They are proven with with math, but their implementation in code certainly isn’t. If it were that simple, we would be using languages like Coq and TLA+ for writing software. But we usually don’t, because math does not cleanly translate into usable programs, it needs a human to distill it into the necessary steps the computer must follow.
No really. They are math themselves. Algorithms have nothing to do with implementation. The whole CLRS books algorithms are written with pseudocode. By your logic Turing machines and many other models of computations are not math. Just something is imperative doesn't mean it's not mathematics.
Plenty of excellent programmers are not mathematicians. How would that work if programming were just math? That’s like saying physics is just math while ignoring all of the experimental parts that have nothing to do with math.
