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Recently, I read an interesting story about A. Weil and J.P. Serre. The general gist of the story is as follows:

During the Autumn of 1955, an international symposium on algebraic number theory was held at Nikko [a small city around 150 km north of Tokyo]. The Japanese mathematicians invited Weil and Serre on a trip to Lake Chuzenji. Upon arriving, Weil and Serre stripped down, and started swimming in the cold lake. The Japanese mathematicians followed suit, but they quickly gave up because of the cold. After a while, the two mathematicians came back out and started running. The Japanese mathematicians ran after the duo, but once again, they gave up. Eventually, Weil came back, smiled at the Japanese mathematicians, and said, "Math is all about physical stamina."

(My translation.)

I think the last Weil quote sums up the main message of the story.

My Question. Based on people's experience, is this a true statement? If possible, I would like to hear what physical activities people pursue, and in what ways that has helped in doing mathematics.

I hope this is not too off-topic. I've never heard something like this from mathematicians I know personally, so I was curious to hear what the community thinks.

Edit. As per helpful comments, I would like to restrict the question to research mathematics (rather than mathematics in general).

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    $\begingroup$ This is probably not the right forum for this question, but I think mathematicians are much like the general population. There are a few who are very serious athletes (Alan Turing for instance) but many others who are not athletic and have other interests. I think it's natural to find mathematical connections in your other hobbies, whatever they may be. $\endgroup$ – Gabe K Jan 30 at 14:43
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    $\begingroup$ The title is quite confusing, and should rather refer to the main question, for which this anecdote is of minor relevance. About the quoted sentence itself ("it's all about..."), it's obviously not to be interpreted literally, I'm not sure discussing seriously about such a sentence can lead to more than idle banter. $\endgroup$ – YCor Jan 30 at 15:00
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    $\begingroup$ I think all the story demonstrates is that (some) mathematicians are extraordinarily competitive and driven to “win” in all things, not just in math. $\endgroup$ – Andy Putman Jan 30 at 15:10
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    $\begingroup$ I think we fall into the classic trap here of flipping the wrong cards. If you want to confirm that math is all about physical stamina, then looking for mathematicians with ample physical stamina provides only weak confirming evidence; the real test is whether we can disprove it by finding mathematicians with normal or less than normal physical stamina. My suspicion is that there are plenty. $\endgroup$ – LSpice Jan 30 at 17:55
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    $\begingroup$ I think what the story demonstartes is that Weil could make a joke. $\endgroup$ – Gerry Myerson Jan 30 at 23:37
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Having been to Japan a few times to work with my collaborators, it might well be that the hosts in your story just gave up to be polite, and would have a few laughs at the silly Westerners later in the drinking session that evening. (-:

I had a similar story. A Russian gentleman I met at a conference told me exactly the same thing Weil supposedly said. I remember him vividly because he would rise up after each talk and said something like: "Grothendieck would have done this, have you considered?". Remarkably, he asked no question after my talk, so we struck a nice conversation and went to the beach to swim (it was winter time in Korea). He was in better shape then I was despite being about 70 (apparently people from Russia have more experience swimming in the cold).

About your actual question, obviously being fit is important in all walks of life. Keep in mind that the physical activities one enjoys depend on many factors: countries of origin, class, race, social circles, etc. Mathematicians I know tend to like walking, hiking, biking. More seem to play soccer than tennis.

Talking about Serre, here is a video of him climbing a rock a few years back, from Robin Hartshorne's FB page. https://www.facebook.com/robin.hartshorne/videos/10200853358373274

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    $\begingroup$ I went rock climbing with Labesse at Luminy a few years ago. I am no great rock climber, but still it was impressive to see how vastly better a climber was this mathematician some decades my senior. $\endgroup$ – LSpice Jan 30 at 17:58
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    $\begingroup$ @LSpice: they did not have social media and Mathoverflow! $\endgroup$ – Hailong Dao Jan 30 at 18:24
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    $\begingroup$ The link does not work. $\endgroup$ – Steven Landsburg Jan 31 at 2:39
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    $\begingroup$ @lspice: I had exactly the same experience (at exactly the same place) with Cartier, decades ago. $\endgroup$ – Steven Landsburg Jan 31 at 12:41
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    $\begingroup$ It would make me (and probably others) very happy if someone who is friendly with Hartshorne could ask for permission to post this video elsewhere. I'm happy to host it if there is no better alternative. $\endgroup$ – Steven Landsburg Jan 31 at 23:31
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Mathematics is not the same as chess, but here is an anecdote from the Preface of Jan Timman's book The Art of Chess Analysis that you may find interesting.

In his Foreword [to One Hundred Selected Games], Botvinnik asks the rhetorical question, "How do I prepare?" and he immediately answers, "That has never been any secret": fifteen to twenty days in the fresh country air, prescribes Dr. Botvinnik.

So it was that Hans Böhm and I, among others, bid farewell to our carefree lifetstyle and began a long retreat at a house in the Friesland countryside. For three months we lived like health fanatics. Our luggage contained little more than chess literature and track suits.

The tournament began…and the first five games were lost. I remember exactly how I felt. During play my body was overflowing with so much energy that I could hardly stay seated in my chair. After each game I still had enough energy to run several times around the Vondel Park. But why bother?

This painful start drove me to a firm decision. I threw all my Spartan habits overboard and indulged myself in everything that had been declared unhealthy. In short, I went back to my old lifestyle. And lo and behold, immediately everything went wonderfully. Thanks to a good winning streak, a total catastrophe was averted and I managed a reasonable result.

So much for that part of the wisdom I had hoped to find in Botvinnik's work. The only lesson I really learned is that you must never change your normal rhythm just because you are faced with an important tournament. As Botvinnik says a little later in the same Foreword: "Possibly some of my suggestions will not be of much benefit to some players; each must consider them critically and apply them with caution, taking his own individual capacities and habits into account."

I should mention, for the benefit of those who do not know anything about Botvinnik, that he did indeed have a lifestyle with daily exercise built in, and he did attribute his success in part to that. So it's not just a matter of Timman misinterpreting the meaning of "fifteen to twenty days in the fresh country air."

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    $\begingroup$ That's a funny story. Having too much energy can definitely affect mental focus. $\endgroup$ – Hailong Dao Jan 30 at 17:41
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    $\begingroup$ Perhaps there was some time long ago when I had too much energy. Now it is my children who have too much energy. $\endgroup$ – Zach Teitler Jan 31 at 4:10
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Apparently this is one of those opinion-based questions that are destined to be closed soon. Still, I'll share my perspective.

IMHO it doesn't matter at all (for doing mathematics, at least) if you can outrun a cheetah or to come up as a winner in a wrestling match with an elephant. What is really required is an ability to concentrate and to think for an extended period of time without developing a headache, falling asleep, or going in circles. I doubt it burns any noticeable amount of calories because the best position I know for doing it is lying on the sofa. If that is the "stamina" we are talking about, I agree, but in all other respects, any physical shape that doesn't give you an obvious trouble and provides enough oxygenation to the brain would, probably, do.

Another possible meaningful interpretation is that perseverance is at least as important as brilliance. I'm not quite sure I believe in Edison's statement that "genius is one percent inspiration and 99 percent perspiration", but I certainly agree that trying to ride the flashes of insight alone often won't bring you very far.

As to the rest, it is in the human nature to show off a bit now and then, and, for a mathematician it is a little difficult to impress a non-mathematician (or even a mathematician in a different area) with his or her professional achievements, so I suspect many of us are in the habit of developing some marketable "side skills" and going into sports is certainly an option (though by no means the only one: somebody can choose to go into, say, arts instead and, if he ever becomes as famous as Weil, leave us pondering on MO if mathematics is all about the powers of imagination and the ability to reflect and transform all that we see and feel into sophisticated creations in the parallel world).

Just my two cents.

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    $\begingroup$ I had hoped that it was acceptable to develop a headache and go in circles, but keep going anyway, with the hope that the headache might clear once one discovers that the circle is really a spiral going only very slowly to infinity. :-) $\endgroup$ – LSpice Jan 31 at 3:15
  • $\begingroup$ @fedja "the ability to reflect and transform all that we see and feel into sophisticated creations in the parallel world." How long does it take you to write your answers? $\endgroup$ – mathworker21 Jan 31 at 9:45
  • $\begingroup$ @mathworker21 Depends on the content. Mathematics is rather slow, pictures are even slower, general stuff like this one is pretty quick: just say what you think and feel, no need to optimize or to check for possible logical errors thoroughly :-) $\endgroup$ – fedja Jan 31 at 23:17
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The analogy to chess reminded me of the saying that high-level chess players burn absurd numbers of calories.

Here is a place where one can find debunked the related ideas (1) that playing intense chess is comparable to intense physical activity and (2) that mental effort per se can lead to increased metabolic activity.

I have deleted the rest of the original answer which, based on assumptions (1) and (2), speculated about the implications for mathematics. Thanks to Gabe K in the comments below for challenging these speculations.

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    $\begingroup$ For now, I'd reiterate Hailong's conclusions: It's widely believed that exercise and diet are important not just for health in general, but for mental well-being in particular, and I can only assume there's a large body of evidence for this thesis. Particularly as a mathematician, I prize my mental well-being dearly, and so I do subscribe to the thesis that good diet and exercise are important to my mathematical pursuits (though following through on the obvious conclusions that I should eat well and exercise may be another matter:) $\endgroup$ – Tim Campion Jan 30 at 19:58
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    $\begingroup$ To be honest, I'm very skeptical of that figure. It would imply that playing a high level chess tournament is roughly as intense from a metabolic perspective as riding in the Tour de France. In any contest where calories are being burned at that rate, nutrition becomes a major strategic factor because your body will deplete its glycogen reserves within about 2 hours. I suspect that chess raises the heart rate and blood pressure and the players lose a lot of weight because they aren't eating enough to compensate, $\endgroup$ – Gabe K Jan 30 at 20:15
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    $\begingroup$ @GabeK Yeah, it does seem a bit out there. In my 10 seconds of googling I was more expecting the top hits would be debunking it as an urban legend. $\endgroup$ – Tim Campion Jan 30 at 20:19
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    $\begingroup$ You might be right that they're not actually burning more calories, but just forgetting to eat. Even if they really are burning more calories, perhaps it's not the mental effort per se leading to weight loss, but just the elevated stress associated with intense competition. In which case (I hope) the situation has even less to do with mathematics. $\endgroup$ – Tim Campion Jan 30 at 20:25
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    $\begingroup$ I believe that they lose a lot if weight and have elevated heartrates. However, the fact that chess players aren't extremely focused on their nutrition during games suggests to me that the weight being lost is caused by not drinking and eating enough rather than burning calories at an extreme rate. $\endgroup$ – Gabe K Jan 30 at 20:26

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