[liadmat]

I always thought it would be nice to have a GitHub-like thing for formal proofs. Where anyone can define a theory using a set of axioms, and everyone else can build theorems on top of it (and on top of existing theorems), with a series of formal steps that are verified by the system.

[JadeNB]

Cameron Freer started something like this, but I think it stagnated: http://vdash.org . Tom Hales put a lot of his formal proof work on Google Code: https://code.google.com/p/flyspeck . I don't know if he has any plans to migrate to GitHub, though.