say that many, if not most, of us know of at least one such example.

There are many possible reasons for discouragement, many of which have been discussed elsewhere (I do not intend to give specific references, especially since what I have in mind are such sources as blogs and discussion forms on the internet, including MO). Examples of such reasons are family arrangements, low salary, high stress (publish or perish kind), difficult personal relations with other members of the department, and other (or, very often, any combination of the above).

Let us assume that discouragement is not the problem, but lack of motivation is. Namely, assume our young mathematician is tormented by questions such as:

Who needs this? What is this all good for? (i.e. lack of immediate, appreciable feedback).

There are many mathematicians far stronger than me contributing significantly to the field; what is my work good for? (self-deprecation)

Would I be happier doing a nine-to-five job, getting my six figures, and living a simple, earthly life? Why am I even concerned with all this abstract nonsense? (resentment, retreat)

I don't necessarily have a problem with academia. In fact, I like being in academia. Maybe I should change fields, but I feel I am now so deep into math, that changing now might actually hurt my career. Besides, I know nothing about other fields, and it would take me some time just to get up to speed. What should I do?

I hope my colleagues do not find out about how I feel, as this is rather embarrassing; however, carrying on with my duties (especially research) is becoming more and more difficult. Should I share my feelings with anyone?

My question is, what would you say if the said imaginary mathematician was your colleague and a close enough friend to come and share her feelings with you?

closed as primarily opinion-based by Will Jagy, Steven Landsburg, Lucia, Karl Schwede, abx Aug 21 '14 at 5:09

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    Are you sure the discouragement and lack of motivation are the causes and not the effects of lack of productivity? – guest Aug 20 '14 at 22:45
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    @guest: This is a good point. Often the other way around (as you are pointing out) is the case. In this case, I'd like to focus on exactly what is written in the question (but I would welcome a discussion on the converse). – vic Aug 20 '14 at 22:46
  • this question will be closed before five minutes either way – guest Aug 20 '14 at 22:47
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    I advise my friends as my friends. I don't see the point in attempting to offer "agony aunt" advice from a distance without any knowledge of the underlying causes or motives – Yemon Choi Aug 20 '14 at 23:03
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    For what it's worth, academia.stackexchange.com has dealt with many, many questions similar to this. If those answers don't satisfy you, you could consider a new question there, but keep in mind that we at Academia.SE are not agony aunts either. – Nate Eldredge Aug 21 '14 at 2:47

There was a panel session on the future of algebraic topology at the birthday conference for Gunnar Carlsson, Ralph Cohen, and Ib Madsen. At the beginning of the panel, Bill Dwyer raised the point that most of us are never going to do work that will be remembered hundreds of years hence by future mathematicians, and largely will be read by a small circle of our peers. Rather than despairing at this fact, he compared this work to "making a nice dinner for your friends," an intrinsically worthwhile and rewarding task. That is, being a part of this community and doing the work that we do is often its own reward.

Not a perfect answer by any means, but one that I find more honest and compelling as time goes by.

Anyone feeling they have lost their motivation might take a look at Surely You're Joking, Mr. Feynman! In the chapter where he starts teaching at Cornell, just after the war, he talks about feeling burned out and incapable of producing anything valuable. His solution was to adopt an attitude of not caring about the value of his work and just approach it as something to have fun with (and this worked out pretty well for him).

There is also this quote from Stephen Hawking that I have found personally inspiring:

Before my condition was diagnosed, I had been very bored with life. There had not seemed to be anything worth doing. But shortly after I came out of the hospital, I dreamed that I was going to be executed. I suddenly realized that there were a lot of worthwhile things I could do if I was reprieved.

Alain de Botton, The Pleasures and Sorrows of Work (Random House LLC, 2010):

"When does a job feel meaningful? Whenever it allows us to generate delight or reduce suffering in others. Though we are often taught to think of ourselves as inherently selfish, the longing to act meaningfully in our work seems just as stubborn a part of our make-up as our appetite for status or money."

  • I have just read a few pages of the book on google books, and my first impression is that recommendation of this book as an answer to some of the questions that our mathematician is asking herself, is a good answer. – vic Aug 20 '14 at 23:26

To say "be honest" may clarify or debunk some commodification or over-hype-ing or iconicization issues that can cloud one's thinking... and apparently increase the distance between "work" and "reality".

Reminding oneself of the apparent human tendency to iconify... can be helpful in discounting the weight of the icons. :)

Asking "what is/was the prior issue?"... as opposed to asking what is "publishable".

Similarly "What is the real confusion/unknown/difficulty...?", as opposed to "what are the questions raised "in the literature".

"The literature" is, in effect, the best that we can do (if we do also nowadays include on-line things, IMHO), but, at the same time, it is "not canon", insofar as it is ... only the best we can do.

That is, one's demotivation due to observing hypocrisy or pointless chatter passing for "research" should not be allowed to be a distraction for genuine issue. Easier said than done, sure, especially when one thinks in terms of tenure or salary increases and so on. But, if one can suspend those concerns, the corrupting of commodification explains many things (as in most human enterprises where people need to make a living).

The far subtler question of whether, apart from the discrepancy between hype and daily life, one simply doesn't care about working on mathematics... well, yes, it's awkward when one has committed a part of one's life to it and changes one's mind.

Conceivably... the ugliness of the commodification may have soured one's feelings... and, conceivably, once recognized, that could be discounted... thus "saving" one's interest in the original thing-itself...

  • Please tell me whether I understand this correctly. Are you saying that there is the essence of mathematics, and there is mathematics, with its many manifestations, uses and practices in the context of our everyday reality, and the two are essentially different? Thus mathematics as a profession, and as a "state of mind", a pure art of sorts, are fundamentally different, even incompatible notions? And mixing the two might lead to the uncomfortable state of mind that the OP's colleague seems to be in? If so, how would you advice to separate the two notions in one's mind? – user39719 Aug 21 '14 at 3:18
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    @William, yes, in various possible wordings, there are two different things, or at least two different extremes on a spectrum, and accidentally trying (in one's mind) to make them be the same thing surely creates stress of several sorts. At the very least, one can try to remind oneself that, for example, there's "the art/science of mathematics", and then there's "the business of mathematics". – paul garrett Aug 21 '14 at 12:41

Let me focus on the first couple of objections (what is my work good for, given that there are many mathematicians far stronger than me). My answer is: your young colleague's activity is good and useful, at least in a weak, yet meaningful sense. Even if one thinks that at last, only the work of the geniuses counts, what is still debatable, he should agree that geniuses stem from the mass of workers, and that great discoveries rest on a great number of easy examples. Archimedes or Gauss grew up in societies were the average maths culture was very high. The same happens in sport: there has been Pele, because virtually every kid in every village of Brazil plays soccer.

There is no scientific society with isolated geniuses: it's a myth usually spread by those governments who want to cut research funding. As I see it, if one is able to do a honest cultural work, and to enjoy it, should do it with no hesitation. It has a great civil value, in a word were a lot of people instead dedicate themselves to drug trade, finance, politics, pornography, war.

It is psychologically much easier to work on a problem jointly with another mathematician. It doesn't have to be a face-to-face interaction, although it is preferable.

Feed your ego: biographies of nine-to-five engineers seldom appear in Wikipedia.

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    I cannot argue to the contrary, but I do not have enough statistical data to affirm that there are fewer nine-to-five engineers (or anyone else for that matter) in Wikipedia than (nine-to-five or otherwise) mathematicians. The truth of the matter is that very few people ever make contributions of fundamental importance, engineer, mathematician, or anyone else. – vic Aug 20 '14 at 22:44
  • You are probably right. Both my undergrad and PhD advisors are in wikipedia; none of my engineering co-workers whom I directly interacted with in 5 different companies are; however the sample is rather small. On the other hand, the major purpose of a career in fundamental science is to make important contributions, and if after, say, 5 years it appears that one cannot do that perhaps a career in application of the learnt science would be an appropriate choice. – Michael Aug 20 '14 at 23:10
  • By an important contribution, do you mean one worthy of a Wikipedia article, or one that is recognized by the peers as an important contribution? If it is the the latter, then it is more difficult to quantify (e.g. many consider a paper accepted to a respectable journal to be an important contribution, yet there are overwhelmingly more such papers than fundamental contributions recognized by, say, the Fields medal or other noticeable awards). In general, I think a contribution is difficult to quantify at a level finer than just "fundamental" and "interesting" (the latter is a huge class). – vic Aug 20 '14 at 23:14
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    Also a rather mixed bag to "appear in Wikipedia"... :) – paul garrett Aug 20 '14 at 23:17
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    Some time ago, I looked up the CEOs of $5$ of the $10$ largest companies on Wikipedia. $4$ out of $5$ had engineering degrees, the last had a degree in agricultural economics. – Douglas Zare Aug 21 '14 at 0:01

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