One particular infinity-related question has persisted since the 1940s, even after Gödel's and Cohen's work: The problem of p and t. Mathematicians believed that if we could crack this problem, we could once and for all solve that darn continuum hypothesis. And, phew, in 2016, the p and t problem was finally solved.

Enter our heroes: Maryanthe Malliaris, of the University of Chicago, and Saharon Shelah, of the Hebrew University of Jerusalem and Rutgers University. The two mathematicians published a proof to this problem in the Journal of the American Mathematical Society and were honored in July 2017 with one of the top prizes in the field of set theory. (Here's a much shorter summary of the proof by Cornell University's Justin Moore, by the way.) But what'd they solve?

The question at hand asks whether p (one variant of infinity) is equal to t (another variant of infinity). Both p and t quantify the minimum size of collections of subsets of the natural numbers in precise (and probably unique) ways. The details of p and t aren't important; just know this: Both sets are larger than the infinite set of natural numbers, and p is always less than or equal to t. If p is less than t, then p would be a medium infinity and the continuum hypothesis would be false. Pretty major.

In 2011, Malliaris and Shelah started working on a totally different problem. (It was about ordering problems based on complexity, building off Keisler's order, in case you were wondering.) In the process, they realized they were also, kind of, accidentally making headway with the p and t dilemma. So they went with it. The two published a 60-page paper that solved their initial problem and the famous p and t problem at the same time. By proving that p and t are equally complex, they concluded that p equals t.

They proved it by carving out their own lane between two branches of mathematics: set theory and model theory. Their work is already opening new frontiers of research in both fields. Why does that matter? The more we know about math, the more we can understand the mysterious ways of the world around us. Thanks, Malliaris and Shelah!

(Psst — There's an unsatisfying end to this breakthrough mathematics story, too: Their work didn't solve the continuum hypothesis like mathematicians thought it would. Oh well! However, experts are pretty sure there have to be medium-sized infinities. Infinity is so weird that even the weirdest theories could be true, probably, maybe. Why not?)