One I remember hearing is a proof that there is no first uninteresting number: If there were, it would be an interesting number, as the first of any kind of number would be interesting!

What are "interesting numbers"?

Itâ€™s your opinion if a number is interesting or not.

You have the proof right but the theorem wrong. What you're proving is that *all numbers are interesting.* Proof: If not, there must be a smallest uninteresting number... etc.

I think I heard the proof specifically for what I said, but one could also use it to prove what you said.