The notion of reduction in #ComputerScience, and particularly the notion of NP-completeness lead to surprising connections between a variety of fields.
Two of my favorite NP-complete problems are:
Kidney Donor Matching Markets (better algorithms literally save lives)
Knot Genus (a seemingly very abstract problem in topology)
Like, oh, you thought you were working on kidney donor matching markets? Surprise your #algorithm can be used to find the genus of a knot! And vice versa!
Big caveat here is: NP-completeness of the decision problems doesn't, by itself, tell you the same relationship between the approximation problems, nor between heuristic algos that might not always get the exact optimum, nor FPT. But TheoryCS has different kinds of reductions that can tell you relationships between those things too!
Which makes me wonder if knot genus is hard to approximate...
h/t @CihanPostsThms for their post on the birdsite about knot genus
