What were some major mathematical breakthroughs in 2016? [closed]

As the year is slowly coming to an end, I was wondering which great advances have there been in mathematics in the past 12 months. As researchers usually work in only a limited number of fields in mathematics, one often does not hear a lot of news about advances in other branches of mathematics. A person who works in complex analysis might not be aware of some astounding advances made in probability theory, for example. Since I am curious about other fields as well, even though I do not spend a lot of time reading about them, I wanted to hear about some major findings in distinct fields of mathematics.

I know that the question posed by me does not allow a unique answer since it is asked in broad way. However, there are probably many interesting advances in all sorts of branches of mathematics that have been made this year, which I might have missed on and I would like to hear about them. Furthermore, I think it is sensible to get a nice overview about what has been achieved this year without digging through thousands of different journal articles.

Solution 1:

Personally, I was kind of fascinated by the solution to the Boolean Pythagorean triples problem which was finally solved in May. The problem asked whether or not the set of natural numbers $\mathbb{N}$ can "be divided into two parts, such that no part contains a triple $(a, b, c)$ with $a^2+b^2=c^2$". Heule, Kullmann and Marek managed to prove (with the help of a lot of computing power) that this is in fact not possible.

References:

Heule, Marijn J. H.; Kullmann, Oliver; Marek, Victor W. (2016-05-03). "Solving and Verifying the Boolean Pythagorean Triples problem via Cube-and-Conquer".

Solution 2:

Don't know if this counts, as the proof was announced in late 2015. Tao's solution of the Erdős discrepancy problem was published in 2016. You can find it here; it was actually the first paper of the Discrete Analysis journal.