/sci/ - Science & Math

I've been thinking. Classical mechanics essentially occurs in the category of manifolds, with every problem having a finite dimensional symplectic manifold or tensor field on a 4-manifold as a solution. On the other hand, quantum mechanics takes place in the category of (generally infinite dimensional) rigged Hilbert spaces of distributions on manifolds. Could a solution to the meme problem arise from constructing the appropriate functors between these categories, i.e finding a way to write problems in smooth manifold theory as equivalent problems in distributional analysis?

Careers in SM (not T or E) don't exist. Or rather, the amount of such careers that exist is not significant and they should thus not be actively pursued by anyone who isn't either extremely well connected or somehow one of the top ten people in their field globally by age 30. Wanting a decent position in a national lab or tenure at a good university that isn't a million miles away is like trying to win the lottery or join the NBA.