Invariant theory

Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions.

Quotes

• The theory of invariants came into existence about the middle of the nineteenth century somewhat like Minerva: a grown-up virgin, mailed in the shining armor of algebra, she sprang forth from Cayley's Jovian head.
  • Weyl, Hermann (1939b), "Invariants", Duke Mathematical Journal 5 (3): 489–502, doi:10.1215/S0012-7094-39-00540-5, ISSN 0012-7094 , p.489

• Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics.
  • Kung, Joseph P. S.; Rota, Gian-Carlo (1984), "The invariant theory of binary forms", American Mathematical Society. Bulletin. New Series 10 (1): 27–85, doi:10.1090/S0273-0979-1984-15188-7, ISSN 0002-9904 , p.27