
Can't solve a quintic? Galois Theory in 1500 words - ColinWright
http://www.lisazhang.ca/2011/12/galois-theory-in-1500-words.html
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nagrom
The background story of Évariste Galois is phenomenal. He was expelled from
school twice, fought in a revolutionary unit, was imprisoned for threatening
the life of the king and revolutionised mathematics forever. He died in a duel
over a woman at the age of 20! <http://en.wikipedia.org/wiki/Évariste_Galois>

Imagine what he would have done if he had lived to 40? There were some really
fascinating characters in the mathematics in the 19th century. A very far
stretch from the world's stereotypes of a repressed, bespectacled geek or the
boring image of mathematics given by high school classes.

~~~
huhtenberg
> _Imagine what he would have done if he had lived to 40?_

Sorry, can't. Marriage alone is a major productivity killer, then there are
also kids and general life problems. There was a study that basically built a
histogram of mathematicians' (?) productivity vs age. The peak was around 25
years old, followed by a very steep decline.

~~~
tokenadult
_Marriage alone is a major productivity killer, then there are also kids and
general life problems._

Leonhard Euler managed to be a productive mathematician for decades.

<http://en.wikipedia.org/wiki/Leonhard_Euler>

He had children and grandchildren, and that didn't stop him from working on
mathematics even in their presence. Blindness didn't stop him either.

~~~
huhtenberg
Sure, but that's a sample of one.

~~~
mahmud
The "rock stars" of mathematics are all mostly romanticized youth, but its
bedrock is mostly gray-matter tucked under grayer hair.

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mahmud
Pro-tip for self-taught mathos: It's pronounced "Gal-wah theory". Also, "Lee
groups", "Paul Erdish", "Kurt Gurdle", "Leonhard 'Oiler'", etc.

~~~
waqf
Don't forget Lebayg integration.

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grot
When I was learning Galois Theory, I found Keith Conrad's notes really helpful
for understanding the details -- <http://www.math.uconn.edu/~kconrad/blurbs/>.
The subject of this post is mostly covered by the paper titled "Galois
correspondence" (For anyone whose interests were piqued by this post.)

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balsam
Mark Kac and Stanislaw Ulam explained these concepts pretty intuitively in
their beautiful book Mathematics and Logic. But, who was the first person who
thought that mathematics could be explained without diagrams? Or equations?

Edit: In particular they showed on pages 58-60, without using jargon, how the
idea of permutations leads to Cardano's formulas for the cubic.

~~~
lurker17
Thanks!

For reference:
[http://www.amazon.com/reader/0486670856?_encoding=UTF8&q...](http://www.amazon.com/reader/0486670856?_encoding=UTF8&query=cardano#reader_0486670856)

Search for "Consider the cubic"

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codebaobab
Does anyone have any insight into _how_ Galois made the mental leap to his
solution? Everything I've read says (or implies) that his solution came
completely out of left-field--i.e. it wasn't really related to anything that
had come before him.

And along those lines, does anyone know of an English translation of Galois'
paper?

~~~
sovande
Samuel Johnson: ''Nothing focuses the mind like a hanging'' Or in Galois case
a duel.

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gujk
I recently started reading now algebra book with a goal of understanding the
Galois theoretical proof of his understanding unsolvability of the Quintic.
This is generally considered the capstone of a complete 2-semester
undergraduate study of algebra for a math major who is not pursuing graduate
level pure math.

The interesting part IMO is the analysis of those normal subgroup chains and
understanding the isomorphism to splitting fields.

Definitions and theorems without proofs or examples or illustrations is like
the box without the gift inside. That post built up a pile of terminology but
then ended before showing any content. It shows where to look out find the
solutions at least.

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Someone
Nice text, but _"This is a very limited set of operations, and certainly not
all real numbers can be written this way -- π clearly can’t be written this
way."_ caught my attention. I know it is true, if that is 'clear', one can
just as well claim "clearly, quintics cannot be solved" and be done with it.

~~~
eric-hu
yes. The proof that pi is transcendental is hardly trivial. This was one of
the three major milestones for my Galois Theory class.

Even proving that it's irrational is nontrivial

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krevis
Just remember: the Galois extension of a Galois extension is not necessarily
Galois.

(Never took number theory myself, but that was the one thing I learned from
those who did.)

