A counterexample of the form "X cycles to X after N steps" is easy to check. A counterexample of the form "starting with X we keep going up forever" is hard to check in finite time.
replyAnd still that requires X to not be particularly large. It could conceivably be in ballpark of BB(40).
replyYou, sir, have a very different definition of "not particularly large" than I do!
replyTo be fair, BB(40) is smaller than almost all positive integers.
replyThis was never about the Collatz conjecture itself. If I understand the original discussion correctly (as of a few days ago, not sure if new stuff has come to light), everybody agreed that that framing was just a flashy gimmick. And some Lean maintainers were unhappy about it, since this framing just added noise to the reproducer; they would have preferred a simple proof of False. Nobody ever thought that the disproof might be real.
replyThis had nothing to do with Collatz itself and everything to do with a Lean bug.
replyThe proof was not a proof because it was not sound, even though Lean admitted the proof.