In grad school, I was interested in statistics so I went to a talk by Laurent Schwartz called Distribution Theory. I thought it meant normal dist etc, but when he started off with tempered representations of Lie groups, I thought WHOA!. Ever go to a lecture beyond your pay grade?
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I enjoy teaching an undergraduate course called "Advanced Number Theory," followed by a much harder graduate course called "Introduction to Arithmetic"... (The titles are not misnomers. The NT is Advanced for undergrads. The Arithmetic is just the beginning of research level...)
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Wasn’t there a story of Ed Witten feeling confused (and excited too) when Micheal Atiyah gave a talk on quantum field theory at Harvard ? This inspired Witten to study more maths and he spent a year at Oxford with Atiyah.
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