Mathematics is not terribly individual

From Oswald Veblen’s opening address to the 1950 ICM:

Mathematics is terribly individual.  Any mathematical act, whether of creation or apprehension, takes place in the deepest recesses of the individual mind.  Mathematical thoughts must nevertheless be communicated to other individuals and assimilated into the body of general knowledge.  Otherwise they can hardly be said to exist.  By the time it becomes necessary to raise one’s voice in a large hall some of the best mathematicians I know are simply horrified and remain silent…

The solution will not be to give up international mathematical meetings and organizations altogether, for there is a deep human instinct that brings them about.  Every human being feels the need of belonging to some sort of a group of people with whom he has common interests.  Otherwise he becomes lonely, irresolute, and ineffective.  The more one is a mathematician the more one tends to be unfit or unwilling to play a part in normal social groups.  In most cases that I have observed, this is a necessary, though definitely not a sufficient, condition for doing mathematics.”

This view of mathematics and mathematicians is deeply alien to me.  I experience mathematics as thoroughly communal.  Does this reflect a change in mathematical practice in the last 60 years, or just a difference in temperament between Ozzie and me?


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21 thoughts on “Mathematics is not terribly individual

  1. Jon Awbrey says:

    I think he’s just throwing out sops to Cerberus.

    Cerberus being three-headed naturally requires throwing sops in several directions.

    That is why he seems to be speaking out of all three sides of his mouth, I guess.

    Nevertheless, I think it remains to be admitted that there are real tensions here, between the personal intimation and the public explication of mathematics.

  2. Jon Awbrey says:

    Compare with the following sentiment by Robert Musil —

    The well-known capacity that thoughts have — as doctors have discovered — for dissolving and dispersing those hard lumps of deep, ingrowing, morbidly entangled conflict that arise out of gloomy regions of the self probably rests on nothing other than their social and worldly nature, which links the individual being with other people and things; but unfortunately what gives them their power of healing seems to be the same as what diminishes the quality of personal experience in them.

    The Man Without Qualities, 3 volumes, translated with a foreword by Eithne Wilkins and Ernst Kaiser, Pan Books, London, UK, 1979. English edition first published by Secker and Warburg, 1954. Originally published in German, Der Mann ohne Eigenschaften, 1930 & 1932.

  3. David Savitt says:

    Another data point: the math building at UA (built in the early 1970s, I think) was designed to minimize the interactions between the occupants of the building, on the grounds that mathematicians want to be left alone. The floor plan is shaped like a plus sign, with an elevator shaft running down the middle so that you can’t see any of the other wings from the wing you’re in. I have a hard time imagining that such an idea would make it to fruition today, if someone proposed it. (On the other hand in those days there might not have been so much consultation about the design of the building, so it’s possible that one or two people with their own ideas might have had outsized influence.)

  4. misc. harvard undergrad says:

    Is it perhaps just that nothing more has changed than that we have finally agreed to give up the charade that one must be solitary to be masterful?

  5. Tom Goodwillie says:

    I think that every human being strikes some balance between solitary and social modes of being: some people are very solitary, some are very social, and there is a whole spectrum in between. This includes mathematicians. There is a stereotype that mathematicians are shy. Maybe there is some statistical truth to this, but a good number of mathematicians are not the least bit shy. And anyway shyness is probably not reasonably regarded as a single trait. Do you favor joint research projects? Do you like to discuss work in progress with people you meet at conferences? How do you feel about public speaking? These are three rather different questions.

    I’m really not sure whether Veblen’s statements are simply reflecting a view that mathematicians all have personalities similar to his, or whether there is a deeper (but still maybe wrong) idea in what he is saying, that one needs to take seriously.

    Certainly some mathematicians love to do joint research. I can think of many examples, headed by Raoul Bott, who spoke very movingly at his sixtieth-birthday conference about the joys of collaboration.

    And it is a cliche that teaching a subject can deepen one’s knowledge of it; I would add that there is truth in the cliche, and that this is all of a piece with the idea that when you have a good new idea, the process of writing down a comprehensible account of it generally helps you to understand it better yourself.

    – Tom Goodwillie

  6. I’m pretty upset someone pulled the Musil quote before me. (Incidentally, that quote is about the protagonist sitting down to do math.)

  7. piper says:

    i was excited to come here and say that i totally agree that mathematics leads to asocial behavior, but sadly i think this quote is nonsensical.

    i think all understanding is terribly individual and thus true communication about anything is virtually impossible. we get by by surrounding ourselves with people with whom we share enough in common that we never have to see how poorly we communicate. (i say “i like math, but i also want to do other things” my friend hears “i’m never going to do anything meaningful with math, but i have other interests i can pursue.” my friend says “yeah, it’s good to have other interests.” we are both satisfied. i say “i like math, but i also want to do other things” and unnamed math prof hears “i have a hard time doing anything other than math, but i sense i might be missing out.” math prof says “taking a break is actually really good for mathematical progress! when you’ve been working hard on a problem sometimes the answer only comes while you’re out on a walk. you should definitely feel free to go on a hike or go to a concert!” math prof feels satisfied. i feel i’ve-made-a-huge-mistake devastated.)

    to me none of the rest of what he says follows from the individualness of math/knowledge.

  8. Anonymous says:

    > i was excited to come here and say that i totally agree that mathematics leads to asocial behavior, but sadly —


    In the past, on this blog, you described at length how you think mathematicians are a bunch of asocial losers. I am confused as to why you imagine that such sentiments are welcome here. May I suggest that you address them to people whom you respect?

  9. JSE says:

    I can delete any comment I want, so you can feel safe in assuming that any comment you actually see is in fact welcome here.

  10. Richard Séguin says:

    The last two sentences are ambiguous. Does “normal social groups” refer to social interaction among mathematicians, or to social activity not related to mathematics, such as belonging to a neighborhood association, or to both? I feel uncomfortable with either interpretation. There are many advantages to discussing your work with colleagues and in turn listening to them thinking about their own work, and withdrawal from non-mathematical social life and living only in the world of mathematics would be like living in a monastery with all the ingrown bizarreness. Could this have been a 1950s thing? Any retired mathematicians out there?

  11. Anonymous says:

    > I can delete any comment I want, so you can feel safe in assuming that any comment you actually see is in fact welcome here.

    Fair point. That was presumptuous of me, I’ll speak for myself.

    I am a mathematician who has some natural “asocial” tendencies (I had my head thoroughly in the clouds through my teenage years) and makes a consistent effort to overcome them. I usually succeed but occasionally I embarrass myself, and I find it painful to be reminded that I’m judged for weaknesses which I make a rather substantial effort to mitigate.

    To anyone who would criticize mathematicians as a group, may I please ask that you keep this in mind?

    Thank you.

  12. piper says:

    dear anonymous, i’ve obviously offended you, and for that i’m sorry, but you’ve also misrepresented my views here. it is taking me all of my strength not to get into it now (i already wrote a reply and have saved it in case of emergency), but i really don’t think it would be appropriate. that is all.

  13. TG says:

    I’m reminded of one of my favourite quotes, from a Harvard professor at lunch with some BPs: “I became a mathematician because it is the most socially acceptable way of being antisocial”.

  14. Dignaga says:

    My two cents. In my experience, what counts as being ‘sociable’ varies greatly with the community that one finds oneself in. I have always been regarded as introverted by people outside the mathematical community for example my friends from school, those at the workplace at my first job. However, at graduate school I was taken to be extroverted. I went to a small, but extremely competitive research institute where every body in the math dept. (unlike the cs dept) kept largely to themselves. Eventually, the loneliness became a problem and I quit my program. I remember one of my profs saying that I should have chosen to apply to certain US depts because they are more communal.

  15. Anonymous says:


    > and for that i’m sorry,

    Thank you very much. I appreciate it.

    > but you’ve also misrepresented my views here.

    You have, previously on this blog, criticized mathematicians as a group for their asocial tendencies. If what you wrote does not reflect your views, then I urge you to retract it.

    However, I put the word “losers” into your mouth, and I suggested that you don’t respect mathematicians, an inference that may not be warranted. To whatever extent I have made wrong assumptions, I apologize for it.

  16. piper says:

    when you say “asocial losers” or even “asocial tendencies” the image that comes to my mind is not of a mathematician. awkward is more what i think. and perfectly social people can be awkward, too. it’s just about frequency of awkward encounters (with no positive resolution) in math depts that i think is different from other areas of life (except in The Office). is awkwardness asocial? i don’t know. the average mathematician in my head does have friends so how can i call him (gender selection on purpose) asocial?

  17. Richard Séguin says:

    Piper: you may find people in other academic or especially in non-academic work settings who are more social, less introverted, and less awkward, but there you are also more likely to encounter back stabbing, getting other people fired to advance one’s own career, and other nasty immature social behaviors that are not discouraged from the top. “Social winners” seem to be much more adept at this than “asocial losers”.

  18. I sometimes feel as though I am one of the few mathematicians left who writes a significant number of one author papers.

  19. Jon Awbrey says:

    Peirce’s “Pickwickian” paragraph comes to mind, said Jon Perennially —

    Two things here are all-important to assure oneself of and to remember. The first is that a person is not absolutely an individual. His thoughts are what he is “saying to himself”, that is, is saying to that other self that is just coming into life in the flow of time. When one reasons, it is that critical self that one is trying to persuade; and all thought whatsoever is a sign, and is mostly of the nature of language. The second thing to remember is that the man’s circle of society (however widely or narrowly this phrase may be understood), is a sort of loosely compacted person, in some respects of higher rank than the person of an individual organism. It is these two things alone that render it possible for you — but only in the abstract, and in a Pickwickian sense — to distinguish between absolute truth and what you do not doubt.

    — C.S. Peirce, Collected Papers, CP 5.421.

    Charles Sanders Peirce, “What Pragmatism Is”, The Monist, Volume 15, 1905, 161–181. Reprinted in the Collected Papers, CP 5.411–437.

  20. Anon says:

    Eric Lander has mentioned that his desire for community endeavors as a factor in his choice to pursue biomedical research as opposed to math

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