By Catarina Dutilh Novaes
(Cross-posted at M-Phi)
Here's a short piece by the New Scientist on the status of Mochizuki's purported proof of the ABC conjecture. More than 2 years after the 500-page proof has been made public, the mathematical community still hasn't been able to decide whether it's correct or not. (Recall my post on this from May 2013; little change seems to have taken place since then.)
Going back to my dialogical conception of mathematical proofs as involving a proponent who formulates the proof and opponents who must check it, this stalemate can be viewed from at least two perspectives: either Mochizuki is not trying hard enough as a proponent, or the mathematical community is not trying hard enough as opponent.
[Mochizuki] has also criticised the rest of the community for not studying his work in detail, and says most other mathematicians are "simply not qualified" to issue a definitive statement on the proof unless they start from the very basics of his theory.
Some mathematicians say Mochizuki must do more to explain his work, like simplifying his notes or lecturing abroad.
(Of course, it may well be that both are the case!). And so for now, the proof remains in limbo, as well put by the New Scientist piece. Mathematics, oh so human!
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