Here is some news of the possible breakthrough of the ABC conjecture. It might already be commonly known, but it is something I only recently discovered was going on. There are rumors that Shinichi Mochizuki from Kyoto university has solved the abc conjecture. You can find his proof here. Not that I understood anything of it, but I though a link would be appropriate. But don’t despair yet, I will have a few more links in this regard.

Mochizuki Shinichi

Even though there are made advances in math every single day, I always find hugely fascinating when someone makes a breakthrough on some problem which is relatively well known. Be it some of the famous problems within number theory of the millennium problems.But back to the ABC conjecture. Ivars Peterson made a good writeup of the conjecture many years ago, so I wont go into trying to beat him, but merely link to it. Also there is of course an entry on Wikipedia as well as the site called abcathome.While I haven’t explained anything about the conjecture, I will still state that it is important. If the ABC conjecture can be proved right, then things like Fermat’s last theorem can be proven in a much simpler way than what Andrew Wiles did back in 1994. A lot of other conjectures follow from the ABC conjecture as well according to Ivars Peterson.

There is a writeup at Mathoverflow which honestly goes way over my head, but take a stab at it.

Besides that I have found two blog posts discussing it, one from Terrence Tao the other from the blog Quomodocumque, and just mentioning Terrence Tao, always seems to put some weight behind the validity. It even seems to be in the public news, since NY times, Huffington post and Business insider covered it.

If you read Danish there is a good summary of the problem here as well.

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