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
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.
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.
Noether’s theorem proclaims that every such
symmetry has an associated conservation law, and
vice versa — for every conservation law, there’s an
Conservation of energy is tied to the fact that
physics is the same today as it was yesterday. Likewise, conservation of momentum, the theorem
says, is associated with the fact that physics is the
same here as it is anywhere else in the universe.
These connections reveal a rhyme and reason
behind properties of the universe that seemed
arbitrary before that relationship was known.
During the second half of the 20th century,
Noether’s theorem became a foundation
of the standard model of particle physics,
which describes nature on tiny scales and predicted the existence of the Higgs boson, a particle
discovered to much fanfare in 2012 (SN: 7/28/12,
p. 5). Today, physicists are still formulating new
theories that rely on Noether’s work.
Constant beauty Symmetries imply that certain
quantities are conserved, according to Noether’s theorem.
The equation above expresses that concept: The quantity
in the parentheses doesn’t change over time.
In her short life, the
changed the face of
physics By Emily Conover