math

I've been studying topology using the famous Munkres book. In fact, if you look up which topology books are good, it's pretty much guaranteed that his name will show up. Not only that, but he's been a professor at MIT for decades. So I got curious to see him talk. Maybe an interview, or even better, a lecture or any sort of speech.

I'm stumped. There is absolutely not a single video anywhere with James Munkres. This guy is probably one of the most famous topology authors in the world, was even elected as a fellow in the AMS in 2018, a professor emeritus at MIT, and still not a single record of him anywhere, except for a single picture of him in his MIT professor profile. Is it because he doesn't want to be recorded anywhere and avoids speaking in conferences? Or did nobody ever think to invite him for any sort of interview?

I'm taking a vector analysis class, and upon reaching the Stokes's theorem, our professor briefly mentioned Stokes did not actually prove his theorem. It's funny, but definitely one of many situations where we name theorems after people just "involved" in the theorem but not actually the provers.

I found this very nice paper¹ describing the history we know. In short, Ostrogradsky proved the first version of what we know as the divergence theorem. Green then proved a different version of it, which when reduced to two dimensions, derives what we know as Green's theorem (except that Green never seems to have done that).

The first version of Stokes' theorem in $\R^3$ was actually in the Smith's Prize exam from 1854 (yes, it was the question to an exam, specifically question #8 found here²), and the one who and the author of the exam was Stokes himself. So we only call the theorem after him for perhaps shedding light on this problem, but from what we know, the first to actually prove it was Hermann Hankel in 1861, using the results of Green.

Back when I was a new undergrad student taking my first analysis course, I was shown many proofs involving the cardinality of sets. I was introduced to the fact that the cardinality of the power set is always strictly greater than the set itself $$\text{card}(X) < \text{card}(\cP(X))$$ But I never bothered with looking into the proof, being scared of it looking complicated. Looking back, that was silly, because I finally got to properly read it, and it couldn't be simpler.