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"My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously."
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Emmy Noethers were old acquaintances from classical physics. ... asserts that any — Emmy Noether
"s were old acquaintances from classical physics. ... asserts that any continuous symmetry leads to a conservation law. It is rather intuitive... After all, symmetry reflects invariance under a transformation, and therefore there must exist a quantity that remains invariant or, in other words, that is conserved. For instance, a circle is invariant under rotations about its centre. ...Hence, the symmetry of a circle is associated with the conservation of distance ...The power of Noethers theorem was to show that this intuitive concept is valid for any continuous symmetry ...from Noethers theorem we discover that the conservation of electric charge is the consequence of the special rotational symmetry of QED... [acting upon] an abstract space defined by the quantum fields."
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Emmy Noether
Emmy Noether
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Amalie Emmy Noether was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's first and second theorems, which are fundamental in mathematical physics. Noether was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. As one of the leading math
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"Ich habe das symbolische Rechnen mit Stumpf und Stil verlernt. I have completely forgotten the symbolic calculus."
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Emmy NoetherQuote
"Es steht alles schon bei Dedekind. [It is already all in Dedekind.]"
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Emmy NoetherQuote
"Emmy Noether introduced the notion of a representation space— a vector space upon which the elements of the algebra operate as linear transformations, the composition of the linear transformations reflecting the multiplication in the algebra. By doing so she enables us to use our geometric intuition. Her point of view stresses the essential fact about a simple algebra, namely, that it has only one type of irreducible space and that it is faithfully represented by its operation on this space. s statement that the simple algebra is a total matrix algebra over a quasifield is now more understandable. It simply means that all transformations of this space which are linear with respect to a certain quasifield are produced by the algebra. This treatment of algebras may be found in s . Recently it has been discovered that this last described treatment of simple algebras is capable of generalization to a far wider class of rings."
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Emmy NoetherQuote
"Her dependence on Gordan did not last long; he was important as a starting point, but was not of lasting scientific influence... Gordan retired in 1910; he was followed first by , and the next year by Ernst Fischer. Fischer’s field was algebra again, in particular the theory of elimination and of invariants. He exerted upon Emmy Noether, I believe, a more penetrating influence than Gordan did. Under his direction the transition from Gordan’s formal standpoint to the Hilbert method of approach was accomplished. She refers in her papers at this time again and again to conversations with Fischer. This epoch extends until about 1919."
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Emmy NoetherQuote
"Another change in the formulation of basic combinatorial properties, made... 1923 to 1930 by a number of men and possibly suggested by Emmy Noether, was to recast the theory of chains, cycles, and bounding cycles into the language of group theory."
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Emmy Noether