to write an equation for conservation of energy
resulted in a tautology: Like writing “0 equals 0,”
the equation had no physical significance. This
situation was a surprise to the pair; no previously
accepted theories had energy conservation laws
like this. The duo wanted to understand why gen-
eral relativity had this peculiar feature.
The two recruited Noether, who had expertise
in relevant areas of mathematics, to join them in
Göttingen and help them solve the riddle.
Noether showed that the seemingly strange
type of conservation law was inherent to a certain
class of theories known as “generally covariant.”
In such theories, the equations associated with
the theory hold whether you’re moving steadily
or accelerating wildly, because both sides of the
theory’s equations change in sync. The result
is that generally covariant theories — including
general relativity — will always have these nontraditional conservation laws. This discovery is
known as Noether’s second theorem.
This is what Noether did best: fitting specific
concepts into their broader mathematical context. “She was just able to see what’s right at the
heart of what’s going on and to generalize it,” says
philosopher of science Katherine Brading of Duke
University, who has studied Noether’s theorems.
On her way to proving the second theorem,
Noether proved her first theorem, about the connection between symmetries and conservation
laws. She presented both results in a July 23, 1918,
lecture to the Göttingen Mathematical Society,
and in a paper published in Göttinger Nachrichten.
It’s not easy to find quotes of Noether reflecting
on the significance of her work. Once she made a
discovery, she seemed to move on to the next thing.
She referred to her own Ph.D. thesis as “crap,” or
“Mist” in her native German. But Noether recognized that she changed mathematics: “My methods
are really methods of working and thinking; this is
why they have crept in everywhere anonymously,”
she wrote to a colleague in 1931.
“Warm like a loaf of bread”
Born in 1882, Noether (her full name was Amalie
Emmy Noether) was the daughter of mathematician Max Noether and Ida Amalia Noether.
Growing up with three brothers in Erlangen,
Germany, young Emmy’s mathematical talent
was not obvious. However, she was known to solve
puzzles that stumped other children.
At the University of Erlangen, where her
father taught, women weren’t officially allowed
as students, though they could audit classes
with the permission of the professor. When the
rule changed in 1904, Emmy Noether was quick
to take advantage. She enrolled and earned her
Ph.D. in 1907.
As a woman, Noether struggled to find a paid
academic position, even after being recruited
to the University of Göttingen. Her supporters
there argued that her sex was irrelevant. “After
all, we are a university and not a bathing establishment,” Hilbert reportedly quipped. But that
wasn’t enough to get her a salary.
Although Göttingen finally began paying
Noether in 1923, she never became a full-fledged
professor. Hermann Weyl, a prominent mathe-
matician at the university, said, “I was ashamed to
occupy such a preferred position beside her whom
I knew to be my superior as a mathematician in
Noether took these knocks in stride. She
was beloved for her buoyant personality. Weyl
described her demeanor as “warm like a loaf of
She made a habit of taking long walks in the
countryside with her students and colleagues,
holding lengthy, math-fueled debates. When
legs began to ache, Noether and company would
plop down in a meadow and continue chatting.
Sometimes she’d take students to her apartment
for homemade “pudding à la Noether,” convers-
ing until remnants of the dessert had dried on
the dishes, according to a 1970 biography, Emmy
Noether 1882–1935, by mathematical historian
When she landed at Bryn Mawr, Noether
continued her research and taught classes of
the standard model of
particle physics. In this
model particles, such as
photons (γ) and electrons
(e), are within the circle.
Around the outer edge
are hypothetical heavier
particles proposed by
a theory called
SOURCE: PARTICLE FEVER, 2015