# Science History: Einstein’s mathematician

## Emmy Noether overcame sexism and antisemitism to become a towering mathematician – and Einstein’s friend. Jeff Glorfeld reports.

Amalie Emmy Noether was born on 23 March 1882, in the Bavarian city of Erlangen.

Her father, Max Noether, was called “one of the finest mathematicians of the nineteenth century” by Leon Lederman and Christopher Hill in their book *Symmetry and the Beautiful Universe*, and she was to follow in his footsteps.

A story in journal *Science News* on 23 June 2018 carried the headline: “In her short life, mathematician Emmy Noether changed the face of physics”.

As with so many women in science, however, it was no easy road.

Prevented from formally studying mathematics at university, for the simple reason that she was female, Noether instead went to a general finishing school and in 1900 was certified to teach English and French.

She was later allowed to audit classes in mathematics at the University of Erlangen-Nuremberg, where her father taught, eventually earning an undergraduate degree.

In 1904 she was allowed to enrol in a doctoral program at the university, and three years later she received a PhD. She spent nearly eight years there, working without pay or an official position.

In 1915 she moved to the University of Gottingen, where she was at first permitted to lecture only as an “assistant” under a male faculty member’s name. She didn’t receive a salary until 1923.

By 1915, however, Noether’s brilliance had been noticed by her colleagues. David Hilbert and Felix Klein, both renowned mathematicians, asked her for help.

A problem had arisen with Albert Einstein’s new theory, general relativity, which had been introduced several months earlier.

It seemed that Einstein’s work did not adhere to a principle known as conservation of energy, which states that energy can change forms but can never be destroyed. Total energy is supposed to remain constant.

She resolved the issue with one of two theorems she proved that year, American science writer Steve Nadis wrote in 2017, “by showing that energy may not be conserved ‘locally’ – that is, in an arbitrarily small patch of space – but everything works out when the space is sufficiently large”.

Nadis continued: “The other theorem, which would ultimately have a far greater impact, uncovered an intimate link between conservation laws (such as the conservation of energy) and the symmetries of nature, a connection that physicists have exploited ever since.

“Today, our current grasp of the physical world, from subatomic particles to black holes, draws heavily upon this theorem, now known simply as Noether’s theorem.”

In 1918 Noether published her work, of which American theoretical physicist Frank Wilczek, of the Massachusetts Institute of Technology, said: “That theorem has been a guiding star to twentieth and twenty-first century physics.”

An article in the *Jewish Women’s Archive*, by Saunders MacLane, one of her students, says that in 1920 she “turned her attention to algebra, with decisive axiomatic treatment of the theory of ideals as they apply to number theory (to factor algebraic integers) and to algebraic geometry (curves and surfaces defined by equations).

“She inspired many students, in particular BL Van der Waerden, who delivered brilliant lectures following her ideas and then presented them in his famous text *Modern Algebra*, which revolutionised the subject.”

In 1933, with the rise of Nazi Germany, Noether was dismissed from her position at Gottingen, but in September, with Einstein’s help, she received a guest professorship in the US, at Bryn Mawr College, in Pennsylvania. She also lectured at the Institute for Advanced Study at Princeton University.

In April 1935, however, she had surgery to remove a uterine tumor and died from a postoperative infection.

A 2015 article in the *Washington Post* cites a letter Einstein sent to the New York Times after Noether’s death.

“In the judgment of the most competent living mathematicians,” penned the great man, “Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.”

*Jeff Glorfeld is a former senior editor of The Age newspaper in Australia, and is now a freelance journalist based in California, US.*

- https://www.revolvy.com/page/Max-Noether
- https://www.penguinrandomhouse.com/books/231102/symmetry-and-the-beautiful-universe-by-leon-m-lederman-and-christopher-t-hill/9781591025757
- https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math
- https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math
- https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math
- https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math
- http://discovermagazine.com/2017/june/the-universe-according-to-emmy-noether
- https://jwa.org/encyclopedia/article/noether-emmy