Sciencefiction.com supports geek girls – women interested in science and technology. So let me tell you about a role model – one of the best scientists and mathematicians who has ever lived. Let’s meet the wonderful Emmy Noether.
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Here’s Emmy at six years old, skipping down the street in Erlangen, Germany, hand in hand with her mother and father. It’s 1888 and she has no idea that when she’s grown-up she’ll create the foundation of modern physics (and be much more famous than her dad).

Mom is Ida Amalia Kauffman, daughter of wealthy merchants; Dad is Max Noether, Professor of Mathematics at the University of Erlangen. Emmy has excellent genes but they’ll become a source of future peril: her parents are Jewish.

Emmy gets her PhD in math in Göttingen in 1907; not easy for women students at the time. In 1915, during the First World War she’s invited by the celebrated German mathematicians David Hilbert and Felix Klein to lecture on Einstein’s recently discovered General Theory of Relativity. She has to do this under Hilbert’s name as women aren’t allowed to hold faculty positions. It’s during this time that she proves her famous theorem.

The fateful year of 1933 comes round soon enough. By now, Emmy is a Professor herself but that simply makes her a bigger target. Adolf Hitler has become German Chancellor and the Nazis are hijacking German Higher Education. Jewish Professors like Emmy are kicked out of academia but she falls on her feet.

The distinguished mathematician Hermann Weyl recommended Emmy to a post in the United States at Bryn Mawr College, which she took up in 1934. Sadly, her life in the States was a short one: she died from cancer the following year and her ashes are buried in the Bryn Mawr Library cloister.

Emmy Noether is the most famous woman mathematician and scientist you have never heard of. So what is this celebrated ‘Noether’s theorem’ that she proved?

Emmy’s Theorem

You remember back in school when you were taught that energy is conserved? You may recall that you also learned similar laws: momentum is conserved both in its linear and angular form. Later you learned that total electric charge is conserved, so it can neither be created nor destroyed.

If you were a particularly precocious or evil-minded student you may have asked the teacher: ‘Why? Why is energy conserved?’

And the teacher will have replied with words that translate as: ‘I have no idea, be quiet you obnoxious child.’

But Emmy knew better. If you had asked Emmy she would have told you that wherever you have something conserved, it’s because there’s an underlying symmetry.

You do an experiment today or you do it tomorrow, you’ll get the same result: physics doesn’t care what day it is. We dignify this obvious fact with a fancy name – ‘time translation symmetry’. So this is a symmetry of nature, and Emmy’s theorem gives us the corresponding conserved quantity. Amazingly, it turns out to be energy. The reason energy is conserved is that the laws of nature are symmetrical in time. Not exactly obvious, is it?

If you do an experiment in this place or that, it makes no difference; the universe respects ‘space translation symmetry’. ‘Emmy,’ we ask: ‘What’s the corresponding conserved quality?’ She replies, ‘Oh yes, that one is linear momentum.’

Similarly, physics doesn’t change if you’re looking in this or that particular direction. Emmy confirms that this gives us the principle of conservation of angular momentum.

So Emmy Noether provided the deep-down reason for the conservations laws of school physics – they are a direct consequence of the space-time symmetry of the universe. But Emmy gave us much, much more. The symmetry that is associated with charge conservation, which we mentioned above, is the global gauge invariance of the electromagnetic field. Digging deeper, the conservation laws of quantum mechanics, which lead to the Standard Model of particle physics, are derived via ‘internal’ symmetries through Noether’s theorem.

Emmy as a person

Emmy was ‘mostly unconcerned about appearance and manners, she focused on her studies to the exclusion of romance and fashion. A distinguished algebraist, Olga Taussky-Todd, described a luncheon during which Noether, wholly engrossed in a discussion of mathematics, “gesticulated wildly” as she ate and “spilled her food constantly and wiped it off from her dress, completely unperturbed.”

‘Appearance-conscious students cringed as she retrieved a handkerchief from her blouse and ignored the increasing disarray of her hair during a lecture. Two female students once approached her during a break in a two-hour class to express their concern, but were unable to break through the energetic mathematics discussion she was having with other students.’ [Wikipedia].

Mathematicians, huh?

A personal note

I first met Emmy Noether (her work, that is) back in the 1980s when I was working in formal software engineering. Our system was based on advanced math: abstract algebra, denotational semantics, category theory and we found Emmy’s work everywhere.

Much later I studied quantum mechanics and there she was again: to my amazement, the same Emmy!

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Emmy Noether (1882–1935): her theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.