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.<p>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)).<p>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?