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The Two Mathematical Careers of Emmy Noether

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Women in Mathematics

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 10))

Abstract

The received view of Emmy Noether as the champion of David Hilbert’s new style of algebra is not false (as you can see from the fact that Hermann Weyl urged this view). But it seriously understates Noether’s mathematical ambition and her influence on young mathematicians around her and on all of mathematics since. In fact Noether was an internationally recognized mathematician by age 30, teaching unofficially in Erlangen, before she took up the new algebra or began any of her work that is remembered today. That first career, though it used quite old-fashioned mathematics even by the standards of Erlangen, gave her insights she carried on throughout her very different, distinctively 20th century career in Göttingen and Bryn Mawr.

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Notes

  1. 1.

    Noether wrote that she meant to restructure Galois theory [50], basic abstract algebra and algebraic topology [55], invariants of groups [56], algebraic number theory and the theory of complex algebraic functions [57], group representation theory [58], and class field theory [59, 60], all by resting them on homomorphism and isomorphism theorems. Her students say she extended exactly this to point set topology [5, p. 108] and algebraic geometry [81, p. 173].

  2. 2.

    For a sketch of classical invariant theory and discussion of Gordan’s remark, see [42]. One student of Hilbert in the 1890s later took the quote to mean the proof was “a ray of light from a higher world penetrating our earthly darkness” [31, p. 25]. Gordan was known for a “keen sense of humor,” though, not piety [83, p. 117].

  3. 3.

    When Norbert Wiener wrote to support Noether for a job in the U.S. he described biases against her in the euphemisms of the times: “sex, race, and liberal attitude” [24, p. 35]. Here “race” was a polite way to avoid saying Jew, and “liberal” a polite term for Marxist. The weight of these biases shifted over time as Noether and the forces around her changed. Anti-woman feeling was strong throughout, as Tollmien, [76], shows. But the public record is skewed because people try to look good. The stern discipline of the traditional, all-male university was easy to frame as a lofty ideal; so it was easy for reactionaries to avow. Anti-semitism, while widespread at every level of society, was especially associated with low class agitators so cultured people did not like to discuss it. And, like a cancer diagnosis, allegations of communism were best not discussed at all—in Germany or in the U.S.

  4. 4.

    Kosmann-Schwarzbach [30] has a great deal more on Einstein and Noether.

  5. 5.

    For each ring, R, notably including the group ring for any group, Noether derives an Isomorphism Theorem specific to R-modules from a corresponding Homomorphism Theorem.

  6. 6.

    She clearly ignores analytic questions of existence of solutions. She may believe these are easily answered when the integrands are “analytic or at least continuous and continuously differentiable finitely often” (meaning infinitely often) [51, pp. 236]. She may consider those questions irrelevant since that assumption lets her use formal Taylor series in the Eulerian style she knew from \(\S \S\) 5–10 of [28]. Or she may echo a remark by Hilbert about “purely formal” calculation which seems to mean ignoring details for the moment [26, p. 470].

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  1. Case Western Reserve University, Cleveland, OH, USA

    Colin McLarty

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Editors and Affiliations

  1. Department of Mathematics, University of Redlands, Redlands, California, USA

    Janet L. Beery

  2. Department of Mathematics, Appalachian State University, Boone, North Carolina, USA

    Sarah J. Greenwald

  3. Department of Mathematics, Lamar University, Beaumont, Texas, USA

    Jacqueline A. Jensen-Vallin

  4. Department of Mathematics, Fordham University, Bronx, New York, USA

    Maura B. Mast

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McLarty, C. (2017). The Two Mathematical Careers of Emmy Noether. In: Beery, J., Greenwald, S., Jensen-Vallin, J., Mast, M. (eds) Women in Mathematics. Association for Women in Mathematics Series, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-66694-5_13

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