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| Évariste Galois | |
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| Tweet Topic Started: Oct 25 2011, 07:04 PM (325 Views) | |
| CJ | Oct 25 2011, 07:04 PM Post #1 |
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A very minor case of serious brain damage
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It's the 200th anniversary of this guy's birth, so I thought I'd make a topic about him: Évariste Galois (1811-1832) was a French mathematician, who is credited as one of the pioneers of group theory (a very broad, abstract branch of algebra); he was the first to use the word 'group' in its current mathematical sense. Probably the main piece of work that he did was related to solving equations: I imagine that, at school, you had to solve a lot of quadratic equations (things like x2 + 4x - 12 = 0) - and you probably wondered what the point was . You probably also learned that there was a general formula that could solve any quadratic equation. This idea was extended further to cubic equations (which also have a term in x3 - so, for example, 2x3 + 4x2 - 7x + 21 = 0), and quartic equations (which also have an x4 term); Italian mathematicians found (very complicated) formulas for solving both in the 16th century. The obvious next step was to try and find a formula for solving quintic equations (which also have an x5 term in them) - but, try as they might, the Italian (and other) mathematicians couldn't find one. And so it remained until Galois came along. You might be thinking that this young man found the 'quintic formula' that other mathematicians had been searching for for nearly three centuries. Well, he didn't; instead, he used his 'groups' to prove that there was no such thing! With this proof, he didn't so much discover one mathematical fact as discover an entire branch of mathematics (because similar methods could be used to determine whether other types of equations could be solved). Sadly, his work wasn't appreciated within his lifetime. In addition to his life as a mathematician, he was a Republican activist, who ended up landing himself in prison at one point. Then, aged only 20, he was killed in a duel, although nobody seems quite sure about the circumstances: some say the duel was over a woman, while others believe it was political. His revolutionary mathematical ideas were only published when his manuscripts were discovered some years after his death. Whatever the circumstances, it's a real shame he died so young (I mean, he was younger when he was killed than I am now!). Who knows what he might have achieved had he lived longer?
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. You probably also learned that there was a general formula that could solve any quadratic equation. This idea was extended further to cubic equations (which also have a term in x3 - so, for example, 2x3 + 4x2 - 7x + 21 = 0), and quartic equations (which also have an x4 term); Italian mathematicians found (very complicated) formulas for solving both in the 16th century. The obvious next step was to try and find a formula for solving quintic equations (which also have an x5 term in them) - but, try as they might, the Italian (and other) mathematicians couldn't find one.
(I mean, he was younger when he was killed than I am now!). Who knows what he might have achieved had he lived longer?



8:35 AM Jul 11