Prove that every whole number is mathematically 'interesting'
1 is interesting because it's the first number. 2 is interesting because it's the smallest prime. 3 is the first odd prime, and so on. Now imagine the set of numbers that are NOT interesting for any reason at all — if that set weren't empty, it would have a smallest member. What happens then?
Reveal the answer
The smallest 'uninteresting' number would, by that very fact, become interesting — it would be the smallest member of a notable set, which is itself an interesting property. That's a contradiction, so the set of uninteresting numbers must be empty, meaning every whole number is interesting. It's a tongue-in-cheek proof by contradiction, poking fun at how slippery the word 'interesting' really is, and it's been kicking around math folklore since at least the mid-20th century.
— Mathematical folklore, Interesting number paradox — Proof by contradiction, informal mathematics