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| THE BEAUTY OF SYMMETRY Emmy Noether had a lasting impact on her colleagues and students, and on the fields of mathematics and physics. |
On a warm summer evening, a visitor to 1920s Göttingen, Germany, might have heard the hubbub of a party from an apartment on Friedländer Way. A glimpse through the window would reveal a gathering of scholars. The wine would be flowing and the air buzzing with conversations centered on mathematical problems of the day. The eavesdropper might eventually pick up a woman’s laugh cutting through the din: the hostess, Emmy Noether, a creative genius of mathematics.
At a time when women were considered intellectually inferior to men, Noether (pronounced NUR-ter) won the admiration of her male colleagues. She resolved a nagging puzzle in Albert Einstein’s newfound theory of gravity, the general theory of relativity. And in the process, she proved a revolutionary mathematical theorem that changed the way physicists study the universe.
It’s been a century since the July 23, 1918, unveiling of Noether’s famous theorem. Yet its importance persists today. “That theorem has been a guiding star to 20th and 21st century physics,” says theoretical physicist Frank Wilczek of MIT.
Noether was a leading mathematician of her day. In addition to her theorem, now simply called “Noether’s theorem,” she kick-started an entire discipline of mathematics called abstract algebra.
But in her career, Noether couldn’t catch a break. She labored unpaid for years after earning her Ph.D. Although she started working at the University of Göttingen in 1915, she was at first permitted to lecture only as an “assistant” under a male colleague’s name. She didn’t receive a salary until 1923. Ten years later, Noether was forced out of the job by the Nazi-led government: She was Jewish and was suspected of holding leftist political beliefs. Noether’s joyful mathematical soirees were extinguished.
She left for the United States to work at Bryn Mawr College in Pennsylvania. Less than two years later, she died of complications from surgery — before the importance of her theorem was fully recognized. She was 53.
Although most people have never heard of Noether, physicists sing her theorem’s praises. The theorem is “pervasive in everything we do,” says theoretical physicist Ruth Gregory of Durham University in England. Gregory, who has lectured on the importance of Noether’s work, studies gravity, a field in which Noether’s legacy looms large.
Making connections
Noether divined a link between two important concepts in physics: conservation laws and symmetries. A conservation law — conservation of energy, for example — states that a particular quantity must remain constant. No matter how hard we try, energy can’t be created or destroyed. The certainty of energy conservation helps physicists solve many problems, from calculating the speed of a ball rolling down a hill to understanding the processes of nuclear fusion.
Symmetries describe changes that can be made without altering how an object looks or acts. A sphere is perfectly symmetric: Rotate it any direction and it appears the same. Likewise, symmetries pervade the laws of physics: Equations don’t change in different places in time or space.
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