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Palomar: A registry of Lean verified mathematics

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Re: Palomar: A registry of Lean verified mathematics

#41
post #11

> The submission process is thorough, but achievable: as a test, I successfully managed to submit my own recent formalization [...] I find this kind of endearing, how he almost makes it sounds like "If even I can do it, you can too!", disregarding he's probably the most prolific mathematician currently alive. Some years ago I suggested it might be interesting to have a kind of blockchain of formally verifiable mathem…

> but was quickly shutdown by people telling me it was a useless endeavor due to Goedels incompleteness theorems

You shouldn't have listened to them, "incompleteness" only applies when you try to encode the language and meta-language in the same encoding—which no one actual does. (For example, programming language syntax is complete.)

Re: Palomar: A registry of Lean verified mathematics

#43

> A zeroth approximation of what Palomar intends to be is the analogue of a preprint server for Lean proofs. More precisely, Palomar (which is named after the astronomical observatory) is a registry of external Github repositories (or more precisely, “snapshots” of such repositories, as represented by a specific Github commit) containing Lean code adhering to the current best practices for such formalizations, Either…

It requires GitHub because it forks the submission repo to keep its own immutable copy. It's just using GitHub as a costless datastore. It was probably just done that way to keep things fast and simple and get something out there as quickly as possible. There are only 15-16 verified submissions so far, so it's not like this needs something complicated yet

Re: Palomar: A registry of Lean verified mathematics

#44
post #11

> The submission process is thorough, but achievable: as a test, I successfully managed to submit my own recent formalization [...] I find this kind of endearing, how he almost makes it sounds like "If even I can do it, you can too!", disregarding he's probably the most prolific mathematician currently alive. Some years ago I suggested it might be interesting to have a kind of blockchain of formally verifiable mathem…

> Some years ago I suggested it might be interesting to have a kind of blockchain of formally verifiable mathematical proofs, How does a blockchain help here? > but was quickly shutdown by people telling me it was a useless endeavor due to Goedels incompleteness theorems. I'm curious about those arguments ... what does incompleteness have to do with this? > But I think the method of proving things will soon go out st…

Maybe some sort of blockchain could make it so that you don't have to verify the whole proof yourself, to know that it's true. Because some of these proofs could take a long time to verify. Similar to a Merkle tree, but you'd have to make it respect the laws of mathematical proof in some way.

edit: Yes I think this should be possible, using a "recursive SNARK".

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