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Standing on the shoulders of silent giants

19 November 2018
By Clare Birch, current Bachelor of Science (Advanced) student at the University of Sydney
How this writer finds inspiration in our female forebears
Emmy Noether

Emmy Noether, leading mathematician who created one of the most important mathematical theorems ever proved in guiding the development of modern physics.

I am a woman in science. I’ve only felt like one since sometime last year, though, when someone informed me that women were just incapable of understanding electromagnetism like men could. Women just shouldn’t do science apparently.

As much as anything, we might chalk this one up to ignorance. After all, save a few essential public figures, we’re pretty lacking in high profile female scientists to use as counterevidence to claims like this. It wasn’t until this semester – just a few weeks ago, actually – that I learned about Emmy Noether, the woman behind "one of the most important mathematical theorems ever proved in guiding the development of modern physics" according to physicists Leon Lederman and Christopher Hill in their 2004 book ‘Symmetry and the Beautiful Universe’.

Born in 1882 in Bavaria, Noether was the eldest of four children. With a mathematician for a father and two brothers with doctorates in mathematics and sciences, you might imagine that Noether’s path to mathematical success was as paved as possible. This wasn’t the case though – Noether didn’t show remarkable academic prowess throughout her childhood and adolescence, and initially trained as a French and English teacher. She never took up teaching though, choosing instead to study astronomy and mathematics at the University of Erlangen, where she was one of only two female students at the university which had 986 students, and was only allowed to audit classes rather than participate fully. She eventually completed her mathematics thesis – summa cum laude – in 1907.

The thesis itself was a major step for women in general, obtained at a university that had until very recently not accepted women as students. This was not the end of Noether’s battle to make herself heard. It was, however, the beginning of an illustrious career.

In 1915, a few years after gaining her doctorate, Noether was invited to work with David Hilbert and Felix Klein, two other hugely influential figures in building the maths behind modern theoretical physics. She started with a giant problem: Albert Einstein’s recently published theory of general relativity.

You see, Einstein’s theory seemed to break one of the most fundamental laws of physics: the total energy of a system with nothing going in and nothing coming out must be conserved. The law of conservation of energy – one of the first steps in any high school physics course – straight out the window!

Noether’s theorem was proved in 1915 and published in 1918 as a solution to this problem. In it, she rigorously formalises the concept of conservation laws, which are what we call absolute statements about values staying the same in a system like the one above. Noether drew a link between the symmetry of a system – that is, how it can remain unchanged when moved, rotated, or reflected – and what properties of that system will not change as time progresses. That means it’s not just energy; it can be a whole variety of quantities, depending on the system.

This was huge. Not only did Noether’s theorem answer a big question for Einstein, it also completely changed the foundations of theoretical physics and the real-life solutions that arise from the area.

As if that wasn’t enough, Noether continued to complete pioneering work in abstract algebra and theoretical physics until her death in 1935. She lectured under Hilbert’s name, was granted an honorary professorship, and was noted to be a patient and nurturing graduate advisor. Her work transcended generations.

If Noether’s anyone to go by, I think it’s pretty clear that women belong in science. The more I learn, the more I find myself proud to be studying in a field built on the shoulders of kind, brilliant, perseverant women.