There have been a number of Scientific discoveries that seemed to be purely scientific curiosities that later turned out to be incredibly useful. Hertz famously commented about the discovery of radio waves: “I do not think that the wireless waves I have discovered will have any practical application.”
Are there examples like this in math as well? What is the most interesting “pure math” discovery that proved to be useful in solving a real-world problem?
Strangest? Functional analysis, maybe. I understand it’s used pretty extensively in quantum field theory, although I don’t actually know firsthand.
That’s a body of mathematics about infinite-dimensional spaces and the operations on them. Even more abstract ways of defining those operations exist and have come up as well, like in Tseirlson’s problem, which recently-ish had a shock negative resolution stemming from quantum information theory.
There’s constructions I find weirder yet, but I don’t think p-adic numbers, for example, have any direct application at this point.