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The statement's a little hyperbolic, but I think you're misunderstanding the author's point. The point is that math is aimed at trying to build understanding i

by pseut 13y ago

The statement's a little hyperbolic, but I think you're misunderstanding the author's point. The point is that math is aimed at trying to build understanding in contrast to producing logically airtight proofs. The proofs are important to make sure that our understanding is right, but there's more to it than that. I agree that's not the literal sentence you quoted, but it's definitely the theme of the article: according to many of the people cited, Mochizuki's shirking his responsibility by not explaining how to understand the result, regardless of whether the proof is correct or incorrect. Caveat: I Am Not A Mathematician (IANAM)

brazzy 13y ago
> The point is that math is aimed at trying to build understanding in contrast to producing logically airtight proofs. The proofs are important to make sure that our understanding is right, but there's more to it than that. Understanding is necessary to be certain the proof is correct. After that is ensured, many mathematicians will happily use the proof and base their work on it without understanding it. > Mochizuki's shirking his responsibility by not explaining how to understand the result, regardless of whether the proof is correct or incorrect. The main problem caused by his "shirking" is that it leaves the correctness of the proof uncertain and trying to fully understand it is a lot of work that could turn out to be wasted. People want to confirm the proof, and Mochizuki could make it much easier and less costly for them, but for some reason declines to do so.
- pseut 13y ago
  From TFA: "Even an incorrect proof is better than no proof, because if the ideas are novel, they may still be useful for other problems, or inspire another mathematician to figure out the right answer." edit: I can see taking issue with the word, "universe" in the original quote. I have trouble seeing how the word "understand" is debatable.

by pseut 13y ago

brazzy 13y ago

> The point is that math is aimed at trying to build understanding in contrast to producing logically airtight proofs. The proofs are important to make sure that our understanding is right, but there's more to it than that. Understanding is necessary to be certain the proof is correct. After that is ensured, many mathematicians will happily use the proof and base their work on it without understanding it. > Mochizuki's shirking his responsibility by not explaining how to understand the result, regardless of whether the proof is correct or incorrect. The main problem caused by his "shirking" is that it leaves the correctness of the proof uncertain and trying to fully understand it is a lot of work that could turn out to be wasted. People want to confirm the proof, and Mochizuki could make it much easier and less costly for them, but for some reason declines to do so.

pseut 13y ago
From TFA: "Even an incorrect proof is better than no proof, because if the ideas are novel, they may still be useful for other problems, or inspire another mathematician to figure out the right answer." edit: I can see taking issue with the word, "universe" in the original quote. I have trouble seeing how the word "understand" is debatable.