# Emmy Noether | Mathematician who proved Noether’s theorem

Emmy Noether was a mathematician who discovered perhaps the most profound idea in contemporary physics. Noether’s theorem, which she formulated in 1915, states that symmetries in the universe give rise to mathematical conservation laws. This statement is a crucial basis for physical laws, from those that control the rotation of a wheel or the planets’ orbits around stars, to the complex mathematical framework of general relativity, quantum physics and particle physics.

Noether was born in the small German town of Erlangen, near Nuremberg, in 1882. Although her father, Max Noether, was a professor at the University of Erlangen, she was initially barred from enrolling there because of her gender.

Such discrimination haunted Noether’s career. Even if she eventually received both a bachelor’s degree and a doctorate, no university would employ her for a permanent faculty position. She eventually became one of the world’s foremost experts in the fields of abstract algebra, algebraic topology and the mathematics of symmetry, and worked at the University of Erlangen and then the University of Göttingen.

But for over a decade she was without appointment, salary or formal title, despite the fact that many of the most prominent mathematicians of the time fought for their work, mainly David Hilbert and Felix Klein. It did not change until 1919, when the end of the First World War and the replacement of the German Empire by the liberal Weimar Republic led to a marked change in attitudes towards women’s education.

## Noethers theorem

Noether’s eponymous theorem was inspired by Albert Einstein’s work on relativity during the first years of the 20th century, culminating in his general theory of relativity in 1915. It formalized an idea that was implicit but unspoken in general relativity and many other theories of physics: that symmetries have the key to new theories that describe how nature works.

The mathematician Hermann Weyl, a contemporary of Noether who was greatly influenced by her work, once described a very simple way of thinking about symmetry. “One thing is symmetrical if there is something you can do with it so that it looks the same as before after you finish it,” he wrote. Noether’s central insight was that every symmetry you can observe is linked to a mathematical conservation law.

Translational symmetry, for example – the idea that physics remains largely the same if you move slightly to the left or right, or backwards or forwards – is nothing more than the law of conservation of momentum. The symmetry of moving in a circle corresponds to the law of conservation of momentum. Symmetry in time – that is, physics remains the same when translated forward or backward in time – corresponds to the conservation of energy.

Noether’s theorem adds a practical recipe for making progress in physics: identify a symmetry in the function of the world, and the associated law of conservation allows you to begin to make a meaningful calculation. Much of physics since its discovery has been a search for these symmetries – or, in the case of the development of the standard model of particle physics, broken symmetries in how quantum fields work that indicate where symmetries were at higher energies when the universe was young.

A broken symmetry in the first fraction of the second of the universe, for example, allowed matter to win against its symmetrical twin, antimatter, and created the matter-dominated universe we live in today. Another broken symmetry, associated with the existence of the Higgs boson, gave the electromagnetic and weak nuclear forces the very different strengths they now have.

So, when ideas in physics go, they become no more basic than Noether’s theorem. Unfortunately, Noether’s life after discovering the theorem was not happy. She came from a Jewish family, and when the Nazis came to power in Germany in 1933, her hard-won right to teach at the University of Göttingen was revoked. She emigrated to the United States and taught at Bryn Mawr College in Pennsylvania, but died of complications from cancer surgery two years later.

The reverence that many of Noether’s colleagues felt for her was only increased by her calm spirit and support for others in the face of Nazi repression. Weyl, whose wife was Jewish and who also emigrated to the United States, later wrote that “Emmy Noether – her courage, her sincerity, her concern for her own destiny, her reconciling spirit – was in the midst of all the hatred and cruelty, despair and sadness that surrounds us, a moral consolation ”.

But it is her outstanding work that is most praised, though perhaps not as much as it should be – as is the case with many pioneering female mathematicians and scientists. As Albert Einstein wrote in *The New York Times*, “Fräulein Noether was the most significant creative mathematical genius ever produced since the higher education of women began.” Others may suggest that the last seven words in that sentence are superfluous.

## Key facts

**Full name**: Amalie Emmy Noether

**Born**: March 23, 1882, Erlangen, Germany

**dog**: April 14, 1935 (age 53), Bryn Mawr, Pennsylvania, USA

Emmy Noether is known for her work in mathematical physics, especially Noether’s theorem, which states that symmetries in the universe give rise to mathematical conservation laws.