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From the post: > More seriously, it’s reasonably well-known among mathematicians that published math papers are full of errors.[1] I think the author's point

by bo1024 5y ago

From the post: > More seriously, it’s reasonably well-known among mathematicians that published math papers are full of errors.[1] I think the author's point is that actually the distinction is less clear: many math papers can't be (easily) replicated, yet people in math aren't too worried. [1] https://twitter.com/benskuhn/status/1419281164951556097 https://twitter.com/benskuhn/status/1419281164951556097

stavros 5y ago
But there's a difference between "can't get the results a second time" and "didn't even get the results the first time". There isn't even so much a notion of "results", just "logically, Y follows from X". If that's wrong, you don't need to run the experiment again (there is no experiment to run), the logic is just flawed.
- topaz0 5y ago
  Right -- you need to run the argument again.
- bo1024 5y ago
  I don’t think it’s quite that simple. A math paper generally says 3 kinds of things: X is true, this is the high level idea of how we can prove X is true, and this is the detailed proof that X is true. As the post mentions, usually when there’s a mistake, X is still true.
  - ConceptJunkie 5y ago
    Well, when there's a mistake found in a proof, the mistake needs to be rectified before the proof can be accepted. There have certainly been proofs that X is true, where X has turned out not to be true based on the fact that there's a mistake in the logic. While it's possible a mistake won't be found, it's a much different problem than running empirical experiments and getting different results.
vlovich123 5y ago
I agree with you. Don’t math proofs build on each other on the assumption that previous results are true? So if you have an incorrect conclusion, you might end up building an invalid map of related results until you find it conflicts (or your a superstar that triple checks the meaningful dependencies you think might be particularly not well scrutinized). In spirit, that’s not unlike scientific lines of inquiry in other disciplines that compound on the errors of previous results (aka replication crisis). It’s obviously quantitatively different in very important and meaningful ways, but the author I think is drawing an apt analogy.

by bo1024 5y ago

stavros 5y ago

But there's a difference between "can't get the results a second time" and "didn't even get the results the first time". There isn't even so much a notion of "results", just "logically, Y follows from X". If that's wrong, you don't need to run the experiment again (there is no experiment to run), the logic is just flawed.

topaz0 5y ago
Right -- you need to run the argument again.
bo1024 5y ago
I don’t think it’s quite that simple. A math paper generally says 3 kinds of things: X is true, this is the high level idea of how we can prove X is true, and this is the detailed proof that X is true. As the post mentions, usually when there’s a mistake, X is still true.
- ConceptJunkie 5y ago
  Well, when there's a mistake found in a proof, the mistake needs to be rectified before the proof can be accepted. There have certainly been proofs that X is true, where X has turned out not to be true based on the fact that there's a mistake in the logic. While it's possible a mistake won't be found, it's a much different problem than running empirical experiments and getting different results.

vlovich123 5y ago

I agree with you. Don’t math proofs build on each other on the assumption that previous results are true? So if you have an incorrect conclusion, you might end up building an invalid map of related results until you find it conflicts (or your a superstar that triple checks the meaningful dependencies you think might be particularly not well scrutinized). In spirit, that’s not unlike scientific lines of inquiry in other disciplines that compound on the errors of previous results (aka replication crisis). It’s obviously quantitatively different in very important and meaningful ways, but the author I think is drawing an apt analogy.