/sci/ - Science & Math

And here's a classic with a ton of information packed into one doodle: Mumford's famous drawing of the "arithmetic surface", with Manin's coordinate axes on the sides.

Here's a detailed explanation:
http://www.neverendingbooks.org/index.php/mumfords-treasure-map.html

>>6389940
They only seem unrelated until you learn algebraic number theory. There's a big picture — it's just not always apparent without deeper study.

>>6341314
Serre's contributions to modern mathematics are quite possibly just as monumental as Grothendieck's — it's just that Serre didn't focus quite as exclusively on theory-building and didn't put everything in huge, multi-volume manuscripts like SGA and EGA, so his contributions seem more scattered. (Grothendieck was the archetypal theory-builder, just as Erdős was the archetypal problem-solver. Most mathematicians work somewhere in the middle.) Also, Serre and Grothendieck frequently collaborated, so a lot of Grothendieck's work was inspired by Serre and vice versa.

Also, although Serre and Grothendieck tend to overshadow everyone else in algebraic and arithmetic geometry, don't forget about other great mathematicians working in the same areas, like Deligne, Mumford, Tate, Langlands, and Artin.

Ring theory
Modular forms
Homological algebra

Math grad student here.