Shinichi Mochizuki has released his long-rumored proof of the abc conjecture, in a paper called Inter-universal Teichmuller theory IV: log-volume computations and set-theoretic foundations.
If true, the proof would be one of the most astounding achievements of mathematics of the 21st century.
The homepage of Professor Shinichi Mochizuki is here.
Excited, but caution
Terence Tao’s comment(from his blog): It’s still far too early to judge whether this proof is likely to be correct or not (the entire argument encompasses \(500\) pages of argument, mostly in the area of anabelian geometry, which very few mathematicians are expert in, to the extent that we still do not even have a full outline of the proof strategy yet). For those that are interested, the Polymath wiki page on the ABC conjecture has collected most of the links to that discussion, and to various background materials.