There are proof assistants https://en.wikipedia.org/wiki/Proof_assistant that would encode a mathematical proof as code, and verify its correctness for you.

Writing completely formal proof is very painstaking, because it means we will need to flash out a lot and a lot of details (which are mostly trivial for experts) for computers to accept it, and we also need to know how to work with proof assistants.

Human proofs often ignore these details to make it readable, yet also make it more prone to mistakes. Whereas formalized prove in proof assistant can very rarely be wrong (unless there is an unlikely bug in the assistant kernel), but mostly unreadable (unless the proof is incredibly elegant).

So in general, translating good human proof to computer proof requires more expert labor than huge conceptual innovation, yet it usually require the steep learning curve of understanding the ins and outs of a proof assistant, which can take years of experience.

LLM used to be pretty bad at this because even filling in trivial details can quickly derail them. Recently a few flagship coding model are finally able to do this, albeit with a large amount of token consumption in thinking.