I remember studying some of Noether's early work in a course on classical mechanics at university. It's one of the things I remember from my degree that still blows my mind.
Noether's theorems in classical mechanics associate symmetries of the laws governing a physical system to conservations laws of that system. For example,
Spatial translation symmetry => Conservation of momentum
Spatial rotation symmetry => Conservation of angular momentum
Time translation symmetry => Conservation of energy
Phase symmetry => Conservation of electric charge
When you study relativity, and unify space and time into four dimensional spacetime, it becomes clear through Noether's theorem that energy and momentum are also related.
Much later on, around 2008, a friend of mine working at Cambridge generalized Noether's result [0] to include non-smooth symmetries as well - showing how CPT (charge-parity-time) symmetry in the Dirac equation leads to new conserved quantities. Epic work.
Yes. Noether theorem is truly a beautiful piece of insight. I also remember fondly spontaneous symmetry breaking [0] as the key mechanism behind phase transitions.
Despite her tremendous insights, Noether suffered constant discrimination from the male-dominated academic society of her time: she was sometimes not even paid for her work, and when she fled Germany during WW2 the best position she could find was at the women's college Bryn Mawr (in an era when other fleeing German scientists were landing positions at the best American research universities).
When she died, the story I recall is that the New York Times printed a very short obituary that mentioned only her brief work as a teacher at Bryn Mawr. Einstein was horrified that such a luminary would receive so little recognition, and he responded by writing a glowing tribute which the Times promptly printed: http://www-history.mcs.st-andrews.ac.uk/Obits2/Noether_Emmy_...
In Göttingen she was at first not tolerated by her peers, but she was strongly supported by Hilbert. In fact she used to announce her lectures under his name, because she was not allowed to give them officially.
I've been circling around group theory and abstract algebra for a while. This incredible Wikipedia article really helps to make the history of these subjects more concrete.
In textbooks, the axioms and theorems seem so dry. It must have been exciting to be in those lectures though, discovering concepts of a new field of mathematics for the first time.
I read quite a lot about Noether when I took a module in the history of mathematics as an undergraduate. Few mathematicians excel so greatly as to have an entire class of ring[0] named after them!
the really sad thing is i was aware (and appreciative) of noether's theorem for years before i learnt she was a woman. she was only ever referred to as "noether" in the textbooks.
Her work on physics was nothing compared to her contributions to algebra and topology. Not only did she basically invent homology groups as we know them today, but she revolutionized the way we think about rings. The ascending and descending chain conditions in algebra are like bread and cheese for the culinary world.
As a physicist, I can't speak to her contributions to pure math -- but Noether's Theorem really is a vitally important part of modern physics. Bread and cheese territory there, too.
Noether's theorems in classical mechanics associate symmetries of the laws governing a physical system to conservations laws of that system. For example,
When you study relativity, and unify space and time into four dimensional spacetime, it becomes clear through Noether's theorem that energy and momentum are also related.Much later on, around 2008, a friend of mine working at Cambridge generalized Noether's result [0] to include non-smooth symmetries as well - showing how CPT (charge-parity-time) symmetry in the Dirac equation leads to new conserved quantities. Epic work.
[0] http://arxiv.org/abs/0808.3943