Actually Ed Witten was not a total newbie to advanced Math before grad school.From his commemorative lecture:
At about age 11, I was presented with some relatively advanced math books. My father is a theoretical
physicist and he introduced
me to calculus. For a while, math was my passion. My parents, however, were reluctant
to push me too far, too fast with math (as they saw it) and so it was a long time after that before I was exposed to
any math that was really more advanced than basic cal
culus. I am not sure in hindsight whether their attitude was
best or not. However, the result was that for a number of years the math I was exposed to did not seem
fundamentally new and challenging. It is hard to know to what extent this was a factor, but
at any rate for a number
of years my interest in math flagged.
That he learned calculus when he was younger doesn't really explain how he so easily transitioned into mathematical physics after a liberal arts education.
Calculus is relatively basic compared to grad level work in that area.
I wound not be surprised if he is the product of a Math Circle:a nice place to stretch one's mathematical abilities while retaining the bragging rights of never having formally studied math in college.
At about age 11, I was presented with some relatively advanced math books. My father is a theoretical physicist and he introduced me to calculus. For a while, math was my passion. My parents, however, were reluctant to push me too far, too fast with math (as they saw it) and so it was a long time after that before I was exposed to any math that was really more advanced than basic cal culus. I am not sure in hindsight whether their attitude was best or not. However, the result was that for a number of years the math I was exposed to did not seem fundamentally new and challenging. It is hard to know to what extent this was a factor, but at any rate for a number of years my interest in math flagged.
https://www.sns.ias.edu/ckfinder/userfiles/files/Comemorativ...