an analogy for the Euclid-Euler characterization of even perfect numbers

Showing that if a gas contains oxygen, then it will support combustion is easy, because a simple demonstration suffices. This is what, analogously speaking, Euclid’s contribution consisted of.

Showing that if a gas will support combustion, then it contains oxygen is very difficult, because you have to eliminate all other possibilities. This is what, analogously speaking, Euler’s contribution consisted of, about two thousand years after Euclid’s contribution. This is one of the most celebrated ‘collaborations’ in the history of Mathematics.

keywords:

[Mathematics]

[Number Theory]

[Proof Theory]

[Logic]