My method — begriffliche Mathematik, purely conceptual mathematics — works directly with abstractions instead of generalising from known examples. It became how the research field of abstract algebra is done.
In Idealtheorie in Ringbereichen (1921) I gave one of the first general definitions of a commutative ring, proved every ideal is finitely generated under the ascending chain condition, and proved the Lasker–Noether theorem in full generality.
Hilbert and Klein brought me to Göttingen in 1915 to apply my invariant theory to general relativity. My 1918 paper resolved Hilbert's energy paradox and gave physics research a general tool for finding conserved quantities.
I am a mathematician: I developed the theories of rings, fields and algebras that shape abstract algebra, and I proved the two theorems that tie every continuous symmetry in physics to a conservation law.
