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I am not well versed in the Physics counterpart of Noether's work, but the mathematics side is quick to explain: the isomorphism theorems in group theory (origi

I am not well versed in the Physics counterpart of Noether's work, but the mathematics side is quick to explain: the isomorphism theorems in group theory (originally, in ring theory) were one of the main impacts of her work. A quick skim of Wikipedia tells me that the isomorphism theorems were later than the theorem in physics [1] [2] by about 5 years. Looking at it quickly, these are not the same thing, and although in spirit similar, I am not sure what the exact historical progression was. I wonder if standard abstract algebra modules could teach this history in a way that tells more about the story behind the isomorphism theorems. In my abstract algebra class, Noether was not really mentioned, and usually the focus is (for example) on the progress from Greek geometry (e.g. squaring the circle) to modern algebra. I don't think anyone is at fault for this, but I would personally like to have a more accessible introduction to Noether's legacy via pure mathematics. [1] https://en.wikipedia.org/wiki/Isomorphism_theorems https://en.wikipedia.org/wiki/Isomorphism_theorems [2] https://en.wikipedia.org/wiki/Noether%27s_theorem https://en.wikipedia.org/wiki/Noether%27s_theorem

Chinjut 7y ago
Ring theory in general was founded in large part via her work. I always find it funny that everyone only makes such a fuss about one physics conservation law/symmetry correspondence she observed (for physical theories that happen to be phrased in terms of Lagrangians/Hamiltonians), while the immense mathematical achievement of her extensive work on ring theory goes largely undiscussed in these kinds of conversations.
- Rerarom 7y ago
  In my pure math studies there was way more emphasis on her work in commutative algebra than on the symmetry / conservation law correspondence. Btw a neglected founder of modern algebra is Steinitz, whose early work on fields (1910) inspired Noether's work on rings.
- thanatropism 7y ago
  Noether's theorem is kind of a grand closure of natural science. It's one of those theorems that gives the sensation of transcending its axiomatic setting and reveal deep philosophical truth. Compare Arrow's impossibility theorem, which is set in the much more familiar realm of order theory, but still appears to say something about the real world.
- mjfl 7y ago
  It's because the physics is more important.

Chinjut 7y ago

Ring theory in general was founded in large part via her work. I always find it funny that everyone only makes such a fuss about one physics conservation law/symmetry correspondence she observed (for physical theories that happen to be phrased in terms of Lagrangians/Hamiltonians), while the immense mathematical achievement of her extensive work on ring theory goes largely undiscussed in these kinds of conversations.

Rerarom 7y ago
In my pure math studies there was way more emphasis on her work in commutative algebra than on the symmetry / conservation law correspondence. Btw a neglected founder of modern algebra is Steinitz, whose early work on fields (1910) inspired Noether's work on rings.
thanatropism 7y ago
Noether's theorem is kind of a grand closure of natural science. It's one of those theorems that gives the sensation of transcending its axiomatic setting and reveal deep philosophical truth. Compare Arrow's impossibility theorem, which is set in the much more familiar realm of order theory, but still appears to say something about the real world.
mjfl 7y ago
It's because the physics is more important.