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Name: yendor
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995


Question:
Could someone explain to me, in elementary terms, what problem Evariste Galois solved. I believe it was in the field of group theory. Also, any references about his life such as books or personal knowledge about him would also be helpful.


Replies:
Actually, Galois sort of invented group theory while trying to solve this problem - the problem was, can you find a formula like the famous quadratic formula that finds the roots of a fifth degree polynomial? Formulas were known at this time for all polynomials of degree 3 or four, but there was no general method for finding roots of higher order polynomials. Galois proved that no such general method could be found, at least using a purely algebra- ic formula. The traditional accounts claim that he figured this all out in his head and only wrote it down in haste one night before a duel over a woman, in which he was unfortunately killed. In fact, it turns out he was just making editing changes in a paper he had submitted on the subject, and had just received back from the publishers. He certainly lived an interest- ing life, was jailed at least once, was involved in all sorts of political activities, etc. and got kicked out of school (he did not put any of his energy in studying anything besides mathematics). There is a pretty good, and I believe accurate, summary of his life in Tony Rothman's book "Science a la mode".

asmith



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