This is a complete misrepresentation of the breakthrough. The breakthrough was showing that incompatible observables in the real, physical world can be represented by non-Abelian operators. This is by no means a meager accomplishment.
Similarly, the Riemannian geometry used in general relativity was already invented before Einstein came along; his genius was relating real physical parameters to the affine parameters used in the equations.
A.D., if discerning working theories from physical data is so trivial compared to the mathematical manipulation used therein, why haven't mathematicians jumped into the game and snatched up every Nobel Prize in physics, chemistry and medicine awarded over the last 100 years?
It's because the collection and analysis of data is not the intellectually trivial and rote undertaking you presume it to be.
Because they're too busy reassuring themselves of their rightful place at the center of the universe, obviously.
Nice Post. Lets see if you get an honest answer (*not holding my breath*)
Physics, chemistry and medicine are beneath the dignity of great minds, as is common household maintenance.
I would argue that (a) they have in some cases, whether they actually call themselves mathematicians, and (b) the Nobel people like finished work that they can understand. It'd be like awarding the house painter for the hard work done on a Frank Lloyd Wright house. Most of the decent economics prizes have gone to people who style themselves mathematicians.
It's because the collection and analysis of data is not the intellectually trivial and rote undertaking you presume it to be.
If you like the wallpaper and the lace curtains, that's very true.
Ah, I'm kidding on that one. The physicists have finally figured out that remaining ignorant of any field of mathematics is going to hurt them. You'd be surprised the concepts that they use outside of the partial differential equations that they seem so fond of.
Econ is pretty much math and psychology and the gap is getting wider every day. The biologists, though, still treat mathematics like, "OK, what's 2+3? Thanks." Two days later: "OK, what's 4+8? Thanks. No! I don't need to learn the whole theory of addition!" Two days later: "I've got one for you. 7-5? Oh really? You can do that?"