Which results from the last 30 years, in any area of mathematics, do you think are the most important ones?

Specifically, which are the ones that will have more impact across all math and/or settle significant questions, in your opinion? It does not matter if they are big, lond-proofed results like a classification theorem, or little, elementary lemmas proved in a paragraph.

To keep this reasonable, I propose that every contributor posts at most 10 results.

Please, write one result per post, so that we can all vote properly and have a real ranking afterwards. Also, please don't just write the name, write a little description (hopefully, self-contained) and put some link if desirable.

(My personal aim with this question is to learn. I hope to be a bit better versed after studying your answers!)

aregood reasons to discriminate between different pieces of mathematics on grounds of value... but writing lists of this sort of thing is so subjective that it bothers me a bit... $\endgroup$ – Nick Gill Jan 17 '17 at 15:09