Friendly warning to those who might not be aware: the vast majority of comments below posts like the above will be left by (otherwise intelligent) programmers who think mathematics is a closed system where one attempts to solve endless Olympiad-type problems. I wouldn’t take any of it seriously at all. Better to listen to what those who actually know what the subject is about have to say.
Unfortunately, mathematics (especially pure mathematics) is by its very nature very, very poorly understood by those who haven’t worked as a mathematician. Even worse, those who don’t understand are seemingly not at all aware of their misunderstanding and are entirely confident in their (very wrong) characterisation of the subject.
My understanding when I was practicing is that the trend in modern mathematics is to focus on spaces with a certain kind of structure, and maps between those spaces that preserve it, and then what are invariants are preserved by those maps. Structure-preserving maps between categories of such spaces - "functors" in the language of category theory - are especially neat.
That's certainly different from Olympiad-style problems.
xanderlewis · · focus · HN ↗
Unfortunately, mathematics (especially pure mathematics) is by its very nature very, very poorly understood by those who haven’t worked as a mathematician. Even worse, those who don’t understand are seemingly not at all aware of their misunderstanding and are entirely confident in their (very wrong) characterisation of the subject.
colonwqbang · · focus · HN ↗
GlobalChubby · · focus · HN ↗
That's certainly different from Olympiad-style problems.