What is the greatest mathematical achievement of the 20th century?

-1/12

>>8294068
The fact that the rationals are countable like the naturals but can be infinitely divided like the reals blows my mind.

What even are the rational numbers? How can they have both of these properties at the same time? Like holy fuck, just this makes them more interesting numbers than the reals. I wonder why most people don't focus on the rationals when there are obviously many hidden theorems lying in this weird relationship the rationals have with the naturals and the reals where it is like an intermediate state of both.

>>8294068
The invention of the atom

the incompleteness theorems

>>8294068
probably the one that contributed the most to the creation of computers, i guess that's gotta be something from Turing or Neumann

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87KB, 750x500px

>>8294092
the middle ground like that is always most interesting, even geometric objects over the rational numbers... when genus 0 they have infinitely many points, in any genus greater than 1 they have finitely many points, but in genus 1 they have this beautiful structure of having both points of finite order and sometimes infinite order, and there's still no algorithm of determining this number of points, even hundreds of years later

>>8294131
Yes, obviously Gödel's Incompleteness.

Data Science.

Now, Math grads can pretend they are learning something useful.

>>8294068
The long-overdue fully rigorous proof of integration by parts, without a doubt.

>>8294068
The classification of finite simple groups

>>8294068
EGA+SGA+FGA

>>8294081
Meme