alt Hacker News> Plus the ancient mathematicians did very well with just their intuition.
They did. But they also got things wrong, such as thinking that pointwise limits are enough to carry over continuity (see here for this and other examples: https://mathoverflow.net/a/35558). Anyway, mathematics has changed as a discipline, we now have strong axiomatic foundations and they mean that we can, in principle, always verify whether a proof is correct.
Certainly I'm glad we have better tools now, and know the rules. Sure beats the old days. As for verification, well I'm big into Lean 4 and it plays well with NSA since transferring theory and proofs between finite and infinite saves a lot of labor on the computer.