My experience learning math as a programmer was that there was a strange relationship between how much math I understood and how useful I felt math was. When I

My experience learning math as a programmer was that there was a strange relationship between how much math I understood and how useful I felt math was. When I didn't understand calculus I thought that was pretty unessential for being a good programmer. Strange thing though, after learning calculus I find myself using to help understand or model problems a couple of times a week at least. When I didn't understand linear algebra I didn't see how useful it was for anything outside of the obvious niches like graphics programming. But once I learned it I was able to reduce a remarkable number of complex problems to literally 1-3 lines of code. Even when I knew statistics, I didn't see much use in all that fancy advanced theoretical stuff. Now I find one of the most useful, practical tools when modeling problems is the Laplace approximation, and knowing the Cramer-Rao bound let's me realize the limits of the results I get from this. Perhaps most famously, the great mathematician G.H. Hardy, in 1940, discussed how permanently impractical and "useless" number theory was (to be clear, he cited this as a virtue of number theory) in his Mathematicians Apology. Just a few years later Alan Turing (and several others) realized that number theory was the key to securing (and undermining) cryptographic systems. The lesson for me has been that programmers (and I'm sure many other professions) have a habit of finding good uses for the math they've learned.