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.

Answer

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 N can “be divided into two parts, such that no part contains a triple (a,b,c) with a2+b2=c2“. 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”.

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YukiJ

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