- Person
- Emmy Noether
- Lived
- 1882–1935
- Field
- Mathematics
- From
- German
The story
In the 1920s Göttingen became a hub of mathematical and physical research, drawing scholars from around the world. Emmy Noether's influence there spread through people as much as through her own papers. She gathered a devoted circle of doctoral students and young colleagues, sometimes called the "Noether boys", who absorbed her abstract, conceptual approach to algebra. Because she was not allowed to supervise dissertations on her own, most were officially registered with Edmund Landau or other professors.
She guided more than a dozen doctoral students at Göttingen. The first was Grete Hermann, who defended her dissertation in February 1925; it was an important contribution to ideal theory, and she later became known for work on the foundations of quantum mechanics, speaking fondly of her "dissertation-mother". Jacob Levitzki went on to Yale and then to the Hebrew University of Jerusalem, where he made lasting contributions to ring theory, including Levitzky's theorem. Max Deuring, considered the most promising of the group, became known for arithmetic geometry, and Hans Fitting gave his name to Fitting's theorem and the Fitting lemma in group theory. Ernst Witt and Otto Schilling began under her but had to finish with other advisers after 1933, and Chiungtze Tsen, known for Tsen's theorem, returned to teach in China.
Her wider school included established mathematicians. Bartel van der Waerden arrived in 1924 and built the second volume of his influential 1931 textbook Moderne Algebra largely on her work. Wolfgang Krull greatly advanced commutative algebra using her methods, and Gottfried Köthe developed the theory of hypercomplex quantities. Notes taken by her students formed the basis of several important textbooks.
She was famously generous, letting students and colleagues develop and publish ideas that were really hers. Van der Waerden wrote that she never claimed anything for herself but promoted the work of her students above all. Once, when the university building was closed for a holiday, she gathered her class on the steps, led them through the woods and lectured in a coffee house. After emigrating in 1933 she formed a new circle at Bryn Mawr College, sometimes called the "Noether girls", including Olga Taussky-Todd, Marie Johanna Weiss, Grace Shover Quinn and her doctoral student Ruth Stauffer.
Nathan Jacobson wrote that the development of abstract algebra was largely due to her, through her papers, her lectures and her personal influence on her contemporaries. Through her students and their students, her methods spread across the mathematical world and still shape how algebra is taught today.
Why it matters
Through her students, Noether's methods spread across the mathematical world and shaped how algebra is taught and practised today.
About Emmy Noether
Erlangen-born mathematician who linked symmetry to conservation laws and reshaped abstract algebra, despite years of unpaid work as a woman and dismissal by the Nazis as a Jew.
More about Emmy Noether
- Emmy Noether's bound solved a problem in invariant theoryIn 1915 Emmy Noether solved the finite basis problem for finite groups, proving a degree limit now called Noether's bound. A last open case was settled only in 2000 and 2001.
- Emmy Noether helped classify division algebrasWith Richard Brauer and Helmut Hasse, Emmy Noether proved the Brauer–Hasse–Noether theorem, which allows all central division algebras over a number field to be classified.
- Emmy Noether helped create algebraic topologyAttending lectures by Pavel Alexandrov and Heinz Hopf in 1926–27, Emmy Noether suggested the idea of homology groups, helping turn combinatorial topology into algebraic topology.
- Emmy Noether's 1921 paper gave us Noetherian ringsIn her 1921 paper Idealtheorie in Ringbereichen, Emmy Noether turned the theory of ideals into a powerful general tool, and objects with her chain condition are still called Noetherian.
- Emmy Noether linked symmetry to the laws of conservationIn 1918 Emmy Noether proved that every continuous symmetry in physics comes with a conserved quantity, tying conservation of energy and momentum to symmetry.
- Emmy Noether unified group representation theoryEmmy Noether gave the first general representation theory of groups and algebras, combining scattered earlier results into a single theory of modules and ideals.
- Emmy Noether worked seven years without payOne of only two women among 986 students at Erlangen, Emmy Noether earned her doctorate in 1907 and then worked at the university's Mathematical Institute for seven years without pay.
- Dismissed by the Nazis, Emmy Noether taught at homeAfter the Nazis barred her from teaching in 1933, Emmy Noether gathered students in her apartment to keep doing mathematics, unruffled even when one arrived in SA uniform.
Sources
- Emmy Noether Wikipedia
- Emmy Noether MacTutor History of Mathematics, University of St Andrews
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