I was just wondering about this, because I've heard it quite often that physics is fertile ground for new ideas in mathematics, historically and currently. In the past we can think of Newton inventing calculus to solve physics problems, Fourier inventing Fourier analysis (now that sounds odd; I doubt he named it after himself, but way to go if he did!)-- or what mathematicians today call Harmonic Analysis-- to solve engineering problems and so on. Today, I've often heard it said that particle physics, QFT, string theory etc. provide many ideas for research for mathematicians. How true is this? How much physics should the mathematician and a mathematics student know? I am reading Peter Woit's book Not Even Wrong and he's convinced me phyics is very important to the research mathematician. Woit received his PhD in physics, but then moved to mathematics. I've also heard this opinion expressed a countless number of other times, from Witten, Atiyah (an admirer of Witten, btw), Bott, Hermann Weyl and many others, to pick on the famous people (I have forgetten most of the places I have heard this). Even in http://www.math.ohiou.edu/~shen/calculus/chen1.pdf" [Broken]. Most universities require math students to have at least a course in general physics, so appearently they think there is some worth in learning physics. How much should you know? I myself have taken courses in EM, QM and classical mechanics, but I have never seen anything I found usefull in any of my mathematics courses, since the only math that ever seems necessary is vector calculus and differential equations, not particularly interesting areas of mathematics in my opinion. Any thoughts?