A ‘Useless’ Perspective That Transformed Mathematics
>“Mathematicians basically know everything there is to know about matrices. It’s one of the few subjects of math that’s thoroughly well understood,” said Jared Weinstein of Boston University.I'm genuinely curious how such a statement can be made. I've recently been wondering about if it were possible to prove that one's theorems are exhaustive about a 'space' of possible theorems in an axiomatic system (or some subset thereof, since I'd assume such a space might be infinite (perhaps)).How can we know that there aren't some really surprising properties of matrices that we've previously been unaware of? As far as I can see, we can merely make a statement about that it fits well together with other (limited) findings we've made so far?