>>12088797>>12088805>>12088809>>12088812I know: Group theory gets used in quantum mechanics and elsewhere in physics, but the group theory used is trivial. E.g., never hear of Sylow's theorem, the Jordan-Holder theorem, the Feit and Thompson work on simple groups, etc. For group representations,you need to know very little about group theory to do group representations (I wrote my undergrad honors paper in it). Heck, I wrote a paper on multidimensional, distribution-free hypothesis tests based on groups of measure-preserving transformations, and the group theory needed was trivial. Similarly for the use of group theory in ergodic theory, ODE, and integer linear programming. Groups are nice, but really need to know only about 10 pages of the basics and can pick it up in an hour whenever need it. Or, you want group theory to attack Rubik's cube?
Yes, Hamming used some finite field theory in error correcting codes: Now that work and a dime won't cover a 10 cent cup of coffee. Instead, coding theory has moved on. Yes, yes, I know, from A. Wiles we finally have a proof of Fermat's last theorem; other than Wiles, who made any money with that?
Algebraic geometry is building expensive houses on-spec that stand empty too long. There's just no significant promise of return on investment there, or elsewhere in abstract algebra. E.g., the US NSA pushed hard on finite field theory for years before RSA showed that they had been wasting their time.
US mathematics' long, disastrous, self-destructive love affair with algebra, algebraic geometry, algebraic topology, algebraic number theory has been a major contributor to shrinking Federal research grants to mathematics, shrinking departments, mathematicians who'd swap their Ph.D. for an electrician's license, and the technology world putting mathematics on the back burner if not in the trash. Can cover nearly all abstract algebra in 1 word: Useless.
