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The Prequel

First, I’m a geek.  I must be the only dude in the neighborhood who has an Emmy Noether t-shirt, and probably the only one in the town who ASKED for an Emmy Noether T-Shirt.  It’s pretty hard to determine actual hotness in V-garb, but even in Victorian-era duds, she looks arright.

And she’s not even on the list that I was gonna talk about, oops. The two I’m thinking of are known in what we call the humanities, in the trashbin that constitutes our segregation of issues of the mind. Noether’s a mathematician.

“Hey, Mister, my eyes are down here…”

This lady had a pair of frontal lobes that won’t quit.  “Hey, Mister, my eyes are down here…”  The usual blurbs make a deal about her being a female mathematician.  I actually ran across her as a MATHEMATICIAN first, E. Noether, and then found out that she was a she.

Wiki says that she was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. I seriously doubt that was meant to highlight her femininity. You can argue, especially from Einstein’s perspective, that the phrase “man-or-woman” could be substituted.

In 1915, she was invited by David Hilbert and Felix Klein to join the mathematics department at the University of Göttingen, a world-renowned center of mathematical research.  Those two may not ring a bell, but they’re two of the most brilliant mathematicians in history.  Good pick, and first-rounder indeed. 

As one of the leading mathematicians of her time, she developed the theories of rings, fields, and algebras. In physics, Noether’s theorem explains the connection between symmetry and conservation laws.

The last sentence gives an awesome fact.  Remember, she’s a mathematician – physics wasn’t her gig.  If Einstein were talking about mathematics, he’d eagerly have allowed Noether to erase his blackboard and fix his thinking.  He was a physicist, although he understood math pretty good.

There’s only one mathematician to compare her to, and that’s Muhammad al-Khwarizmi. She’d probably have agreed, and so would have al-Khwarizmi, although he’s gone about 1200 years ago.  Sorry, but when it comes to the All-Star Game, there’s no White Euro Boys on the team.  Suck it up, mates.

Sports Analogy

To pick analogies out of professional sports, there’s nobody.  Babe Ruth came close, he’d be an A- on this list.  If he had gone on with his very promising pitching skills, as well as hitting, he might have made the list.  Sorry, Babe.

In the mathematics of physics, there are truly several eras:

  1. Observational physics“Hey, Ug, apple fall from tree!”  That continued until…
  2. Newtonian physics.  Newton (and Leibniz) came up with some useful mathematical tools that allowed for very accurate guesses at how things move.  Newton offered some empirical laws for how things move.
  3. The Physics of Light.  James C. Maxwell wrote a rough notebook about light, and Oliver Heaviside read it.  He understood it.  He turned it from a decent set of ideas into an awesome set of ideas.  He proposed principles in physical mathematics – many of which were not rigorously derived by him but subsequently worked through to be valid.  His name is all over pure and applied mathematics – but not in the popular press.  His famous four equations for light are called “Maxwell’s Equations.”  They were never written by Maxwell, nor did he imply them.  But Heaviside was a loony, and even worse, not from a Prestigious University (or even any University at all.)  Modern times were sinking in, and he was ignored.
  4. Noether’s Theorem.  Physicists were flying by the seat of their pants in areas like Conservation of Stuff.  It seemed that Some Stuff, like momentum and energy, were conserved whenever they looked.  Therefore, there must be a law.  Review (1) above, “Hey, Ug, apple fall from tree!”  Then, in one principle, Noether unlocked the mathematics of Conservation of Stuff.  Everything after came through her ideas.

After Hiroshima and Nagasaki, Einstein was (erroneously) credited with E=mc2, which was not his idea (it was Lorentz, and predated his birth.)  He had some great ideas in physics, but not really in mathematics.

You should look at al-Khwarismi.  He took arithmetic from adding and subtracting arabic numerals, to algebra, in around 800 AD.  He moved the playing field completely.  If you guessed on how many mathematicians it took to go from Point A to Point B, you’d guess about twenty.  Nope.  Him.

Then algebra lay around in the weeks for a millennium or two, until Emmy Noether did the same thing.  Her revolutions were more focused, rather than the broadness of al-Khwarismi.

Sports Analogy II

To offer an analogy, say that Noether and A.K. were starting pitchers on the same team, National League.  They’re each starting a game in a doubleheader.

AK starts first, pitches a complete game, goes three-for-three on the basepaths with 3HR, 6RBI, and pitches a perfect game.

Noether starts the second game, goes one-for-one on the basepaths (with two intentional walks), 1HR  1RBI, and also pitches a perfect game.

How would you compare their performances?  AK had a little better outing, better at the plate.

After AK’s game, there would be chaos in the stands, and wildness in the park.  It would be the best performance in the history of baseball.  And Noether would put in what, arguably, could be called the second-best-performance in the history of baseball.  Maybe that’s why she’s not remembered much (Neither are AK or Heaviside).

Unbelievable.  It’s just unbelievable.  If you weren’t there to see it, you wouldn’t believe it.

American physicists Leon M. Lederman and Christopher T. Hill argue in their book Symmetry and the Beautiful Universe that Noether’s theorem is “certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics, possibly on a par with the Pythagorean theorem”.

And that’s just my warmup game for this discussion.  So much for Emmy Noether (and tip of the hat to A.K.).