Emmy Noether

Here is a little text that I’ve had almost finished for some time. I thought today, 8th of March, would be a suitable day to post it:

Some time ago a colleague of mine was revising his book on the history of science and creative thinking for a new edition. He had noticed that basically all the names he had mentioned from the history of science were men. He had written something on Marie Curie of course, but that was it. He came to me and asked if I knew about any women who had made outstanding contributions to the development of science. One name that immediately came to my mind was Emmy Noether.

Emmy Noether (1882-1935) was a German mathematician who worked at the University of Gottingen, until she moved to USA in the 1930’s, to escape the German nazi -regime. For many years, she worked without being paid, because women were not supposed to do research. The famous mathematician David Hilbert announced Noether’s courses in his own name, to avoid that they were stopped by the university board (Hilbert wrote an angry letter to the board, asking if the university was supposed to be an academic institution or a spa).

Emmy Noether has made important contributions to both abstract algebra and to theoretical physics. As a student, I first heard about her work in the quantum mechanics and quantum field theory courses, and this amazing property known as Noether’s theorem. It states the relationship between mathematical symmetries and conservation laws. Well known to anyone who had basic physics in high school is the principle of conservation of energy. Using Noether’s theorem, this follows from symmetry with respect to time: The potential energy of a bucket of water running off the Niagara Falls would be the same if it was measured today or next week. It’s the vertical drop that counts, not the day you measure it.

The symmetries related to space and time are relatively simple to understand. But Noether’s theorem applies to more abstract cases too. One example is the so-called gauge symmetries that lead to conservation of electric charge (these currents that flow through all our electric and electronic devices). Electric currents can not just appear or disappear. A similar, but even more abstract, example is the gauge symmetries leading to conservation of “color” in quantum chromo dynamics, the theory of nuclear forces (these enormous forces that we release in nuclear power plants).

Finally, there are empirical conservation laws that are not related to known symmetries, and the converse of Noether’s theorem has never been proved. Not even Emmy Noether was able to do that.