You should take some time to read this very well-written piece about Shin Mochizuki’s claimed proof of the abc conjecture: “The Paradox of the Proof”, by Caroline Chen.

It covers the story from all angles: a biog of Mochizuki, a clear, non-nonsense description of the conjecture, the tale of the mathematical community’s attempts to understand it, and some insightful rumination on the nature of proof.

via Marcus du Sautoy on Twitter, among others

(TL;DR – still nobody knows whether the proof is correct or not)