4 ms·
Reminds me of my favorite math essay: "When is one thing equal to some other thing?" It's a great question, much deeper and more interesting than it seems. The
by tikhonj 5mo ago
Reminds me of my favorite math essay: "When is one thing equal to some other thing?"
It's a great question, much deeper and more interesting than it seems. The essay suggests thinking in terms of isomorphisms (relative to the structure you care about) rather than equality in some absolute sense, and I've found a fuzzy version of that to be a really useful perspective even in areas that can't be fully formalized.
https://people.math.osu.edu/cogdell.1/6112-Mazur-www.pdf https://people.math.osu.edu/cogdell.1/6112-Mazur-www.pdf
- card_zero 5mo agoMathematics is all just explanations for why this is really that. If it didn't have to respect its human audience, and their failure to grasp similarities, the whole edifice could be one implicit statement. (After all, since this is really that, there is no this or that.) So mathematics is about people.
- moi2388 5mo agoYes, I found the same and was very pleasantly surprised when I first learned about the ideas of cubical type theory.