

Evariste Galois . . . group theory in elementary terms
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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