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View Diary: Women in Science: Emmy Noether 1882-1935 (22 comments)

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  •  Modern Algebra (10+ / 0-)

    Although she proved many fundamental results in Algebra -- such as the finite generation of invariants of various rings (this requires a fair background in Math to understand), perhaps her greatest lasting influence is in what's called Modern Algebra.  She gave many lectures in the 1920's and notes were faithfully taken by the young mathematician B. L van der Waerden.  He later published a groundbreaking book called Modern Algebra (originally in the German, later in many translations).  This book revolutionized the way that mathematicians (and physicists) looked at Algebra.  If one looked looks at what research Algebra looked like in the mid to to late 19th century (such as by her advisor -- Paul Gordan -- "the king of the invariants") you'd see lots of heroic calculation mostly oriented to the specific problem at hand.  Modern Algebra is more abstract and general, but seeing previously unrecognized connections between different parts of mathematics.

    There are no solved problems; there are only problems that are more or less solved. Henri Poincare

    by Bourbaki on Tue Apr 09, 2013 at 07:16:08 AM PDT

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