Amy Noether was a force to be reckoned with in math—and knew it. He had complete confidence in his abilities and ideas. Yet even after a century has passed, those ideas and their contributions to science often go unnoticed. Most physicists are aware of his fundamental theorem, which places symmetry at the heart of a physical law. But how many people know anything about him and his life?
Noether Celebrations, a conference in London this week, hopes to change that. This is a welcome step. In a world where young scientists are looking for inspirational female role models, it is hard to think of a more qualified candidate.
Noether was born in 1882 in Erlangen, Germany. Her parents wanted all of their children to receive doctorates, so many universities at the time did not formally accept women, but she left. After graduation, sexist rules prevented Noether from getting a job in academia. Fearless, for many years he lectured in Erlangen and, from 1915, at the University of Göttingen – often for free.
At the time, the city was the center of the mathematical world, largely due to the presence of its two titans – Felix Klein and David Hilbert. But while Noether was being paid to teach at Göttingen and make his most important contribution, fate and further discrimination intervened: Hitler took power in 1933 and was fired for being Jewish. She fled to the United States and taught at Bryn Mawr College in Pennsylvania, until her death in 1935 at the age of only 53.
Noether devoted his career to algebra and came to see it in a new light. “We all prefer to rely on figures and formulas,” wrote his former student Bartel van der Waerden in his obituary of Noether. “She was concerned only with concepts, not visualization or calculation.”
Noether saw mathematics in what is now called structures. For him, the characteristics of the components of the structure – whether they are numbers, polynomials or anything else – matter less than the network of relationships between the whole set of objects. This enabled him to give evidence that applied to structures more general than the original, and which revealed unseen connections.
It was a new and elegant approach that changed the face of algebra. And Noether realized that this could affect other parts of mathematics. One was topology, a field in which “he published half a sentence and had an everlasting effect”, wrote one mathematician. Before Noether, topologists were counting holes in donuts; She brought to bear the full force of her structures to create something called algebraic topology.
The results Noether published 100 years ago were for him a rare foray into physics that he was not particularly interested in. Albert Einstein had just developed his general theory of relativity, and was struggling to understand how energy fit into his equations. Hilbert and Klein were also working on it, and asked Noether for help.
He helped, that’s an understatement. Noether’s expertise in symmetry led him to discover that the symmetry of a physical system is inextricably linked to physical quantities conserved as energy. These ideas became known as Noether’s theorem (e. Noether Nacher. D. Gess. D. Wis. zu Göttingen, Mathematica.-Physics. Cl. 1918, 235–257; 1918).
As well as answering a riddle in general relativity, this theorem became a guiding principle for the discovery of new physical laws. For example, researchers soon realized that the conservation of net electric charge—which can neither be created nor destroyed—is related to the rotational symmetry of a plane around a point. The effect was profound: those who created the Standard Model of particle physics, and researchers who attempt to extend it, think in terms of Noether’s symmetry.
Some biographies incorrectly portray Noether as a somewhat helpless genius at the mercy of the charitable works of men. In fact, she was an outspoken personality, recognized leader, and the first female plenary speaker at the International Congress of Eminent Mathematicians.
The status of women in mathematics and science has improved since Noether’s time, but prejudice and discrimination remain. Very few prominent female mathematicians get the recognition they deserve. (Only one woman, Maryam Mirzakhani, has received the Fields Medal, and none has won the Abel Prize – the field’s top prize.) Noether is an inspiration: including the UK mathematician Elizabeth Mansfield, who co-organized the London meeting. done and worked. A modern extension of Noether’s work.
We don’t know how many potential Emmy noethers have been unfairly denied the opportunity to showcase their talents. More people should know – and celebrate – that turned the scientific world against the odds.