The result of Ono and Bruinier is significant, but I don't know if it really belongs on this list. Euler's pentagonal number theorem already gives a simple alg

The result of Ono and Bruinier is significant, but I don't know if it really belongs on this list. Euler's pentagonal number theorem already gives a simple algebraic description of the partition numbers. The so-called "finite algebraic formula" of Ono and Bruinier is only more "finite", "algebraic" or "formula" in a very artificial, press-release-exaggerated sense. Sort of like claiming that any of the contorted "prime formulas" that various people have come up with (http://mathworld.wolfram.com/PrimeFormulas.html http://mathworld.wolfram.com/PrimeFormulas.html) provide a better finite description of the primes than the good old sieve of Eratosthenes. Now, this comparison is not quite fair. Unlike those prime formulas, the Ono-Bruinier result is actually mathematically significant in that it does give you more information about the partition numbers. It's a nice result, but is it more interesting than hundreds of other interesting results in mathematics in the last 5ish years? Even if we just look at the extremely narrow field of mathematics that is the study of partition numbers, there are other nice recent achivements such as Radu's proof of Subbarao's conjecture. Ono is certainly an excellent mathematician, but he might be even more excellent at getting extreme amounts of publicity for his results. I don't want to give the impression that I'm sour about this. On the contrary, I think it's awesome that mathematics can get this kind of publicity, and Ono earned it (other mathematicians should learn from his example!), but it's something to keep in mind. Likewise, about HOTT. It's very promising, but is it really an "achivement" yet? Who knows, the hype could turn out to be justified. I guess if you want to assess scientific progress as recent as in the last five years, you have to try to predict the future as well.