GitHub for mathematicians.

For every theory, define its axioms and valid logical steps. Let anyone build theorems based on these (validate them automatically), and allow people to fork others theorems to create their own.

It's probably possible to get a lot of proofs from projects like Mizar and Metamath to start with, then let the community build on top of it.

Maybe even a crowd sourced bounty program for unproven theorems, like P=NP. Let people pledge and automatically pay to whoever proves or disproves it.

I think this can really change how mathematical research is done.