This is not really true. It can become very difficult for mathematicians to review the work of their peers. Many times, mistake also evade the scrupulous verifications and the test of time/of many is the best test.

You're confusing yourself w/ fancy words like "proof space". The LLM is not doing any kind of traversal in any meaningful sense of the word b/c the "proof" is often just grammatically coherent gibberish whereas an actual traversal in an actual space of proofs would never land on incorrect proofs.