Mathematics has undergone some rather nice developments recently with the adoption of new techologies, things like on-line journals, the arXiv, this website, etc. I imagine there must be many further developments that could be quite useful.

What I'm thinking of is a website where anyone can contribute formal proofs of theorems. In particular there would be many proofs of the same theorem provided the proof is different -- like a constructive proof of Brouwer's fixed point theorem, and non-constructive proof, etc.

The idea would be to build up a large web of formal proofs, one building on another so that one could eventually do searches through this space of formal proofs to find out what the most efficient proofs are, in the sense of how many ASCII characters it would take to write-up the proof using Zermelo-Frankel set theory. One hope would be to have a big, active database of verified formal proofs. Another would be to have a webpage where you could hope to discover whether or not there are simpler proofs of theorems you know, that you may have not been be aware of.

Being a web-page there would be certain useful efficiencies -- the webpage could "compile" your proof and check to see it's valid. Being a wiki would make it relatively easy for people to contribute and build on an existing infrastructure. And you'd be free to use pre-existing proofs (provided they've been verified as valid) in any subsequent proofs. One could readily check what axioms a proof needs -- for example to what extent a proof needs the axiom of choice, and so on.

Is there any efforts towards such a development? Such a tool would hopefully function like the publishing arm of some sort of modern internet-era Bourbaki.

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