All the mathematicians quoted above can successfully write proofs that convince experts that something is true and why something is true; the quotes are about the difficulty of conveying the way the mathematician found that truth. All those mathematicians can convey the that and and the why — except for Mochizuki and his circle.
The matter of Mochizuki’s work is intriguing because the broader research community has neither accepted his proof nor refuted it. The way to bet now is that his proof is wrong:
Professional mathematicians have not and will not publicly declare that “Mochizuki’s proof is X% likely to be correct”. Why? I’d guess one reason is that it’s their job to provide a definitive verdict that serves as the source of truth for probabilistic forecasts. If the experts gave subjective probabilities, it would confuse judgments of different kinds.
Most people with an opinion regard Mochizuki as refuted by Scholze and Stix. They simplified his theory to do it and Mochizuki says they oversimplified, but no one has managed to understand how the details of the full theory would make any difference.
If I was trying to resolve the issue, I might start by formalizing (in Lean) Kirti Joshi’s claimed proof of abc, which is inspired by Mochizuki but which uses more familiar mathematics.
Yeah the next level of the question is something like “we can prove something to a small circle of experts, now how do we communicate the reasoning and the implications to policymakers/interested parties/the public in general”
All the mathematicians quoted above can successfully write proofs that convince experts that something is true and why something is true; the quotes are about the difficulty of conveying the way the mathematician found that truth. All those mathematicians can convey the that and and the why — except for Mochizuki and his circle.
The matter of Mochizuki’s work is intriguing because the broader research community has neither accepted his proof nor refuted it. The way to bet now is that his proof is wrong:
Professional mathematicians have not and will not publicly declare that “Mochizuki’s proof is X% likely to be correct”. Why? I’d guess one reason is that it’s their job to provide a definitive verdict that serves as the source of truth for probabilistic forecasts. If the experts gave subjective probabilities, it would confuse judgments of different kinds.
Most people with an opinion regard Mochizuki as refuted by Scholze and Stix. They simplified his theory to do it and Mochizuki says they oversimplified, but no one has managed to understand how the details of the full theory would make any difference.
If I was trying to resolve the issue, I might start by formalizing (in Lean) Kirti Joshi’s claimed proof of abc, which is inspired by Mochizuki but which uses more familiar mathematics.
Yeah the next level of the question is something like “we can prove something to a small circle of experts, now how do we communicate the reasoning and the implications to policymakers/interested parties/the public in general”