Re:What is it like to understand advanced mathematics?
by selimthegrim on Wednesday August 17, 2016 @08:12PM
(#12309532)
A bigger problem is the difference between Hermitian and self adjoint, a lot of physics professors don't understand that.
Or for example, this famous dialogue between Geoffrey Chew and Arthur Wightman from the 1960s bootstrap fad:
Wightman asked Chew: why assume from the start that the S-matrix was analytic? Why not try to derive it from simpler principles? Chew replied that "everything in physics is smooth". Wightman asked about smooth functions that aren't analytic. Chew thought a moment and replied that there weren't any.
Re:What is it like to understand advanced mathematics?
by selimthegrim on Monday August 22, 2016 @01:57PM
(#12338079)
By the way, the reason they said that was no doubt to motivate the students to choose correct boundary conditions for some Sturm-Liouville problem (as the previous poster sort of alluded to)
No, they said what I wrote they said. It was at YouTube, from MIT, from a course in quantum mechanics.
Uh, I do understand this stuff: E.g., given a positive integer n, the set of real numbers R, the usual topology for R^n, a set C a subset of R^n closed in that topology, there exists a function
f: R^n --> R
so that for x in R^n, f(x) is 0 for x in C, f(x) > 0 for x not in C, and f infinitely differentiable. E.g., for n = 1, the result applies for set C a Cantor set or a Cantor set of positive measure. For n > 2, the result applies for a sample path of Brownian motion or the Mandelbrot set.
When I was a grad student, I discovered and proved this result. Later I published the result in JOTA.