When Mochizuki's (claimed) ABC-proof came out, various media and forums, e.g. New Scientist & MathOverflow, suggested that he used “Inter-universal geometry” (for which Wikipedia has no article or redirect as of 2015-05-10), others (correctly) that his papers on “Inter-universal Teichmüller theory” are where he gives his proof. Is this a mix-up on someone’s part? What is the difference between the subjects, if any? Is “geometry” just his older terminology?

He does have papers on both, but IUG is a handwritten PDF from 2004 of what look like lecture notes, while those on IUTT (I to IV under References in Wikipedia) are cleanly type-set papers from 2012. The fourth of these includes the claim to prove ABC. Some searching on my part found various references, but left me unclear what the relevance of IUG was.

  • To my understanding Teichmuller theory is a subfield of geometry, so one term is just less specific than the other. – Ian May 10 '15 at 14:20
  • @Ian: Do you only deduce that from the definitions of the terms, or have you seen that Mochizuki uses them thus? – PJTraill May 10 '15 at 15:10
  • Teichmuller theory itself is not something that Mochizuki created, it's an older subject. – Ian May 10 '15 at 15:27
  • Does that apply to inter-universal geometry too? And did Mochizuki invent the inter-universal form of Teichmüller theory? – PJTraill May 10 '15 at 15:35
  • My understanding (which is quite limited; I am neither a geometer nor a number theorist) is that Mochizuki created the "inter-universal" versions of the subjects that he studied. – Ian May 10 '15 at 15:37

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