A lot of math results are curiosities at first but turn out to be important in unexpected ways. The original proof of the existence of irrational numbers depen

A lot of math results are curiosities at first but turn out to be important in unexpected ways. The original proof of the existence of irrational numbers depends on using the Pythagorean theorem to show that the leg of an isosceles right triangle is simultaneously odd and even if irrational numbers do not exist. The proof works because somebody had thought out the seemingly trivial notions of what it means for a number to be odd and even and the effect this has on their squares and ratios. [1] I have always had this picture of somebody's spouse in 500 BC yelling at him to get in and do some useful work instead of standing around in the square drawing numbers. [1] https://en.wikipedia.org/wiki/Irrational_number#Ancient_Greece https://en.wikipedia.org/wiki/Irrational_number#Ancient_Gree...