I wondered whether physical experiments can find the outcome of otherwise intractable mathematical problems.
For example, solitons or other non-perturbative effects in QFT cannot be seen at any order in perturbation theory, and are difficult to calculate, but could in principle be measured. Is nature doing the whole path integral/the whole perturbative expansion at once? Does that mean a computer could, in principle do it, in a finite time? or can nature solve math problems that are otherwise impossible?