TITLE: Is physical stamina important for doing mathematics?
QUESTION [6 upvotes]: 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).

REPLY [5 votes]: 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.