3 ms·

I'm not in academia. How is it possible for people to check if the proof is peer reviewed? Do they have to rely on their own verification?

by yipbub 8y ago

syn0byte 8y ago
It's a proof. It validates itself or it doesn't.
- TimTheTinker 8y ago
  Not so fast. Yes, many proofs do follow from formal logic and maths, but new proofs often connect things or draw inferences that haven't been done previously, thus requiring human review to verify.
- throwawaymath 8y ago
  That's a non-answer. Peer review is a thing in mathematics precisely because it's difficult to verify if a proof is valid. In a sense you can say something like, "A proof is valid or it isn't", but that's vacuous because you still need someone to check it. There are many examples available of proofs which have been initially accepted but later discredited in the mathematical community. There are also many examples of proofs which have been polarizing from their first publication. Consider the controversy surrounding Mochizuki and his Inter-Universal Teichmuller Theory. Also consider that there have been credible (though ultimately incorrect) proofs published by credible people for several famous problems, such as P = NP. The academic community at large can't just eyeball a proof and know it to be true, and often even fundamentally flawed proofs require more than a week of careful attention to be declared incorrect. If you want to argue that peer review is an imperfect system then that's one thing. But to say that a proof is demonstrably true or it isn't ignores the entire complexity of actually figuring out whether or not it's true. Some people can rely upon their own ability to do this, but for the most part the mathematical community is so heavily specialized that even most mathematicians cannot find errors in advanced proofs unless it's their particular subfield of research.
  - syn0byte 8y ago
    Yes, it was a mostly non-answer to a mostly non-question. It was in response to citing a proof in your own work, not a comment on the need for peer review of proofs in general. The bulk of your rebuttal is exactly my own point. Peer review doesn't actually prove anything one way or the other. The ultimate truthfulness of a cited proof is all that matters. The idea that cited proofs should be peer reviewed don't add intrinsic validity, it just fosters academic laziness. "Boy that's a fantastical claim that doesn't seem right; but all the citations are peer reviewed and I see nothing obviously wrong so I guess its true!" -OR- "Boy That's a fantastical claim that doesn't seem right; I don't see anything obviously wrong here so lets double check the cited proofs they based this on." What's the practical upside to only using peer-reviewed proofs besides speed at the cost of fidelity? What's the practical downside to using unreviewed proofs besides "more work"?
    - Jweb_Guru 8y ago
      People do use unreviewed proofs. They just mark those results separately from the rest of the paper so that people (correctly) know not to rely on them, or at least to continue to treat them as tainted; they also usually try to avoid relying on such theorems for critical results. Which is a way better solution than what you're proposing, which is to just mix them in with proofs that people are reasonably confident in and hope for the best.

I'm not in academia. How is it possible for people to check if the proof is peer reviewed? Do they have to rely on their own verification?

by yipbub 8y ago

I'm not in academia. How is it possible for people to check if the proof is peer reviewed? Do they have to rely on their own verification?

syn0byte 8y ago

It's a proof. It validates itself or it doesn't.

TimTheTinker 8y ago
Not so fast. Yes, many proofs do follow from formal logic and maths, but new proofs often connect things or draw inferences that haven't been done previously, thus requiring human review to verify.
throwawaymath 8y ago
That's a non-answer. Peer review is a thing in mathematics precisely because it's difficult to verify if a proof is valid. In a sense you can say something like, "A proof is valid or it isn't", but that's vacuous because you still need someone to check it. There are many examples available of proofs which have been initially accepted but later discredited in the mathematical community. There are also many examples of proofs which have been polarizing from their first publication. Consider the controversy surrounding Mochizuki and his Inter-Universal Teichmuller Theory. Also consider that there have been credible (though ultimately incorrect) proofs published by credible people for several famous problems, such as P = NP. The academic community at large can't just eyeball a proof and know it to be true, and often even fundamentally flawed proofs require more than a week of careful attention to be declared incorrect. If you want to argue that peer review is an imperfect system then that's one thing. But to say that a proof is demonstrably true or it isn't ignores the entire complexity of actually figuring out whether or not it's true. Some people can rely upon their own ability to do this, but for the most part the mathematical community is so heavily specialized that even most mathematicians cannot find errors in advanced proofs unless it's their particular subfield of research.
- syn0byte 8y ago
  Yes, it was a mostly non-answer to a mostly non-question. It was in response to citing a proof in your own work, not a comment on the need for peer review of proofs in general. The bulk of your rebuttal is exactly my own point. Peer review doesn't actually prove anything one way or the other. The ultimate truthfulness of a cited proof is all that matters. The idea that cited proofs should be peer reviewed don't add intrinsic validity, it just fosters academic laziness. "Boy that's a fantastical claim that doesn't seem right; but all the citations are peer reviewed and I see nothing obviously wrong so I guess its true!" -OR- "Boy That's a fantastical claim that doesn't seem right; I don't see anything obviously wrong here so lets double check the cited proofs they based this on." What's the practical upside to only using peer-reviewed proofs besides speed at the cost of fidelity? What's the practical downside to using unreviewed proofs besides "more work"?
  - Jweb_Guru 8y ago
    People do use unreviewed proofs. They just mark those results separately from the rest of the paper so that people (correctly) know not to rely on them, or at least to continue to treat them as tainted; they also usually try to avoid relying on such theorems for critical results. Which is a way better solution than what you're proposing, which is to just mix them in with proofs that people are reasonably confident in and hope for the best.