IIRC Dijkstra advocated constructing a proof of your program first. This also involves debugging, mistakes and trial-and-error, just at a different level. Mathematical representations and proofs are powerful because general and certain; but they aren't magic and don't write themselves.

It's a lot easier - and a lot more fun - to deal with specific instances, that are concrete, and can be examined and experimented with on a computer.

Logically, one could also work with proofs with a computer to give the same benefits (e.g. coq proof assistant), but for some reason, it doesn't seem to be as much fun in practice. Perhaps because the abstract versions don't have a direct impact; they aren't "live" (idk).