Symplectic manifolds and big stones
Before I stepped away from mathematics, I was heading to the study of differential geometry. Which since has become quite popular, and even contentious. Mohamed Abouzad explains the lack of a complete proof for one of its major conjectures thusly:
There are two conceptions of mathematics. There’s mathematics as: The currency of mathematics is ideas. And there’s mathematics as: The currency of mathematics is proofs.
I think I agree more with Dusa McDuff.
The photo left shows a large stone ball in Bosnia. Suad Keserovic is cleaning away its cotangent bundle. The contention there is whether it is natural or man-made.