Over the last couple of days I’ve had cause to read a little bit about the life of the German mathematician Emmy Noether, who was responsible for some of the most important work in abstract algebra during the first third of the 20th century; in addition, Noether’s Theorem is important in theoretical physics, where it describes the connection between symmetry and conservation laws.
Born in Erlangen in 1882 into a Jewish family (to the algebraic geometer Max Noether and his wife Ida Kauffmann) she displayed an early talent for languages, and qualified as a teacher of French and English, but decided she wanted to study mathematics at university. At the time (c.1900) women weren’t permitted to formally enrol at German universities, although with the individual lecturers’ permission they could sit in on lectures. Nevertheless, she succeeded in persuading Erlangen to admit her as a student in 1904 (after the restrictions were lifted) and successfully completed her PhD in 1907. For the next eight years she taught at Erlangen, essentially as her father’s unpaid teaching assistant, before Felix Klein and David Hilbert succeeded in arranging a more substantive post at Göttingen (at the time, one of the most prestigious mathematics departments in Europe). Initially (due largely to complaints from the philosophy department) she taught under Hilbert’s name, but in 1919 she was awarded her habilitation diploma and promoted to the rank of Privatdozent (lecturer).
She worked at Göttingen for the next couple of decades, along the way making some really important discoveries in algebra: amongst other things, she formulated and proved the First, Second and Third Isomorphism Theorems which are a standard component of pretty much every undergraduate group theory textbook; also Noetherian rings are an important class of algebraic structures which she studied and were subsequently named after her. She supervised 14 doctoral students (according to the Mathematics Genealogy Project) and in 1932 was invited to give a plenary address at the International Congress of Mathematicians.
The following year, she was dismissed from Gottingen along with several other colleagues (including Max Born and Richard Courant) as a result of legislation enacted by the new Nazi government, forbidding Jewish academics from working at German universities. She reacted with stoicism and continued unofficially lecturing to students at her house. Her colleague Hermann Weyl later remarked that “her courage, her frankness, her unconcern about her own fate, her conciliatory spirit, was in the midst of all the hatred and meanness, despair and sorrow surrounding us, a moral solace”. Shortly afterwards, she was invited to take up a visiting professorship at Bryn Mawr College, Pennsylvania. She worked there and at the Institute for Advanced Study in Princeton, for the next year and a half, until her sudden death in April 1935 as a result of complications from surgery.
I’d been aware of some of the details of her life, and obviously I learned the Isomorphism Theorems as an undergraduate (although I only learned of her involvement relatively recently) but reading about her in more detail over the last few days I’ve been struck by how particularly impressive her achievements were given that she was Jewish and a woman working in an environment that was often unsympathetic to both.