I want to keep the tradition alive that this is an ‘interdisciplinary’ blog, i.e. to post about stuff I don’t understand, i.e. physics and math.
The first item is an interesting ongoing real life experiment in the sociology of science. 8 years ago, Shinichi Mochizuki claimed to have proven the abc-conjecture (I henceforth refuse for the indefinite future to be shamed by mathematicians for unimaginative technical terms in linguistics). Apparently, this is a conjecture about a deep and unexpected relationship between addition and multiplication.
To achieve that, Mochizuki developed a whole theory of his own, Interuniversal Teichmüller theory (again…), dropped like 1500 pages of impenetrable, idiosyncratic notation on the arXiv and left it at that. He refuses to give talks on it or hold lectures outside of Japan and leaves it to his colleagues to try to explain this to other mathematicians. In these 8 years, nobody was able to verify the proof. Granted, a lot of people simply didn’t try because the volume of necessary reading was way too much and because they couldn’t follow the style of presentation. Then, Jakob Stix and Peter Scholze (of Fields Medal fame) worked through the material, found an alleged gap in the proof and a week-long meeting with Mochizuki in Japan couldn’t remove their doubt (portrayed in this Quanta article).
Now, the math journal of Mochizuki’s institute (of which he is an editor) decided to publish his proof, a weird choice given that this usually means that the proof has been vetted and verified in the peer review process – while at the same time, most experts in the field can’t follow the logic of the proof.
Peter Scholze also commented on the current situation on Peter Woit’s blog, with an ongoing discussion with people who claim to understand the proof.
The last bits are from Scott Aaronson’s answers in his post “AMA: Apocalypse Edition“: here are his thoughts on the It from Qubit idea in fundamental physics (the whole spacetime emerges from quantum entanglement business) and whether undecidability/uncomputability are relevant for physics.
Finally, the editor’s choice for interesting article today appears in Quanta about progress in the Langlands program (a set of conjectures relating vastly different fields in maths to each other in deep and surprising ways).