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This title is extremely clickbaity. If a few people in Japan believe something that nobody else believes, that thing is not "only true in Japan", nobody knows if it's true anywhere.
Well, not quite. Sometimes believing in things makes them true.
What can be proven depends on what is allowed be a part of mathematics and logic. Zero, negative numbers, imaginary numbers and a lot other stuff had go through the acceptance first before they can be used in proofs. A lot of foundational concepts in logic, reality, causality, boolean exclusivity, spatial locality - had to be rewritten due to advances in quantum physics etc.
We went through this over a 100 years ago, math now sits on very solid axioms (look up ZFC), they're not questioning that.
People question C all the time. That might be the most prominent ideological difference in mathematical philosophy.
Does it matter? Of course not, but people question it anyway.
> The error concerned a part of the proof called Conjecture 3.12, seen as a vital part of Mochizuki’s efforts to solve the abc conjecture, which Scholze and Stix claimed suffered from an unjustified leap of logic. “We came to the conclusion that there is no proof,” wrote the pair, who didn’t respond to a request to comment for this article. This is hard to understand. This element of the "proof" is named "Conjecture…
This title is extremely clickbaity. If a few people in Japan believe something that nobody else believes, that thing is not "only true in Japan", nobody knows if it's true anywhere.
Well that's hardly suspicious at all.
> The error concerned a part of the proof called Conjecture 3.12, seen as a vital part of Mochizuki’s efforts to solve the abc conjecture, which Scholze and Stix claimed suffered from an unjustified leap of logic. “We came to the conclusion that there is no proof,” wrote the pair, who didn’t respond to a request to comment for this article. This is hard to understand. This element of the "proof" is named "Conjecture…
Well, I think it's not even called "Conjecture 3.12", but "Corollary 3.12", which is funnier :D
I think the intrigue is mainly that it's at such a high level that lay mathematicians (like me) have no hope of understanding the debate. It's a situation that lends itself to crazy speculation, because nothing you say about it can easily be challenged.
This title is extremely clickbaity. If a few people in Japan believe something that nobody else believes, that thing is not "only true in Japan", nobody knows if it's true anywhere.
I really do wish "extremely clickbaity" just meant something like this. Clearly our experiences with clickbait must be very different.
> Another prize is also awarded annually to people who have made important progress in studying IUT – the first such prize, with an award of $100,000, went to Mochizuki and his colleagues. Well that's hardly suspicious at all.