Tuesday, September 25, 2012

Badass Mathematicians - 2: Emmy Noether

(Part 2 of an occasional series where I profile some influential mathematicians. Part 1, covering the volatile Frenchman Evariste Galois, is here )

Emmy Noether was that special type of badass whose contributions to pure mathematics ended up becoming the impetus for much of modern physics. Before we get to that bit of badassery, some details about her life. She was born in Germany in 1882. Father Max was a mathematician also. Wikipedia tells me he names a couple theorems in his own right. Couple of her brothers got doctorates and such. In short, she was part of an academically inclined family.
What a badass bowtie

After going through routine schooling, where she was a pretty good student, she reach a dead end. Society expected her to become a teacher for girls' school. Noether had other ideas. The powers that be at her university saw great ills in allowing mixed education. They let her enroll grudgingly. Within a few years, she hammered out a fine PhD thesis titled "On Complete Systems of Invariants for Ternary Biquadratic Forms". Later she called it crap. Sounds perfectly fine to me, but hey what do I know.

Contemporary mathematical beast David Hilbert invited her to join him at Gottigen university. There, despite toiling hard as a superb professor without pay for the first two years, she produced some solid papers on topics well above my pay grade.

It was there she formulated the theorem that would propel her into the pantheon of badasses. Here's the statement:

"To every differentiable symmetry generated by local actions, there corresponds a conserved current."

Huh? What? Here is what it means in plain (relatively speaking) English: if a physical law does not change under conditions of space and time, it must have a quantity that is conserved.

This theorem basically explains why conservation of momentum and energy are true. This became key in formulating advanced models for quantum mechanics and particle physics. Since any model describing a physical law (something like the nuclear force, for example) has to have a conserved quantity, one's job of finding possible models just became (relatively) easier.

The explosion of theories to describe exotic particle interactions through the 1960's and 1970's owes a lot to Noether. You might remember all the hoopla about the Higgs Boson couple months ago. Noether's theorem operating behind the scenes there too.

When Hitler came to power in Germany, Noether came to the States. Here she spent two happy years teaching at Bryn Mawr college before she passed away of complications due to an ovarian cyst.

As if concocting one seminal theorem wasn't enough, Noether proved several key results in stuff like abstract algebra, ring theory, noncommutative algebras (look these things up on wiki if you're interested. The last one is pretty cool).

Next time someone asks you at a cocktail party why energy is conserved just snap back, "Because Emmy says so!"

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