Emmy Noether: pillar of 20th century mathematics and physics

With all the attention given lately to the tentative discovery of the long-sought Higgs boson in experiments at the Large Hardon Collider (LHC) in Europe, one would think that more attention would be drawn to Amalie Emmy Noether, a woman who made groundbreaking contributions to both mathematics and physics.

Noether (pronounced “ner-ter”) was born in 1882 to a Jewish family in Bavaria, Germany. Both her father and her brother were also mathematicians of some renown. She started out studying English, French and piano, which were thought to be more appropriate for a woman, but inevitably she became interested in mathematics. Although she was barred from formally enrolling in mathematics at the University of Erlangen, she simply audited all of the courses, and did so well on her exams that she was grudgingly granted the equivalent of a bachelor’s degree.

She then studied at the University of Erlangen, where she received a Ph.D. in 1907. She worked at the Mathematical Institute there for seven years without pay, since at the time women were largely excluded from academic positions.

But ultimately her brilliance was obvious to everyone she worked with. Famed mathematician David Hilbert in particular fought an ultimately successful battle to secure for her a faculty appointment the University of Gottingen in 1915. “I do not see that the sex of the candidate is an argument against her,” Hilbert railed indignantly to the university administration. This relationship is movingly detailed in Loving and Hating Mathematics  (Princeton University Press, 2010)  by mathematician Reuben Hersh) and  social scientist Vera John-Steiner.

Noether remained at Gottingen until 1933, when with the rise of the Nazi regime in Germany, she fled to the United States, where she taught at Bryn Mawr College in Pennsylvania until her untimely death from ovarian cancer two years later at the age of 53.

Noether made signal contributions to the mathematics of rings, fields and algebras. The Dutch mathematician B. L. van der Waerden became a leading expositor of work, which he incorporated into the second volume of his influential 1931 work Moderne Algebra.

However, her most notable achievement was her work in the area of application of these algebraic concepts to physics. Her interest in physics began in 1917, when she fell “head over ear” with Einstein’s general relativity, and began to apply her earlier work in invariance to some of the complexities of the theory. Ultimately, this led to her most famous work, now known as “Noether’s theorem.”

“Noether’s theorem” is fundamental to all modern physics. In colloquial terms, she demonstrated that whenever a symmetry is observed in physics, it is deeply connected with an underlying conservation law. For example, she showed that the symmetry of time inherent in physical laws is directly connected to the law of conservation of energy. Similarly, the symmetry evident when an object is spinning is directly connected to the law of conservation of angular momentum.

Physicists Leon Lederman and Christopher Hill have termed Noether’s theorem “one of the most important mathematical theorems ever proved in guiding the development of modern physics” [Leon M. Lederman and Christopher T. Hill, “Symmetry and the Beautiful Universe,” Prometheus Books, Amherst, 2004, pg. 23-25]. Similarly, Lisa Randall, a well-known Harvard physicist, remarked that when she learned that the author of Noether’s theorem, which she had learned from early study in physics, was a “she,” Randall commented that it was “exciting and inspirational.”

Additional details can be found in a well-written [NY Times article], from which some of the above was taken.

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