In Honor of Ada Lovelace Day: Emmy Noether

Today, March 24, is Ada Lovelace Day. In honor of Ada Lovelace, sponsor of Charles Babbage and arguably the world;s first computer programmer, bloggers have pledged to post about the contributions of women to science and technology.

If you ask a professional mathematician to name the woman who has made the greatest contribution to math, the odds are very high that the  answer will be Emmy Noether. Yet this major figure in 20th century mathematics is all but unknown to the general public, probably because her groundbreaking work is not terribly accessible to non-mathematicians.

Amalie Emmy Noether was born in 1882 in the university town of Erlangen, Germany, and studied mathematics there. In 1915, she was invited to the University of Göttingen by David Hilbert, the preeminent mathematician of the time. The Göttingen faculty, however, to strong exception to a woman joining them, so Noether ended up teaching courses nominally offered by Hilbert. In 1919, her habilitation, the equivalent of a doctoral dissertation, was accepted and she became a privatdozent, more or less an assistant professor.

At Goettingen, Noether joined some of the greatest minds of early 20th century mathematics, including Hermann Weyl, B. L. van der Waerden, Edmund Landau, and Richard Courant. But in 1933, she and many of Goettingen’s other leading lights lost their positions in the new Nazi government’s purge of Jewish academics. American mathematicians, led by Oswald Veblen of Princeton, mounted a campaign to bring their displaced German colleagues to the U.S., and Noether accepted a post at Bryn Mawr. Unfortunately, the new position did not last long; Noether developed serious complications after surgery and died in 1935 at the age of 53.

Noether worked in many fields of modern mathematics, but she is best known for her efforts in abstract algebra, the study of the fundamental structures of mathematics, particularly the study of rings and ideals. (As a really simple example, the integers form a ring, a structure with two operations–addition and multiplication–that meets a number of other conditions. All of the multitples of 5 form an ideal. And to be really precise, the integers are an example of a Noetherian ring, a concept that is too complex for this post.)

Noether also made important contributions to mathematical physics. Her work there is best known for Noether’s theorem, which states that every symmetry of a system is associated with some quantity that is conserved. For example, symmetry of rotation in a  physical system is associated with the conservation of angular momentum.

Although women are still underrepresented in the ranks of research mathematicians, they are hardly a rarity anymore. Emmy Noether helped lead the way.