nostalgebraist:

hpgross:

Mochizuki summary.

This whole situation is really interesting to me for reasons unrelated to the mathematical content – I guess because Mochizuki seems like “what crackpots would be if they were actually as smart as they think.”

A guy works on his own for many years, developing his own system, coining many new terms no one else uses, gives his system a grandiose name, claims that it can solve a famous open problem – and it doesn’t turn out to be (1) a restatement of things already known or (2) gibberish.

His four papers (1, 2, 3, 4) are way, way over my head – I recognize some of the terms, but can’t follow along or even get the gist of anything – but they’re still interesting to look at.  Compared to almost any other mathematical text, they display a certain … “breathless excitement about the novelty of the author’s inventions,” I guess, which is typical of crackpot papers.  Major technical terms are bolded, which has the effect of emphasizing how many new terms he’s introducing, and many phrases are italicized as though Mochizuki is excitedly stressing the novelty or remarkableness of an idea.  And every page is so jam-packed with fancy math terms that if you told me it was all nonsense, some sort of pastiche of hard math papers, I would believe you.

(Andrew Wiles also worked in secret and wrote a long complex proof filled with specialized concepts, but AFAIK he generally didn’t invent those concepts, and was building closely on the work of others.)