Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Evariste Galois . . . group theory in elementary terms
Name: yendor
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1995

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.

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".


Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory