[DoktorL]

> E.g. "By repeating the process enough times, the probability that you never catch me becomes smaller than, say, getting struck by lightning" doesn't seem to show it's a proof?

That's fine though, because the point isn't really to publish math papers without disclosing proofs. For example, presenting a valid digital signature is sometimes colloquially called a proof that you had the private key, even though there is 1 in gazillion chance that you didn't. For such practical tasks, very high chance tends to be good enough.