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.
Unification of representation theory and algebras
4 milestones
Core of my third epoch (1927–1935); Göttingen lectures tied representations to algebraic structures.
Gave at least five semester-long Göttingen courses (1924–1929), treating lectures as public research.
In my second epoch (1920–1926) I used the Teilerkettensatz and Vielfachenkettensatz to drive ring-theoretic advances.
Introduced (1918) the general method showing continuous symmetries imply conservation laws, foundational for physics.
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.
I made the ascending and descending chain conditions central tools: one simple finiteness assumption on ideals gives finite generation, primary decomposition and the structure of Dedekind domains.
