The Relativity Engine

“Oh, no! I was wondering who the third one might be!”

–Arthur Eddington

Amalie Noether, born 23 March 1882 in Erlangen, Germany, was named for her mother and grandmother, but soon insisted on adopting her middle name for everyday usage. Max Noether, Emmy’s father, was an esteemed mathematician, sometimes credited as one of the finest of the 19th century.

A half-century after her birth, Max found himself outshined by a daughter who enlightened not only the greatest scientist of the 20th century but perhaps the greatest scientist of all time!

Emmy Noether originally intended to pursue French and English. Her proclivity toward mathematics, however, pushed her to continue that academic avenue. She did so against the prevailing winds, as well. At the turn of the century, she entered the University of Erlangen. Just two years prior, the powers-that-be at the university proclaimed that allowing women to study with men would “overthrow all academic order.” Perhaps they were correct. One of only two women in the student pool of 986, she graduated in 1903 and began a career in mathematics rivaled by few of the era.
Emmy Noether circa 1900 - photographer unknown

Noether taught at the University of Erlangen after finishing a dissertation, though she did so without pay for seven years. As a professor, she encountered the works of David Hilbert, a visionary in the field of abstract algebra. Noether managed to expand Hilbert’s methods into new territory. She was such a budding star in abstract algebra that Hilbert recruited her to move to the University of Göttingen, where he taught.

She received more sexist pushback, however. Some members of the faculty attempted to block her from becoming a professor. One said, “What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?” Hilbert retorted, “I do not see that the sex of the candidate is an argument against her admission as privatdozent. After all, we are a university, not a bathhouse.”

At Göttingen, she quickly became a powerhouse. One of her first contributions became her most famous and long-lasting contributions to mathematics. Now called Noether’s Theorem, she proved that a conservation law is associated with any differentiable symmetry of a physical system. Perhaps that sounds like German to you, but it had wide-ranging ramifications.  Physicists Leon M. Lederman and Christopher T. Hill stated in their book, Symmetry and the Beautiful Universe, that the notion is “certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics, possibly on a par with the Pythagorean theorem.”

The proof of that claim about Noether’s proofs is proven by the giant her work elucidated (sorry for this sentence).

Emmy Noether, probably sometime after 1930

In 1915, Albert Einstein presented the General Theory of Relativity to the world. The theory was the generalized form of Special Relativity, which had revolutionized physics a decade earlier. The effect of Einstein’s equations on the scientific and philosophical realms really cannot be overstated. They are the denotations of “paradigm shift.”

David Hilbert had solicited Noether to join him in Göttingen partially to help him understand General Relativity. Hilbert had noticed the theory seemed to violate the law of conservation of energy. Shortly after Einstein’s unveiling, Noether produced her eponymous theorem, which resolved the confusion in General Relativity. She showed that a system of physical laws that possesses some continuous symmetry can conserve quantities. Her ideas and equations were so good that they became a generalized tool of physics. She set out to illuminate that General Relativity did not violate the laws of the universe but ended up showing how every system of physical laws conforms to conservation.

The 33-year-old German had provided the proof for the engine of Relativity.

Hilbert sent her work to Einstein, who wrote, “Yesterday I received from Miss Noether a very interesting paper on invariants. I’m impressed that such things can be understood in such a general way. The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff.”

Noether circa 1930 - photo by Konrad Jacobs

Though immortalized for her first theorem, Noether produced a slew of mathematical achievements. She either broke ground or progressed work in the areas of rings, fields, topology, invariants, hypercomplex numbers, and noncommutative algebra.

Unfortunately, despite this success, life was not a cakewalk. The Nazis expelled Noether from the university in 1933 because she was Jewish. Fortunately, she and many other intellectuals forced from their homelands found welcome in the United States. Bryn Mawr College provided her with a new lease on mathematical studies. She also began to lecture at the Institute for Advanced Study in Princeton, alongside her famous contemporary, Albert Einstein, though Princeton University-proper did not welcome women at the time.

In 1935, a tumor presented in her pelvis. During surgery, doctors found an ovarian cyst the size of a “large cantaloupe” and two benign tumors in her uterus. Noether seemed to recover normally after the procedure for several days. However, a fever that reached 109 degrees Fahrenheit soon emerged and Emmy Noether exited this life on 14 April.

Noether's ashes lie at Bryn Mawr College

Accolades poured in from the world’s great mathematicians. Today, historians often rank her as one of the 20th century’s premier mathematical purveyors. Her theorem continues to hold renown in theoretical physics.

In the early days of the post-Relativity world, as scientists attempted to understand the difficult equations and implications, one of the earliest proponents of the theory, Arthur Eddington, produced one of science’s great quips. He had just presented some astronomical evidence that supported General Relativity. A gentleman named Ludwik Silberstein was somewhat less convinced, though he believed he grasped the concepts. He stated petulantly that Eddington must believe he was one of only three people in the world who actually understood General Relativity. Silberstein’s implication was that Einstein, Eddington, and he were the only three who truly got it. Eddington stood mute, so Silberstein told him not to be so bashful, to give himself credit.

Eddington replied, “Oh, no! I was wondering who the third one might be!”

A truly great scientific burn.

Though General Relativity is a rough concept, the notion that only three people understood it upon publication is an absurdity. Einstein himself dismissed the idea many times. Yet, the myth lives on thanks to Eddington’s wit.

However, if the notion were correct, I think we know who the third person was.

A German woman named Emmy, who well deserves her induction into the Hallowed Halls of Woman Crush Wednesday here at the Headquarters of The Mountains Are Calling.

Further Reading and Exploration

Emmy Noether – Famous Scientists

Emmy NOETHER – History of Scientific Women

In her short life, mathematician Emmy Noether changed the face of physics – ScienceNews

The Woman Who Clarified Einstein’s Idea – Wall Street Journal

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