I was just thinking about how Schroedinger 'worked up' his famed equation. A physics historian told me (not in these words) that he didn't actually 'derive it' but sort of ... 'arrived at' it.
The WP bio says that in his fourth paper on the subject (which first involves time), he greatly simplified the -equation- by introducing complex numbers ... and then:
"something magical happened, and all of wave mechanics was at his feet.... Schrödinger was not entirely comfortable with the implications of quantum theory. He wrote about the probability interpretation of quantum mechanics, saying: 'I don't like it, and I'm sorry I ever had anything to do with it.'"
Introducing complex numbers -made the equation more beautiful-. The equation e^(i*pi) = i^2 is amazing, but may also suggest that we're not looking at the math's basement level.
It's been suggested that all of the pyramids' stones couldn't have been cut with two-foot-long copper saws. It may be that the 'beauty' people are seeking is limited by their tools, as much as their imaginations.