4 ms·

The problem with that rule of thumb is that unless there's some status/reward for completing the result, it won't happen. People will just put up the formally

by pfdietz 2mo ago

The problem with that rule of thumb is that unless there's some status/reward for completing the result, it won't happen. People will just put up the formally verified result and call it a day, and there's no incentive for them or anyone else to clean things up. We'll end up with incomprehensible math because comprehensibility isn't rewarded. No one is going to get a Fields Medal, or tenure, for digesting someone else's results.

cubefox 2mo ago
> The problem with that rule of thumb is that unless there's some status/reward for completing the result, it won't happen. He says it shouldn't be able to published if they can't explain it. Publishing it is the reward.
- pfdietz 2mo ago
  The thing is, the cost of creating these results, and the expertise needed, is being greatly reduced. So it's possible for people who wouldn't actually care about the results to spoil them by just putting out a formalized proof (for example, to Tao's Palomar site). These people wouldn't care about the prestige; they aren't on a career track where that would matter.
  - cubefox 2mo ago
    I guess then the likely outcome is that nobody will get any more prestige from presenting new proofs. The fall of the theorem economy, as David Bessis says: https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e... Edit: I just saw Tao actually mentions the above essay in his paper.
BeetleB 2mo ago
> People will just put up the formally verified result and call it a day, and there's no incentive for them or anyone else to clean things up. The incentive will be to be able to publish in a top tier journal. I suspect what Tao is advocating for is having journals reject such manuscripts. > No one is going to get a Fields Medal, or tenure, for digesting someone else's results. I'm sure no one gets a Field's Medal if others can't digest their results.

by pfdietz 2mo ago

cubefox 2mo ago

> The problem with that rule of thumb is that unless there's some status/reward for completing the result, it won't happen. He says it shouldn't be able to published if they can't explain it. Publishing it is the reward.

pfdietz 2mo ago
The thing is, the cost of creating these results, and the expertise needed, is being greatly reduced. So it's possible for people who wouldn't actually care about the results to spoil them by just putting out a formalized proof (for example, to Tao's Palomar site). These people wouldn't care about the prestige; they aren't on a career track where that would matter.
- cubefox 2mo ago
  I guess then the likely outcome is that nobody will get any more prestige from presenting new proofs. The fall of the theorem economy, as David Bessis says: https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e... Edit: I just saw Tao actually mentions the above essay in his paper.

BeetleB 2mo ago

> People will just put up the formally verified result and call it a day, and there's no incentive for them or anyone else to clean things up. The incentive will be to be able to publish in a top tier journal. I suspect what Tao is advocating for is having journals reject such manuscripts. > No one is going to get a Fields Medal, or tenure, for digesting someone else's results. I'm sure no one gets a Field's Medal if others can't digest their results.