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Culture, Education, Mathematics, Society

Who is Emmy Noether?

My graduate education in mathematics at Michigan State University (more long ago than I care to remember) must somehow have been more broadminded than I thought at the time, since I can recall being made aware of the mathematician Amalie (Emmy) Noether and studying her work. Natalie Angier’s column in the New York Times this week introduces her readers to Emmy Noether with the observation that while “Scientists are a famously anonymous lot, but few can match in the depths of her perverse and unmerited obscurity the 20th-century mathematical genius Amalie Noether.”

Albert Einstein called her the most “significant” and “creative” female mathematician of all time, and others of her contemporaries were inclined to drop the modification by sex. She invented a theorem that united with magisterial concision two conceptual pillars of physics: symmetry in nature and the universal laws of conservation. Some consider Noether’s theorem, as it is now called, as important as Einstein’s theory of relativity. (New York Times)

Perhaps it was in Lee Sonneborn’s class in Abstract Algebra, studying rings and groups, the subject of some of Noether’s work that I first heard of Emmy Noether. Angier notes that Noether was born in Erlangen, Germany, 130 years ago this month, and Angier seeks to correct the mistreatment science and mathematics have given to Noether by having seemingly forgotten her. What I want to know is why does it seem thus so often, why does it seem that we either forget about the contributions of women mathematicians and physicists; or if, as in the case of Emmy Noether, when the contributions are so important we can’t forget them, we apparently forget who made them.

Noether was a highly prolific mathematician, publishing groundbreaking papers, sometimes under a man’s name, in rarefied fields of abstract algebra and ring theory. And when she applied her equations to the universe around her, she discovered some of its basic rules, like how time and energy are related, and why it is, as the physicist Lee Smolin of the Perimeter Institute put it, “that riding a bicycle is safe.”

Ransom Stephens, a physicist and novelist who has lectured widely on Noether, said, “You can make a strong case that her theorem is the backbone on which all of modern physics is built.”

What is Noether’s Theorem? Angier describes it especially well.

What the revolutionary theorem says, in cartoon essence, is the following: Wherever you find some sort of symmetry in nature, some predictability or homogeneity of parts, you’ll find lurking in the background a corresponding conservation — of momentum, electric charge, energy or the like. If a bicycle wheel is radially symmetric, if you can spin it on its axis and it still looks the same in all directions, well, then, that symmetric translation must yield a corresponding conservation. By applying the principles and calculations embodied in Noether’s theorem, you’ll see that it is angular momentum, the Newtonian impulse that keeps bicyclists upright and on the move.

Some of the relationships to pop out of the theorem are startling, the most profound one linking time and energy. Noether’s theorem shows that a symmetry of time — like the fact that whether you throw a ball in the air tomorrow or make the same toss next week will have no effect on the ball’s trajectory — is directly related to the conservation of energy, our old homily that energy can be neither created nor destroyed but merely changes form.

Noether’s Wikipedia entry is appropriately lengthy and adds to the list of mathematicians and physicists who considered her the most important female scientist of all time. Wikipedia discusses all of Noether’s work, throughout her life, in consderable detail and is very well worth reading.

I particularly noted this passage about Noether’s influence on the revolution in mathematics that occurred in the 19th and the 20th Centuries.

In the century from 1832 to Noether’s death in 1935, the field of mathematics—specifically algebra—underwent a profound revolution, whose reverberations are still being felt. Mathematicians of previous centuries had worked on practical methods for solving specific types of equations… [Beginning with work by Gauss, Gal,ois, and others in 1830...] research turned to determining the properties of ever-more-abstract systems defined by ever-more-universal rules. Noether’s most important contributions to mathematics were to the development of this new field, abstract algebra. (Wikipedia)

Perhaps this is why I think it must have been in Professor Sonneborn’s Abstract Algebra that I first learned of Emmy Noether.


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