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31 August 2008 / April

Why I will now associate sandwiches with Galois

Do you ever experience those moments when you’re sitting around eating a sandwich, and all of a sudden you think, “Damn, this really tastes like a sandwich!

Not that I do, of course.

And now, let us move on to my main topic of discussion: the quintic.  Or maybe group theory.  Or maybe physics.  Or maybe Galois (sigh! Galois!).

Or maybe, says Mario Livio, author of The Equation That Couldn’t Be Solved, all of the above!

As the above transition suggests, this is a book somewhat similar in spirit to Hofstadter’s GEB, in that it uses a mathematical idea as a jumping off point to talk about a great variety of subjects.  This is an approach I approve of, partly because GEB is sheer genius but also because I am a person who likes a great variety of subjects and likes seeing them interwoven with math in cool and mind-blowing ways.

But you are already shaking your head, because nothing compares well to GEB when it’s me doing the comparing.  Sorry, Livio.  It’s a good book, really.

The only problem lies with that phrase “a mathematical idea.”  Hofstadter takes 742 pages to luxuriate over analyzing the proof and implications of one mathematical idea: Gödel’s incompleteness theorem.  Not “number theory” or “logic;” just this one theorem.  Livio takes a much more portable 290 pages to discuss group theory, which is a sprawling field that reaches its tendrils of implication into just about everything you can think of, including thinking itself.

That being said, the subtitle of this book is “How Mathematical Genius Discovered the Language of Symmetry.”  So while the math (and physics, psychology, sciences in general) is perhaps best suited for someone who has not yet heard of isomorphisms, the history portions are quite fascinating.  The repeated instances of vastly important math papers being lost by inept committees made me want to strangle various historical figures (I’m looking at you, Cauchy). I absolutely love the dramatic story of solving the cubic.  And I absolutely love Galois.

I learned that Galois was a political live wire and spent time in prison for possibly threatening to assassinate the king of France.  But all anyone seems to care about is his death, so okay.  (Spoiler alert!)  The man died.  In a duel.

As an aside, I am tickled by how Livio writes, “Let me note at the outset that from the purely mathematical point of view, or for the history of group theory and its application to symmetries, it is unimportant why Galois died or who killed him.”  Then he goes on to devote 14 pages to dissecting the evidence surrounding this “unimportant” event.  Because he couldn’t resist.

Galois’s death is certainly shrouded in mystery, but it is safe to say that it was not quite as a certain Precalculus teacher would have us believe: a man insulting Galois’s girlfriend and forcing him to defend her honor in an ultimately fateful duel.  Instead, it involved more of Galois insulting his girlfriend (who, to be fair, had already cold-heartedly rejected him) and two other men defending her honor in an ultimately fateful duel.

Which makes Galois seem much more like an obnoxious emo kid than a romantic hero, but I think we can forgive him because his life pretty much sucked and he also happened to be a genius.  But I’ll let Livio tell you about that.


Next time your math teacher claims your work is illegible, just tell him you’re emulating Galois.  Also, is that not the prettiest sigma you’ve ever seen?



Leave a Comment
  1. Joe O'Rourke / Nov 13 2008 10:39 pm

    When reading the book, I commented to my wife that I thought this was another book by Hofstadter in disguise. It wasn’t, although both authors attempt to reach out to audiences [like me] that have the mathematical curiosity if not the skills. I think the book succeeded at introducing ‘symmetry’ as a mathematical concept but spent more time about the famous mathematician’s lives than the book title invited. On the other hand, if I can use Galois’ concepts to get my grandchildren interested in the symmetry found in nature…

  2. April / Nov 14 2008 9:46 pm

    I agree– the historical parts were a little more than I expected, though still well-done. And any book attempting to make math accessible gets props from me. 🙂

  3. Sepiraph / Nov 24 2008 5:13 am

    I love the story of Galois and the man is pure genius. The central idea in Galois theory is extremely abstract yet elegant. I tried spending months in the past to *really* understand his ideas (i.e. not only how but *why*), but to be honest I never really did because to prove his theory you need to have a *deep* understanding of both group theory and field theory. In comparison, I find theories like vector classic, linear algebra, non-relativistic quantum mechanics to be fairly easily understood.

  4. April / Nov 24 2008 3:02 pm

    I hope to one day be advanced enough to even attempt to understand Galois theory… hah, I seem to be having enough trouble in my linear algebra class.


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