The solution to the Dichotomy Conjecture for Constraint Satisfaction Problems [1] (also [2], but this proof is much more difficult). This gives a clear dividing line between the types of problems that are easy to solve exactly and the types of problems that are difficult to solve exactly, for a fairly large class of problems. I wouldn't even dare to dream that something like this could be done until I saw it happen!

[1] https://arxiv.org/pdf/1704.01914.pdf [2] https://arxiv.org/pdf/1703.03021.pdf