Substrate

Grothendieck views the mathematician and the problem as complimenting each other, the mathematician using the problem’s natural structure in its solution, rather than striking it with a foreign, invasive method. My view is that any problem that has resisted repeated direct attack from problem solvers, should naturally be of interest to theory builders. If you can’t solve a problem directly, then grow a crystal of theory around the problem and then hope that the solution you are looking for can be located somewhere inside the crystal. This is hard because the same person needs to know about both category theory and the problem domain, which is quite a heavy demand on a human brain.