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Biography of Emmy Noether
Emmy Noether: The Greatest Forgotten Mathematician in History
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 MathWhen Emmy Noether was born on 23 March, 1882, it was into a family that was almost designedto produce geniuses. Her father, Max Noether, was a highly-respectedmathematician attached to Erlangen University. Her mother came from the wealthy Kaufmannfamily of Cologne. Although Emmy was the eldest, her brotherFritz 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 Noethernot succeed? Yet this outward advantage masked a less-privilegedreality. The Noethers were Jewish.
Max’s ancestors had changed their namesto try and blend in with German society. But while Germany in the late 19th Centurywas much less anti-Semitic than it would become, the first traces of poisonous racism werealready there. Although Noether’s Jewishness would turnher 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 bornfemale. We say “bad luck” not to rile up femaleviewers, but because it really was a disadvantage back then. While as a very young girl Noether was desperateto follow her father into mathematics, society at the time was all kinda like “Pfft, girlscan’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 thatshe was always laughing. In fact, happiness seems to have been Noether’sdefault setting throughout her life. She spent her childhood dancing to made upsongs, telling jokes, and getting highly excited about anything that grabbed her fancy. Yet there were also signs of something deeperat work. As she entered her teens, Noether began spendinglonger amounts of time lost in her own head, like she was distracted by a voice only shecould hear. Already, it seems she was spending more timepuzzling out reality than she was living in it. But puzzles weren’t for nice girls, so Noetherspent 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, shereceived the second-highest possible grade. But Emmy Noether would never do even an hourof paid language teaching in her life. That same year, 1900, Noether seems to havedecided to Hell with what society wanted. She applied to study math at Erlangen University. At the dawn of the 20th Century, women wereforbidden from attending University classes in Germany. At least, they were officially. Unofficially, professors were given leewayover who they allowed to sit in on lectures. This was something of an advantage if, ohI dunno, your dad just happened to be a respected math professor at the university you wantedto attend. Not long after, Noether began sitting in onErlangen’s math courses, one of only two women in the entire university. For the next two years, she progressed soquickly that, when she sat an equivalent exam in 1903, she passed with flying colors.
Had she been male, Noether would’ve doubtlessnow found herself riding a rocketship to the very heights of academia. But unfortunately her double X chromosomedisqualified her from doing anything remotely fulfilling, so instead she went to GöttingenUniversity to sit in on yet more classes. However, Noether’s winter stint in Göttingenwould turn out to be a blessing in disguise. While there, she studied under David Hilbertand 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 ChangeIn spring, 1904 the German government suddenly dropped a bombshell.
From the following semester onward, womenwould be allowed to enroll at the empire’s universities. For Noether, this was like spending your entirelife standing on the sidelines at a dance, only to suddenly be invited to join in - althoughadmittedly 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 joinedone of the first mixed-sex math courses in Germany. Remarkably, she doesn’t seem to have encounteredany real resentment. While it likely existed in some form, mostof 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 withthe highest honors possible. To return to our earlier metaphor, this momentis Noether dancing so spectacularly the entire hall stops to watch. It’s also the moment some asshole janitorsnaps the lights back on and brings the whole dream to an abrupt end. Although Noether had a Phd in math, she wasn’tactually allowed to do anything with it. The law thought women should be able to study,but not lecture. So Noether found herself in possession ofa brilliant mind and a stellar education, but absolutely nothing she could do with eitherof them. Still, she did have a couple of aces up hersleeve. The first was her mother’s money. Thanks to her family, Noether didn’t haveto get a job. If she wanted to, she could devote her timeto the unpaid study of math. The second ace was her father. By 1908, Max Noether was suffering more andmore from a disability brought on by childhood polio. He needed more time off, and a substitutewho could cover him when he couldn’t attend class.
A substitute just like Emmy. Subbing for her dad was an unpaid role, butone 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 invitedto go to Salzburg, to address the German Mathematical Society. In 1911, she came to the attention of ErnstSigismund Fischer, who championed her work at Erlangen and sparked her own interest inabstract math. By 1915, shortly after the outbreak of WWI,she was even overseeing two of her father’s Phd students, advising them on their doctoraltheses.
It’s entirely possible she could have goneon like that forever. Kept right on working away in Erlangen, perhapseventually even making it onto the salaried staff. But 1915 was the year that everything wasgonna change, both in mathematics, and in Noether’s personal life. That’s because 1915 was the year that aformer patent clerk named Albert Einstein blew up the entire scientific world. Einstein’s Theory of General Relativitywas the most transformative event in math since Newton decided to discovery gravityand save us all from a lifetime of weightlessness. It turned almost everything we thought weknew on its head, and lit a fire under the asses of every math department on the planet. Among those with suddenly burning backsideswere Emmy’s old mentors David Hilbert and Felix Klein.
That same year, the two identified what appearedto be a problem in Einstein’s theory, one that seemed to imply Einstein’s work contradictedlaws on the conservation of energy. But the two of them alone weren’t up tothe 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 askingher to come back to Göttingen. She said yes. Einstein’s DreamsWhen Noether arrived in Göttingen that year, it’s fair to say the all-male faculty wasn’tpleased to see her. Hilbert’s plan had originally been to haveNoether appointed associate professor. To which some long-forgotten stuffy German-dudereplied: "What will our soldiers think when they returnto 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 carriedthe day, and Hilbert was forced to give Noether the unpaid position of “guest lecturer”. At which point Noether showed everyone upby solving the problem with Einstein’s work in, like, fifteen minutes.
It turned out that the problem wasn’t actuallya problem. Hilbert and Klein had just been thinking toosmall. Using Einstein’s work, Noether was ableto 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 beremembered. Noether’s Theorem would change the world. OK, we’re gonna level with you here: weread a ton of articles trying to get our heads around Noether’s Theorem so we could explainit to you, but it turns out it’s super confusing to people - like us - whose primary job ishistory and who usually respond to the word “algebra” with a bloodcurdling scream. So we’ll let an expert do the talking, inthis case the New York Times’s Pulitzer Prize-winning science journalist, NatalieAngier: “What the revolutionary theorem says, incartoon essence,” she wrote, “is the following: Wherever you find some sort of symmetry innature, some predictability or homogeneity of parts, you’ll find lurking in the backgrounda corresponding conservation — of momentum, electric charge, energy or the like…” For example, “Noether’s theorem showsthat a symmetry of time — like the fact that whether you throw a ball in the air tomorrowor make the same toss next week will have no effect on the ball’s trajectory — isdirectly related to the conservation of energy.” Got that? Throwing balls, conservation of energy, relativitysolved. Err, sure? Still, even mathematical luddites like uscan appreciate the historical significance of Noether’s work.
Her Theorem would go on to hugely influencea new generation of scientists working in the 1950s and 1960s. Scientists who used her work to predict theexistence of new particles. One of those was the Higgs Boson, the so-calledGod Particle discovered in 2012. Take away Emmy Noether and her Theorem, andthe cutting edge of physics today suddenly looks very different. Unfortunately, there was a major barrier tomost people actually hearing about Noether’s discovery. During WWI, scientists working for the CentralPowers were forbidden from sharing discoveries with rival nations, in case it lead to a militarybreakthrough. But one person did get to hear about Emmy’swork. After reading of Noether’s Theorem, Einsteinwrote to Hilbert. In his letter, he used a simple term to describethe woman who’d come up with it.
He called her a genius. The New GermanyThe 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 refusingto pay her and, with the German economy shattered by war, even money from her parents wasn’tenough to stop her sliding into poverty. At least she was able to continue working. During this period, Hilbert managed to getaround the university’s prohibition on solo female lecturers by advertising Noether’sclasses in his own name and then “forgetting” to show up. It wasn’t much, but it allowed Noether tofollow 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, Noetherand 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 Theoremto a wider audience. Everyone knew she was a mathematician of staggeringtalent. But, no. The stuffy German dudes on the university’sboard had somehow missed the whole “discovering a world changing theorem” bit, and remainedintensely un-keen on lady lecturers. They maintained this position all the waythrough 1921, even as Noether published her paper Idealtheorie in Ringbereichen, now seenas a major milestone in the advent of modern algebra. Finally, in 1922, the university condescendinglyawarded 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 stuffyGermans were dicks enough to make sure it didn’t feel like one.
Yet Noether doesn’t seem to have reallycared. She was able to teach now, to work on herpassion. She became one of the most popular lecturerson campus, with a dedicated student clique forming around her known as “the NoetherBoys”. 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 thatwere still swirling around at the time. In 1927, for example, Noether began a collaborationon non-communicative algebras with two male mathematicians, but was only rarely able toput her name on the papers. Still, the community itself championed her. In 1928, for example, she was invited to addressthe International Congress of Mathematicians at Bologna. In 1929 she was briefly given the job of visitingprofessor at Moscow university. As time passed, signs slowly began to appearthat things were, indeed, changing.
In 1930, Noether met the 24-year old Czechmath superstar Olga Taussky. After, she told her friends how pleased shewas that women were finally being accepted in math. Yet while acceptance might have been growingwhere Noether’s gender was concerned, an even more violent wave of oppression was aboutto come crashing down on her. Noether was a prominent Jewish woman livingin 1930s Germany. Unfortunately, we all know what’s comingnext. The Age of HorrorThe same year that Noether met Olga Taussky, the Weimar Republic held one of its frequentelections. But while every previous election had returnedmessy, but expected results, the election of September, 1930 returned an unpleasantsurprise. 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 itsend. Around the corner lurked a time of unspeakablehorror. The coming nightmare wasn’t immediatelyapparent in Göttingen, especially for the apolitical Noether. Oh, sure, a couple of her students startedturning 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 accompaniedby the steady drumbeat of jackboots and despair. In October, 1930, the SA undertook its firstmajor anti-Jewish action, destroying storefronts in Berlin. Two years later, Weimar Germany again wentto the polls, this time giving the Nazis the largest number of seats and over 37% of thevote. Yet Noether still didn’t realize the dangershe was in. The same year that the Weimar Republic teeteredon the edge of annihilation, she was accepting awards for her math work and addressing internationalcongresses in Switzerland. But her ignorance couldn’t last. On January 30, 1933, Hitler was made Chancellorof Germany, a momentous event celebrated nationwide by torchlit SA and SS parades through cities.
Not three months later, on March 24, the Reichstagpassed the Enabling Act, handing Hitler absolute power. The very next month, Noether was fired fromGöttingen for being Jewish. It was almost like someone had been waitingfor an excuse to get rid of her. Noether was given no compensation for theloss of her job, denied a pension, and told she would be unable to teach again. The mathematician’s response was impressivelyupbeat. Noether wrote to a friend:“I must say, though, that this thing is much less terrible for me than it is for manyothers. At least I have a small inheritance (I wasnever 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 continuedto teach in private, opening up the front room of her home to any students who wantedto learn math. She even allowed her brownshirt students toattend these informal classes, ignoring the fact that these boys had likely marched throughthe city chanting Nazi slogans just a few months earlier. As a friend of Noether’s later noted, shenever “doubted (the brownshirt students) integrity”. This was about math. Politics could be damned. Thankfully, Noether never got to experiencethe true faces of her Nazi students. That fall, worried about Noether’s increasinglyprecarious position, Albert Einstein arranged for her a job lecturing at Bryn Mawr Collegein Pennsylvania. Remarkably, she turned him down. If she was going to emigrate, she wanted togo to England to teach at Oxford, not some American college. But it soon became apparent that she didn’thave a choice.
Across 1933, the Nazis passed a raft of anti-Semiticlaws, excluding Jews from many professions, and subordinating all Jewish intellectualoutput to Goebbels himself. Although physical violence against Jews wouldn’tbecome state policy until 1935, it was clear now even to the optimistic Noether which waythe wind was blowing. That October, Noether boarded a boat boundfor the USA. Not long after, she began her visiting professorshipat Bryn Mawr. With remarkable luck, Noether had just escapedthe clutches of one of the most-destructive, racist regimes of all time. Although she would return to Germany oncemore, she would never again be victimized by Nazi policies. Unfortunately, her escape would only turnout to be a reprive. Nobody knew it yet, but the fifty one yearold Noether was only 18 months away from the end of her life. Death and LegacyWhen death finally came for Noether, it was with a suddenness that was painfully unfair. Across 1934, Noether had settled into hernew 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 probablyfelt the most accepted she ever had in her life. No-one in the States seemed to care that shewas a woman who wanted to teach math. That she was Jewish. Finally, after half a century, Noether hadfound somewhere that seemed to accept her for who she was. Somewhere she could live out the rest of herlife without trouble. She even felt comfortable enough to take atrip back to Germany that year. While riding on the Hamburg metro with herbrother, she struck up an excited conversation about Idealtheorie - a mathematical conceptthat in German uses the term “Führer”. Her brother’s wife would later remark thatNoether seemed completely oblivious to how close she came to being arrested for thatdiscussion. 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 hadan ovarian cyst. They recommended her for surgery and, on April10, she went under the knife.
As they operated, the doctors made a gruesomediscovery. Noether’s insides were riddled with tumors. The great mathematician was dying. But death wouldn’t even have the decencyto 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 weretoo late. Emmy Noether died that same afternoon. At the time she passed away, she’d onlyjust turned 53. Today, her name is all but forgotten outsideof math and science circles. Even some who know her theorem know nothingabout her. They may even assume the “Noether” it’snamed after was male. And this is a tragedy, because her work changedthe world. A whole lot of modern theoretical physicsis underpinned by her ideas, and her contributions to abstract algebra were so huge that we’veseen people claim she basically invented the discipline. The weirdest part of all this, is that peopleknew how special she was.
After Noether died, Albert Einstein wrotein the New York Times: “In the judgment of the most competent livingmathematicians, Fräulein Noether was the most significant creative mathematical geniusthus 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 hasslipped into the fog. The most significant thinker the world somehowforgot. 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, helpingus 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 ofall 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 smilingaway; the mathematician who changed the world.
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