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It’s 2 pm on a Wednesday. At Perimeter Institute for Theoretical Physics, that means colloquium time, and if you’re a certain sort of nerd, that’s exciting. The Time Room is packed. Typically the colloquium is on some recent cutting-edge bit of science, but today is a little different. Yvette Kosmann-Schwarzbach is giving a talk: “Emmy Noether’s two theorems, a hundred years later”.
I’ve gone through a tough time recently and have started having doubts about academia. It feels like I’ve opened Pandora’s box: a single doubt unleashes a swarm of doubts about my abilities as a physicist, threatening to engulf.
It is in this mood that I sit now, listening to an amazing woman scientist talk about another amazing woman scientist: the “mother” of modern algebra. The inventor of Noether’s theorem almost a century ago. The discoverer of symmetries and conserved charges. The master of group theory. The one without whom modern physics could not be where it is now. The one of whom there are only a few black-and-white photographs. The one hidden in plain sight – the name universally known among physicists, the gender far less so.
Goosebumps rise on my arm.
As an aspiring scientist growing up in India, meddling around with makeshift labs, cutting out newspaper clippings on black holes and spacetime, I was much influenced by the stories of great scientists who have shaped the history of physics. The scientist in my head – the one I romanticized being – looked like the caricature in every book or movie: an eccentric white man with a shock of white hair that crackled like electricity. I forced my size three feet into his size nine shoes, and those of Dirac, Newton, Pauli, Heisenberg, Schrödinger, Bose. In my mind I strolled, shapeless in my own clothes, while figuring out the geometry of the world. I stumbled onto gravity and held on tight.
But often, the image wavered. I could find no reference to my struggles in any of my heroes’ narratives. They were not constrained by what their gender “could” and “could not” do. They never had periods; their thighs did not chafe under dresses during physics class. They were not asked, again and again, if they “really” intended to become a physicist.
My heroes wrote of physics as a seductress, a flighty, elusive temptress who brought the universe into play. I wanted to write of her in that romantic way too, but I was unfortunately mostly straight. I didn’t have a language for my passion.
I first heard the word “Noether” one fine afternoon in a dusty undergraduate class in the jungles of Mohanpur, India. I automatically attached “him” to the name. Noether’s theorems were everywhere. I named them, used them many times in my calculations, without knowing that behind them was someone who had looked like me in her figure and – maybe – in her brain. Who had achieved what I yearned to.
Four years later, in 2015, when I was a master’s student at Perimeter, Emmy Noether’s gender was revealed to me. I felt a peculiar shame. How happy I could have been, I thought, if I’d known.
Now, four years later still, I’m back as a visiting researcher, rediscovering Emmy Noether’s legacy in a colloquium.
Professor Kosmann-Schwarzbach brings a dispassionate, raw energy to the room. When she whispers, the whole room leans forward imperceptibly to hear. She’s been researching Noether for years. She talks about Noether’s contributions. Were they original? What did Noether uncover about the energy conservation problem in general relativity? What did she write in her letters? What was her family like? Kosmann-Schwarzbach talks with the authority born of a lifetime of scholarly pursuits.
The room disappears before my eyes, and I am a flâneuse, walking along in Noether’s (size three?) shoes, her stiff dresses. I see myself poring over Hilbert’s notes. I am in the room in 1915 when Klein and Hilbert invite Noether to Göttingen in the hope that her expertise on invariant theory will help them understand some of the implications of Einstein’s newly formulated theory of general relativity. I am in the room in 1916 when there are flurried exchanges of letters between Einstein and Hilbert. In one, Hilbert encloses a note from Noether to Einstein. I am right there when Einstein writes back to ask for a clarification and says: “Of course, it would be sufficient if you ask Fräulein Noether to clarify this for me.”
Her first year in Göttingen and already an expert! It must have been stormy, the day in 1918 when Noether solved a central problem arising in general relativity – one on which the whole theory turned, really – and proved the theorems that would be known by her name. She proved and vastly generalized a conjecture made by Hilbert concerning the nature of the law of conservation of energy and how it must be phrased generally through group theory. A triumphant moment.
But then the story took a turn.
Time passed. Noether’s seminal paper was never much mentioned again, either by her or by others. Weyl, who performed similar computations to hers, only referred to her in a footnote in his third and subsequent editions. Even though Courant and Markow knew about her work and referred to her briefly in their writings, it is not obvious that this knowledge was transferred down to Rumer. He cited Weyl but not Noether. Never Noether! And neither did Fock.
Here Kosmann-Schwarzbach pauses and asks, “Was it because she was a woman? Or because she was Jewish?”
Emmy Noether never wrote another paper on the symmetries in general relativity. Rather, she focused on algebra. Papers by other philosophers “proved” the same generalizations without glancing at Noether’s 1918 papers to learn that she had already proved them long before!
How did she feel then, I wonder? Did she even care? How did the other hardships in her life as a Jew during one of the most dangerous eras in human history transform her? Did she mourn the family members she lost? Did her work become her faith, keep her sane? How did she feel when her gender was bandied about as a reason to not appoint her at the university? Did she laugh when Hilbert, in support of her appointment to the university, argued that Noether’s sex should not be an argument against her? (“After all, we are a university, not a bathhouse,” he indignantly told the administration, to no avail.) Or did she struggle privately with her anger, as so many of us do?
Today, in our memories, Emmy Noether does not need to be a vocal feminist. She does not need to have done more for women. She is quite enough in the fact that she existed and she changed the course of humanity. She is quite enough in the fact that she never let societal expectations of her gender confine her. She is now rightly considered as one of the greatest mathematicians in history. That is enough. Or it should be.
Why do we care, in the end, about credit? Why do we need – why do I need – to see the person behind the idea? Because when we do, we see a glimmer of possibilities for ourselves. Emmy Noether is a hero for her work. But even more so, in this moment, for herself: a person sharing some of my characteristics, who allows me to envision physics as my own world. She makes me accept myself. I am not a colonizer. I belong here.
Sonali Mohapatra was a Perimeter Scholars International master’s student in 2014/15 and is now pursuing her PhD at the University of Sussex.
Watch the talk: Yvette Kosmann-Schwarzbach’s colloquium “Emmy Noether’s two theorems, a hundred years later”
In profile: Emmy Noether and the poetry of logical ideas
Fun stuff: Noether’s theorem explained, from kindergarten to PhD
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