Human history is littered with people who
changed the world, only to have their achievements
erased from popular memory.
Gay men like computing pioneer Alan Turing,
women like mathematician Ada Lovelace, even
pure oddballs like Nikola Tesla were left
out the curriculum for decades.
Thankfully, this is no longer the case.
On the internet, everyone from the Navajo
code talkers, to NASA’s black, female number
crunchers are having their stories told.
But what if we told you that there’s a name
still missing from their ranks, one that should
be on everyone’s lips.
The name of a female mathematician so influential
her work may be second only to that of Albert
Einstein.
Her name was Emmy Noether, and her work changed
history.
Born into a German-Jewish family in the late
19th Century, Noether grew up in a world designed
to reject people like her.
Barred from attending university due to her
gender, she nonetheless managed to attain
a grasp of mathematics so phenomenal that
her work created an entire discipline.
Anonymous in her lifetime, ignored by posterity,
this is the life of Emmy Noether, the most-important
mathematician the world forgot.
Nice Girls Don’t Do Math
When Emmy Noether was born on 23 March, 1882,
it was into a family that was almost designed
to produce geniuses.
Her father, Max Noether, was a highly-respected
mathematician attached to Erlangen University.
Her mother came from the wealthy Kaufmann
family of Cologne.
Although Emmy was the eldest, her brother
Fritz would become almost as famous a mathematician
as their father.
In short, this was a family of wealthy brainboxes,
intimately connected to a very prestigious
university.
With such an upbringing, how could Noether
not succeed?
Yet this outward advantage masked a less-privileged
reality.
The Noethers were Jewish.
Max’s ancestors had changed their names
to try and blend in with German society.
But while Germany in the late 19th Century
was much less anti-Semitic than it would become,
the first traces of poisonous racism were
already there.
Although Noether’s Jewishness would turn
her into a target later in life, it wasn’t
solely what made her early years difficult.
No, that was Nother’s bad luck to be born
female.
We say “bad luck” not to rile up female
viewers, but because it really was a disadvantage
back then.
While as a very young girl Noether was desperate
to follow her father into mathematics, society
at the time was all kinda like “Pfft, girls
can’t do math.
Learn the piano instead.”
Noether’s childhood may not have been fulfilling,
but at least she was happy.
At elementary school, her teachers noted that
she was always laughing.
In fact, happiness seems to have been Noether’s
default setting throughout her life.
She spent her childhood dancing to made up
songs, telling jokes, and getting highly excited
about anything that grabbed her fancy.
Yet there were also signs of something deeper
at work.
As she entered her teens, Noether began spending
longer amounts of time lost in her own head,
like she was distracted by a voice only she
could hear.
Already, it seems she was spending more time
puzzling out reality than she was living in
it.
But puzzles weren’t for nice girls, so Noether
spent her day to day life training to be a
language teacher.
She did a pretty good job, too.
When she took the teaching exam in 1900, she
received the second-highest possible grade.
But Emmy Noether would never do even an hour
of paid language teaching in her life.
That same year, 1900, Noether seems to have
decided to Hell with what society wanted.
She applied to study math at Erlangen University.
At the dawn of the 20th Century, women were
forbidden from attending University classes
in Germany.
At least, they were officially.
Unofficially, professors were given leeway
over who they allowed to sit in on lectures.
This was something of an advantage if, oh
I dunno, your dad just happened to be a respected
math professor at the university you wanted
to attend.
Not long after, Noether began sitting in on
Erlangen’s math courses, one of only two
women in the entire university.
For the next two years, she progressed so
quickly that, when she sat an equivalent exam
in 1903, she passed with flying colors.
Had she been male, Noether would’ve doubtless
now found herself riding a rocketship to the
very heights of academia.
But unfortunately her double X chromosome
disqualified her from doing anything remotely
fulfilling, so instead she went to Göttingen
University to sit in on yet more classes.
However, Noether’s winter stint in Göttingen
would turn out to be a blessing in disguise.
While there, she studied under David Hilbert
and Felix Klein, two of the most distinguished
mathematicians in Germany.
Neither of the three geniuses knew it in 1903,
but they were just over a decade away from
a collaboration that would change the world.
A Time of Change
In spring, 1904 the German government suddenly
dropped a bombshell.
From the following semester onward, women
would be allowed to enroll at the empire’s
universities.
For Noether, this was like spending your entire
life standing on the sidelines at a dance,
only to suddenly be invited to join in - although
admittedly in this metaphor “dancing”
involves a whole lot more algebra than usual.
Anyway, Noether raced back to Erlangen and,
on October 24, sat her entrance exam.
Did she pass?
Of course she did.
That year, 1904, Noether officially joined
one of the first mixed-sex math courses in
Germany.
Remarkably, she doesn’t seem to have encountered
any real resentment.
While it likely existed in some form, most
of her professors seem to have realized she
had a gift for the subject.
Three years after joining, on Friday, 13 December,
1907, Noether took the examination for her
Phd.
She passed so handily that she graduated with
the highest honors possible.
To return to our earlier metaphor, this moment
is Noether dancing so spectacularly the entire
hall stops to watch.
It’s also the moment some asshole janitor
snaps the lights back on and brings the whole
dream to an abrupt end.
Although Noether had a Phd in math, she wasn’t
actually allowed to do anything with it.
The law thought women should be able to study,
but not lecture.
So Noether found herself in possession of
a brilliant mind and a stellar education,
but absolutely nothing she could do with either
of them.
Still, she did have a couple of aces up her
sleeve.
The first was her mother’s money.
Thanks to her family, Noether didn’t have
to get a job.
If she wanted to, she could devote her time
to the unpaid study of math.
The second ace was her father.
By 1908, Max Noether was suffering more and
more from a disability brought on by childhood
polio.
He needed more time off, and a substitute
who could cover him when he couldn’t attend
class.
A substitute just like Emmy.
Subbing for her dad was an unpaid role, but
one which allowed Noether to remain in Erlangen.
To keep on studying, to keep publishing papers.
The more she worked, the more notice she got.
In 1909, for example, Noether was invited
to go to Salzburg, to address the German Mathematical
Society.
In 1911, she came to the attention of Ernst
Sigismund Fischer, who championed her work
at Erlangen and sparked her own interest in
abstract math.
By 1915, shortly after the outbreak of WWI,
she was even overseeing two of her father’s
Phd students, advising them on their doctoral
theses.
It’s entirely possible she could have gone
on like that forever.
Kept right on working away in Erlangen, perhaps
eventually even making it onto the salaried
staff.
But 1915 was the year that everything was
gonna change, both in mathematics, and in
Noether’s personal life.
That’s because 1915 was the year that a
former patent clerk named Albert Einstein
blew up the entire scientific world.
Einstein’s Theory of General Relativity
was the most transformative event in math
since Newton decided to discovery gravity
and save us all from a lifetime of weightlessness.
It turned almost everything we thought we
knew on its head, and lit a fire under the
asses of every math department on the planet.
Among those with suddenly burning backsides
were Emmy’s old mentors David Hilbert and
Felix Klein.
That same year, the two identified what appeared
to be a problem in Einstein’s theory, one
that seemed to imply Einstein’s work contradicted
laws on the conservation of energy.
But the two of them alone weren’t up to
the task of figuring out all the implications.
What they needed was a fresh set of eyes.
Someone with expertise in invariant theory.
Not long after, Noether got a call asking
her to come back to Göttingen.
She said yes.
Einstein’s Dreams
When Noether arrived in Göttingen that year,
it’s fair to say the all-male faculty wasn’t
pleased to see her.
Hilbert’s plan had originally been to have
Noether appointed associate professor.
To which some long-forgotten stuffy German-dude
replied:
"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.
After all, we are a university, not a bathhouse.”
But, in the end, stuffy German dude carried
the day, and Hilbert was forced to give Noether
the unpaid position of “guest lecturer”.
At which point Noether showed everyone up
by solving the problem with Einstein’s work
in, like, fifteen minutes.
It turned out that the problem wasn’t actually
a problem.
Hilbert and Klein had just been thinking too
small.
Using Einstein’s work, Noether was able
to prove that energy would indeed be conserved
across a sufficiently large patch of space.
But it was what she discovered alongside that,
that made Noether’s name.
That became the reason she deserves to be
remembered.
Noether’s Theorem would change the world.
OK, we’re gonna level with you here: we
read a ton of articles trying to get our heads
around Noether’s Theorem so we could explain
it to you, but it turns out it’s super confusing
to people - like us - whose primary job is
history and who usually respond to the word
“algebra” with a bloodcurdling scream.
So we’ll let an expert do the talking, in
this case the New York Times’s Pulitzer
Prize-winning science journalist, Natalie
Angier:
“What the revolutionary theorem says, in
cartoon essence,” she wrote, “is the following:
Wherever you find some sort of symmetry in
nature, some predictability or homogeneity
of parts, you’ll find lurking in the background
a corresponding conservation — of momentum,
electric charge, energy or the like…”
For example, “Noether’s theorem shows
that a symmetry of time — like the fact
that whether you throw a ball in the air tomorrow
or make the same toss next week will have
no effect on the ball’s trajectory — is
directly related to the conservation of energy.”
Got that?
Throwing balls, conservation of energy, relativity
solved.
Err, sure?
Still, even mathematical luddites like us
can appreciate the historical significance
of Noether’s work.
Her Theorem would go on to hugely influence
a new generation of scientists working in
the 1950s and 1960s.
Scientists who used her work to predict the
existence of new particles.
One of those was the Higgs Boson, the so-called
God Particle discovered in 2012.
Take away Emmy Noether and her Theorem, and
the cutting edge of physics today suddenly
looks very different.
Unfortunately, there was a major barrier to
most people actually hearing about Noether’s
discovery.
During WWI, scientists working for the Central
Powers were forbidden from sharing discoveries
with rival nations, in case it lead to a military
breakthrough.
But one person did get to hear about Emmy’s
work.
After reading of Noether’s Theorem, Einstein
wrote to Hilbert.
In his letter, he used a simple term to describe
the woman who’d come up with it.
He called her a genius.
The New Germany
The next few years of Noether’s life were
odd, to say the least.
Although she’d just made a major breakthrough,
most of the world didn’t know about it.
On top of that, the university was still refusing
to pay her and, with the German economy shattered
by war, even money from her parents wasn’t
enough to stop her sliding into poverty.
At least she was able to continue working.
During this period, Hilbert managed to get
around the university’s prohibition on solo
female lecturers by advertising Noether’s
classes in his own name and then “forgetting”
to show up.
It wasn’t much, but it allowed Noether to
follow her passion.
Then end of the war brought its own problems,
as Germany plunged into chaos at the end of
1918, a chaos that only ended in August, 1919,
with the creation of the Weimar Republic.
With the era of upheaval at an end, Noether
and Hilbert fixed their sights on a new target.
Getting Noether a real job at Göttingen University.
By now, she’d been able to publish her Theorem
to a wider audience.
Everyone knew she was a mathematician of staggering
talent.
But, no.
The stuffy German dudes on the university’s
board had somehow missed the whole “discovering
a world changing theorem” bit, and remained
intensely un-keen on lady lecturers.
They maintained this position all the way
through 1921, even as Noether published her
paper Idealtheorie in Ringbereichen, now seen
as a major milestone in the advent of modern
algebra.
Finally, in 1922, the university condescendingly
awarded the cleverest person in their midst
with a role as untenured associate math professor,
and allotted her a pitifully small salary.
It was a victory, sort of, but the stuffy
Germans were dicks enough to make sure it
didn’t feel like one.
Yet Noether doesn’t seem to have really
cared.
She was able to teach now, to work on her
passion.
She became one of the most popular lecturers
on campus, with a dedicated student clique
forming around her known as “the Noether
Boys”.
Yep: boys.
Despite the law change and Noether’s presence,
there were almost zero women studying math
at Göttingen.
And that reflected the deeper attitudes that
were still swirling around at the time.
In 1927, for example, Noether began a collaboration
on non-communicative algebras with two male
mathematicians, but was only rarely able to
put her name on the papers.
Still, the community itself championed her.
In 1928, for example, she was invited to address
the International Congress of Mathematicians
at Bologna.
In 1929 she was briefly given the job of visiting
professor at Moscow university.
As time passed, signs slowly began to appear
that things were, indeed, changing.
In 1930, Noether met the 24-year old Czech
math superstar Olga Taussky.
After, she told her friends how pleased she
was that women were finally being accepted
in math.
Yet while acceptance might have been growing
where Noether’s gender was concerned, an
even more violent wave of oppression was about
to come crashing down on her.
Noether was a prominent Jewish woman living
in 1930s Germany.
Unfortunately, we all know what’s coming
next.
The Age of Horror
The same year that Noether met Olga Taussky,
the Weimar Republic held one of its frequent
elections.
But while every previous election had returned
messy, but expected results, the election
of September, 1930 returned an unpleasant
surprise.
From one of the smallest parties in the Reichstag,
the Nazis were catapulted into second place,
netting nearly a fifth of the vote.
The era of Weimar democracy was reaching its
end.
Around the corner lurked a time of unspeakable
horror.
The coming nightmare wasn’t immediately
apparent in Göttingen, especially for the
apolitical Noether.
Oh, sure, a couple of her students started
turning up to her lectures wearing Nazi brownshirts,
but Noether laughed it off.
She knew these boys.
She knew they would never harm her.
The next couple of years were accompanied
by the steady drumbeat of jackboots and despair.
In October, 1930, the SA undertook its first
major anti-Jewish action, destroying storefronts
in Berlin.
Two years later, Weimar Germany again went
to the polls, this time giving the Nazis the
largest number of seats and over 37% of the
vote.
Yet Noether still didn’t realize the danger
she was in.
The same year that the Weimar Republic teetered
on the edge of annihilation, she was accepting
awards for her math work and addressing international
congresses in Switzerland.
But her ignorance couldn’t last.
On January 30, 1933, Hitler was made Chancellor
of Germany, a momentous event celebrated nationwide
by torchlit SA and SS parades through cities.
Not three months later, on March 24, the Reichstag
passed the Enabling Act, handing Hitler absolute
power.
The very next month, Noether was fired from
Göttingen for being Jewish.
It was almost like someone had been waiting
for an excuse to get rid of her.
Noether was given no compensation for the
loss of her job, denied a pension, and told
she would be unable to teach again.
The mathematician’s response was impressively
upbeat.
Noether wrote to a friend:
“I must say, though, that this thing is
much less terrible for me than it is for many
others.
At least I have a small inheritance (I was
never entitled to a pension anyway) which
allows me to sit back for a while and see.”
And that’s exactly what she did.
Through the summer of 1933, Noether continued
to teach in private, opening up the front
room of her home to any students who wanted
to learn math.
She even allowed her brownshirt students to
attend these informal classes, ignoring the
fact that these boys had likely marched through
the city chanting Nazi slogans just a few
months earlier.
As a friend of Noether’s later noted, she
never “doubted (the brownshirt students)
integrity”.
This was about math.
Politics could be damned.
Thankfully, Noether never got to experience
the true faces of her Nazi students.
That fall, worried about Noether’s increasingly
precarious position, Albert Einstein arranged
for her a job lecturing at Bryn Mawr College
in Pennsylvania.
Remarkably, she turned him down.
If she was going to emigrate, she wanted to
go to England to teach at Oxford, not some
American college.
But it soon became apparent that she didn’t
have a choice.
Across 1933, the Nazis passed a raft of anti-Semitic
laws, excluding Jews from many professions,
and subordinating all Jewish intellectual
output to Goebbels himself.
Although physical violence against Jews wouldn’t
become state policy until 1935, it was clear
now even to the optimistic Noether which way
the wind was blowing.
That October, Noether boarded a boat bound
for the USA.
Not long after, she began her visiting professorship
at Bryn Mawr.
With remarkable luck, Noether had just escaped
the clutches of one of the most-destructive,
racist regimes of all time.
Although she would return to Germany once
more, she would never again be victimized
by Nazi policies.
Unfortunately, her escape would only turn
out to be a reprive.
Nobody knew it yet, but the fifty one year
old Noether was only 18 months away from the
end of her life.
Death and Legacy
When death finally came for Noether, it was
with a suddenness that was painfully unfair.
Across 1934, Noether had settled into her
new life in America.
She’d begun additional lectures at Princeton,
and built a small but devoted following in
both universities.
In fact, it was in America that she probably
felt the most accepted she ever had in her
life.
No-one in the States seemed to care that she
was a woman who wanted to teach math.
That she was Jewish.
Finally, after half a century, Noether had
found somewhere that seemed to accept her
for who she was.
Somewhere she could live out the rest of her
life without trouble.
She even felt comfortable enough to take a
trip back to Germany that year.
While riding on the Hamburg metro with her
brother, she struck up an excited conversation
about Idealtheorie - a mathematical concept
that in German uses the term “Führer”.
Her brother’s wife would later remark that
Noether seemed completely oblivious to how
close she came to being arrested for that
discussion.
As 1935 dawned, Noether was ensconced in Pennsylvania,
working on her theories, and seemingly enjoying
a new lease of life.
And then she got the news.
On April 8, doctors discovered Noether had
an ovarian cyst.
They recommended her for surgery and, on April
10, she went under the knife.
As they operated, the doctors made a gruesome
discovery.
Noether’s insides were riddled with tumors.
The great mathematician was dying.
But death wouldn’t even have the decency
to wait another couple of months.
Four days after her surgery, on April 14,
1935, Noether developed a sudden, extreme
fever.
An infection had developed.
The doctors rushed to save her, but they were
too late.
Emmy Noether died that same afternoon.
At the time she passed away, she’d only
just turned 53.
Today, her name is all but forgotten outside
of math and science circles.
Even some who know her theorem know nothing
about her.
They may even assume the “Noether” it’s
named after was male.
And this is a tragedy, because her work changed
the world.
A whole lot of modern theoretical physics
is underpinned by her ideas, and her contributions
to abstract algebra were so huge that we’ve
seen people claim she basically invented the
discipline.
The weirdest part of all this, is that people
knew how special she was.
After Noether died, Albert Einstein wrote
in the New York Times:
“In the judgment of the most competent living
mathematicians, Fräulein Noether was the
most significant creative mathematical genius
thus far produced since the higher education
of women began.”
Yet while Einstein remains a household name,
while Kepler, Cantor, and John Nash all trigger
hints of recognition, Noether’s name has
slipped into the fog.
The most significant thinker the world somehow
forgot.
But we shouldn’t be too sad for Noether.
While she certainly deserves more recognition,
it can’t be denied that her work lives on,
influencing millions of thinkers, helping
us to understand the universe.
She may have slipped into obscurity today,
but when the final sum total of the human
race is added up, and the achievements of
all the billions and billions who have ever
lived are weighed…
…it’s comforting to know that Emmy Noether
will be up there at the very top, still smiling
away; the mathematician who changed
the world.
