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Emmy Noether and her Theorem

Posted June 03, 2015 8:41 AM by Bayes

The Center of the Mathematics' Universe

In the early 20th century, Göttingen Germany was the center of the Mathematics' world. Among other greats, here you could find Emmy Noether, who made profound contributions to abstract algebra and theoretical physics (through Noether's theorem). It is near impossible to overestimate Noether's influence on modern theoretical physics. Her theorem explains the connection between symmetry and conservation laws and is utilized in modern theoretical physics frequently.

Given that background, you can understand my interest when I came across the following article:

The female mathematician who changed the course of physics-but couldn't get a job

By 1915, any list of the world's greatest living mathematicians included the name David Hilbert. And though Hilbert previously devoted his career to logic and pure mathematics, he, like many other critical thinkers at the time, eventually became obsessed with a bit of theoretical physics. With World War I raging on throughout Europe, Hilbert could be found sitting in his office at the great university at Göttingen trying and trying again to understand one idea-Einstein's new theory of gravity. Göttingen served as the center of mathematics for the Western world by this point, and Hilbert stood as one of its most notorious thinkers. He was a prominent leader for the minority of mathematicians who preferred a symbolic, axiomatic development in contrast to a more concrete style that emphasized the construction of particular solutions. Many of his peers recoiled from these modern methods, one even calling them "theology." But Hilbert eventually won over most critics through the power and fruitfulness of his research.

For Hilbert, his rigorous approach to mathematics stood out quite a bit from the common practice of scientists, causing him some consternation. "Physics is much too hard for physicists," he famously quipped. So wanting to know more, he invited Einstein to Göttingen to lecture about gravity for a week. Before the year ended, both men would submit papers deriving the complete equations of general relativity. But naturally, the papers differed entirely when it came to their methods. When it came to Einstein's theory, Hilbert and his Göttingen colleagues simply couldn't wrap their minds around a peculiarity having to do with energy. All other physical theories-including electromagnetism, hydrodynamics, and the classical theory of gravity-obeyed local energy conservation. With Einstein's theory, one of the many paradoxical consequences of this failure of energy conservation was that an object could speed up as it lost energy by emitting gravity waves, whereas clearly it should slow down. Unable to make progress, Hilbert turned to the only person he believed might have the specialized knowledge and insight to help. This would-be-savior wasn't even allowed to be a student at Göttingen once upon a time, but Hilbert had long become a fan of this mathematician's highly "abstract" approach (which Hilbert considered similar to his own style). He managed to recruit this soon-to-be partner to Göttingen about the same time Einstein showed up.

And that's when a woman-one Emmy Noether-created what may be the most important single theoretical result in modern physics.

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#1

Re: Emmy Noether and her Theorem

06/07/2015 1:16 AM

Thanks for reminding me of these achievements. My math and physics background is (just) enough to know who Emmy Noether was, but I haven't studied her results in detail.

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Re: Emmy Noether and her Theorem

06/09/2015 2:43 AM

I should add that the connection of overarching principles such as symmetry and conservation is very elegant.

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#2

Re: Emmy Noether and her Theorem

06/08/2015 12:12 AM

Couldn't get a job? What, any job?

She should have emigrated.

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