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Over here I post a ton of physics / math / general interesting posts in an attempt to make your brain feel good. My aim is to be as informative as possible, all while posting fascinating things that hopefully enlighten us both a little to the mysteries of our truly wondrous universe(s?). Plus, how would you know if the blog exists or not unless you observe it? Boom, just pulled the Schrödinger’s cat card. Now you have to check it out - trust me, it said so in an equation somewhere.

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Possibly the Greatest Mathematician You’ve Never Heard Of

So I was recently reading The Universe in the Rearview Mirror by Dave Goldberg (which I really recommend), and a little less than halfway through I read the name Emmy Noether for the first time. In retrospect, I’m embarrassed that I had never heard of her before; as Goldberg writes, “few people in the twentieth century did more to explain how the universe ultimately works.” 

The New York Times wrote:

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.

Noether (pronounced NER-ter) was born in Erlangen, Germany, in 1882. Despite her father being a prominent mathematician of the time, she had a number of things working against her - not only was she a female in Germany at a time when most German universities didn’t even accept female students, but she was also a Jewish pacifist in the midst of the Nazis’ rise to power. 

Due to her brilliance, she managed to achieve the equivalent of a “guest-lecturer” position at Göttingen, where she began to study the mathematical topic of invariance, numbers (variables) that can be transformed and manipulated in various ways and still remain constant in certain ways. “In the relationship between a star and its planet, for example, the shape and radius of the planetary orbit may change, but the gravitational attraction conjoining one to the other remains the same — and there’s your invariance.”

In 1915, once Einstein published his general theory of relativity, Noether began working her invariance work with it, and eventually derived Noether’s theorem, a remarkably deep expression that combines symmetry with conservation - it effectively states that every symmetry corresponds to a conserved quantity. 

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.

With this in mind, it’s quite surprising that Noether has been largely forgotten outside of especially nerdy circles. Nonetheless, she was one of the most remarkable theoreticians of all time, and her work has resounding applications that still fascinate and push our greatest minds forward today. 

Sources: NYTimes, Goldberg

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