A Has the ABC Conjecture Been Proven?

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Shinichi Mochizuki's claimed proof of the ABC Conjecture remains controversial, with mathematicians expressing uncertainty about its validity following a recent conference. The proof is extensive, potentially exceeding a thousand pages, leading to difficulties in peer review due to its complexity and originality. Concerns arise about whether Mochizuki provides sufficient detail in areas where others struggle, which could hinder acceptance. The ongoing debate highlights the risks involved in evaluating such groundbreaking research, especially given Mochizuki's established reputation. The significance of the ABC Conjecture continues to be questioned within the mathematical community.
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Oh, all the great headlines the press could write...
"Mathematicians still unsure if a+b=c"
"Conference on whether a+b=c or not, no solution"

Does Mochizuki write down more details and steps in regions where other mathematicians struggle? It looks like an obvious thing to do.
 
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mfb said:
Oh, all the great headlines the press could write...
"Mathematicians still unsure if a+b=c"
"Conference on whether a+b=c or not, no solution"

Does Mochizuki write down more details and steps in regions where other mathematicians struggle? It looks like an obvious thing to do.

Usually the proof is with a consistent level of detail. It is already very long, perhaps a thousand pages. It could be that different mathematicians struggle with different steps, or maybe they are just overwhelmed with the whole thing. That's the trouble with highly original research: peer review could take many man-years, and there is risk that the whole thing will be useless. If Mochizuki didn't have a heavy rep there would be no chance that his proof would be accepted: too risky an investment.
 
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I never took number theory, but I've taken lots of combinatorics and I usually stay up on math related "news." But I've heard more about this conjecture in the press than I've heard from anybody I know in the math community. Does anyone really think it's really such an important conjecture?

-Dave K
 
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