Comment by zodiac

We still care about computation and algorithms even when proving theorems in a classical setting!

For e.g., imagine I'm trying to prove the theorem "x divides 6 => x != 5". Of course, one way would be to develop some general lemma about non-divisibility, but a different hacky way might be to say "if x divides 6 then x ∈ {1, 2, 3, 6}, split into 4 cases, check that x != 5 holds in all cases". That first step requires an algorithm to go from a given number to its list of divisors, not just an existence proof that such a finite list exists.