women — a change of pace from her previous students, who were known as “the Noether boys.” She
also lectured at the Institute for Advanced Study
in Princeton, N.J. Her death, less than two years
after her 1935 arrival, left the academic community grieving.
Russian mathematician Pavel Aleksandrov
called Noether “one of the most captivating human
beings I have ever known,” and lamented the
unfortunate circumstances of her employment.
“Emmy Noether’s career was full of paradoxes,
and will always stand as an example of shocking
stagnancy and inability to overcome prejudice,” he said in 1935 at a meeting of the Moscow
But Noether’s theorems remained relevant, particularly within particle physics. In the minute,
enigmatic world of fundamental particles, teasing
out what’s going on is difficult. “We have to rely
on theoretical insight and concepts of beauty and
aesthetics and symmetry to make guesses about
how things might work,” Wilczek says. Noether’s
theorems are a big help.
In particle physics, the relevant symmetries are
hidden kinds known as gauge symmetries. One
such symmetry is found in electromagnetism and
results in the conservation of electric charge.
Gauge symmetry appears in the definition of
electric voltage. A voltage — between two ends of a
battery, for example — is the result of a difference
in electric potential. The actual value of the electric
potential itself doesn’t matter, only the difference.
This creates a symmetry in electric potential:
Its overall value can be changed without affecting
the voltage. This property explains why a bird can
sit on a single power line without getting electrocuted, but if it simultaneously touches two wires
at different electric potentials — bye-bye, birdie.
In the 1960s and ’70s, physicists extended this
idea, finding other hidden symmetries associated
with conservation laws to develop the standard
model of particle physics.
“There’s this conceptual link that — once you
realize it — you have a hammer and you go in
search of nails to use it on,” Wilczek says. Anywhere they found a conservation law, physicists
looked for a symmetry, and vice versa. The standard model, which Wilczek shared a 2004 Nobel
Prize for his role in developing, explains a plethora of particles and their interactions. It is now
considered by many physicists to be one of the
most successful scientific theories ever, in terms
of its ability to precisely predict the results of
At the Large Hadron Collider, at CERN in
Geneva, physicists are still searching for new
particles predicted using Noether’s insights. A
hypothetical hidden symmetry, dubbed supersymmetry because it proposes another level of
symmetry in particle physics, posits that each
known particle has an elusive heavier partner.
So far, no such particles have been found, despite
high hopes for their detection (SN: 10/1/16, p. 12).
Some physicists are beginning to ask if supersymmetry is correct. Perhaps symmetry can only
take physicists so far.
That notion is leaving some physicists in a bit
of a lurch: “If that’s not going to be your guiding motto all the time — that more symmetry is
better — then what will be your guiding motto?”
asks mathematical physicist John Baez of the
University of California, Riverside.
Holograms get symmetric
Despite such disappointments, symmetry maintains its luster in physics at large. Noether’s
theorems are essential tools for developing potential theories of quantum gravity, which would
unite two disparate theories: general relativity
and quantum mechanics. Noether’s work helps
In an era when women
weren’t encouraged in math,
Emmy Noether achieved a
March 23, 1882
She is born in Erlangen,
Max Noether and Ida Amalia
December 13, 1907
She earns her Ph.D. from
the University of Erlangen.
Noether begins working
at the University of
Göttingen at the invitation
of mathematicians David
Hilbert and Felix Klein.
July 23, 1918
She presents her
theorems to the
Mathematical Society in
June 4, 1919
Noether gets permission
to teach under her name at
Göttingen, where she helps
launch abstract algebra.
She finally gets a salary, but
is not a full professor.
The German government
removes Noether from her
post at the university.
She leaves Germany to
become a visiting
professor at Bryn Mawr
College in Pennsylvania.
April 14, 1935
Noether dies after surgery.