Most people name the Fields Medal as the math-equivalent of a Nobel prize. In recent history, there was a lot of work figuring out the math required to get string theory to work. There's also a bunch of big unsolved problems in a few different veins of mathematics. A famous one to computer people is P != NP, which would prove the complexity and consequent intractability of many problems. There's stuff related to predicting prime number which always makes cryptography nerds perk their ears up. In another vein, there's Gödel's incompleteness theorems which say that it is impossible to prove that system of logic underlying all of mathematics is consistent, using that same system of logic. So on the more philosophical end of the spectrum, there are people studying other systems of logic to extend the domain of what is provable and what we know for certain about what we have proven.OK don't be mad, but what sort of breakthroughs can still be made in Mathematics for someone to earn a Nobel prize equivalent?