The Göttingen Period (1915–1933)

Abstract

IN 1893, Hilbert traced the historical development of the theory of algebraic invariants, dividing it into three periods:

• The naive period, represented by the originators of the theory of invariants, the “invariant-twins” Cayley (1821–1895)— from whose forehead, to quote H. Weyl (1885–1955), “this theory sprang around 1850 not unlike Minerva from the forehead of Jupiter, covered with the brilliant shield of algebra”—and Sylvester (1814–897), whose penetrating intelligence, according to MacMahon (1854–1929), made of it a perfect work of art, admired by generations of mathematicians;

• The period of symbolic calculus, invented by Aronhold (1819“1884) and Clebsch (1833–1872), much applied by the latter and his school and used with greatest virtuosity by Gordan even in carrying out gigantic mathematical operations, and still used by Hilbert in his dissertation and several later papers;