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12 July 2010

another margin scrawl ./ young Evariste has some sort of thing going with a woman named Motel / Je n'ai pas le temps / Ne pleure pas, Alfred!

 Click image for larger.

M**** liked my Kepler stamps, here's V.6 [see earlier post], I think I'll swear an oath to stop futzing with it now, but the cones needed an old-fashioned razor blade to cut the section curves.
There's one other Fairy Tale about marginalia, and everybody loves this one because it's worse than tragic -- it's tragic and sordid and icky and squalid and tawdry.
The ancient Greeks tattooed about a dozen Thingies (a technical term) on all subsequent mathematics. A few of them were sorta useless and not much more valuable than being annoying, a few of them were Wrong Guesses, but most of them were amazingly profound insights into the heart of math, and they've remained deeply ingrained in the way everybody does and thinks about math ever since. On Planet Earth since about 500 BC (Pythagoras), math has dressed, smelled, tasted and spoken Greek.
The Gods gave Athenians three problems:
1. On the Acropolis, the statue of Athena stood on a pedestal which was a cube. The Gods commanded the Athenians to replace it with a bigger pedestal -- a cube with twice the volume of the original.
2. Given a square with side length s and Area = s² , construct a circle with the same Area.

3. Given any arbitrary angle, divide it into three equal angles.

Oh, and you have to do all this using only these tools:

* unmarked straightedge (ruler, but blank)
* compass or dividers (like nautical chart dividers)

The three problems remained unsolved, no one made any progress toward solving them, all the world's math geniuses were clueless, until one night in Paris in 1832.

Descartes showed that the straightedge and divider thing -- the essence of Greek geometry -- has specific meaning and definition in algebra. So a modern restatement of the 3 problems would say

using only whole numbers,
and the arithmetic operations
+ - x / and [square root]

From the start, Evariste Galois' math teachers saw he had enormous talent, but he was a wild teenage screwball with toxic interpersonal skills. His talent should have rocketed him to the top of France's math establishment, but his personality kept him hopelesly stuck at the bottom. 

His other problem was that when he did try to publish his discoveries, they were so original and unprecedented, nobody understood them.  

This was the Golden Age of French mathematics, and the establishment was determined Galois would play no part in it.

To add to the lad's woes, he had a flawless instinct for political activities and loud treasonous speeches that was always getting him into trouble -- sometimes a little time in the Bastille, other times the death sentence. And he had a Very Messy Romantic Life.

He had some sort of relationship with a woman named Motel, and some other guy, or several other guys, also had some sort of relationship with Mlle. Motel. One of them said something so uncomplimentary about Mlle. Motel that Galois -- an aristocrat long since disowned by his dad -- challenged the guy to a pistol duel. They chose a place and a time a few days away.

Like most math nerds, Galois had no skills in pistol duelling, so he guessed a long, relaxing math career was not in his future.
But he'd already solved the 3 Ancient Greek Puzzles. And he knew it, and he knew how important and groundbreaking his solution was. 
He just hadn't taken a leisurely month to write it all down in clear, publishable form, after which the world would immediately honor him as the most brilliant mathematician of the age.

In fact he had only one night, the night before the early-morning duel, to put his ideas down on paper. And these are very long, complicated, and entirely new ideas.

What a very messy, barely legible paper it is.

And all around the margins, time after time, is the horrible scrawl:

Je n'ai pas le temps
Early in the morning of May 30, 1832, he was shot in the abdomen and died the following day at ten in the Cochin hospital (probably of peritonitis) after refusing the offices of a priest. He was 20 years old. His last words to his brother Alfred were:
Ne pleure pas, Alfred! J'ai besoin de tout mon courage pour mourir à vingt ans! (Don't cry, Alfred! I need all my courage to die at twenty.)
Today his last scrawl is universally called Galois Theory, sometimes also Abstract Algebra.

Oh, what was his solution to the 3 ancient problems? He proved that they can't be solved, there is no solution, it can't be done.

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