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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

41 votes
26 answers
12k views

What are some slogans that express mathematical tricks?

Many "tricks" that we use to solve mathematical problems don't correspond nicely to theorems or lemmas, or anything close to that rigorous. Instead they take the form of analogies, or general methods …
18 votes
4 answers
915 views

Arrow's theorem and the postseason

There are a number of instances of sports teams intentionally losing matches in order to secure a more favorable situation in a playoff round. While this doesn't happen terribly often, when it does it …
157 votes
11 answers
20k views

Why are flat morphisms "flat?"

Of course "flatness" is a word that evokes a very particular geometric picture, and it seems to me like there should be a reason why this word is used, but nothing I can find gives me a reason! Is th …
6 votes
4 answers
3k views

Where can I find the text of Weyl's Fields Medal speech for Serre?

I thought about asking this question a while ago, but decided against it. But now I see a question about Eichler's "modular forms" quote, so while I guess it's probably still, um, questionable, what t …
13 votes
15 answers
2k views

Most helpful heuristic?

What's the most useful piece of mathematical "folk wisdom" you've encountered? I'm talking here about things that aren't theorems, or even conjectures, or even shadows of conjectures -- just broad ana …