I don't know about beauty, but I realized I was done with math during my functions of a real variable class when we did a proof to the extent of, "There exists a rational number between any two irrational numbers. There exists an irrational number between any two rational numbers. Prove that their are more irrational numbers then rational numbers." Re countably infinite versus uncountably infinite.

Thankfully my crypto course came along a few years later and restored my faith in math.