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.
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.
All areas3 of 20 fields
Dominant mathematics focus
Algebra & Number Theory · Geometry & Topology
