We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work.
We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem.
While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.
However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).
Following encouraging feedback, I decided to make my proof-auditing Codex plugin public. It revolves around a hierarchical way of writing proofs, called Lamport proofs, where one breaks each step down and justifies why it follows. This idea was introduced to me by @nasqret as a semi-formal way of verifying work that is not quite yet ready for formal verification in Lean. It has three skills:
1. $convert-lamport restructures a prose proof into a Lamport proof.
2. $forward-lamport audits a Lamport proof from assumptions to conclusion.
3. $reverse-lamport starts at the conclusion and traces back through what actually supports it. This one's my own little invention and my favorite of the three. It often catches gaps the forward direction can read right past.
I hope it will be useful both for professional mathematicians wanting another pair of careful eyes on their own work as well as amateurs who can use it before seeking feedback from professional mathematicians.
https://t.co/3CUeRaqV7W