Learn proofs well and you get pretty good and knowing when you’re right. Enough for almost any problem you’ll be likely to encounter in a math textbook anyway.
That's what seperates them both, it's not about immediate formal checking from a compiler here, but rather if our proof is being justified adequately according with the rules of deduction and reasoning, it's a more intuitive approach in math, although you do end up knowing whether something is right or wrong, akin to programs.
