Mathematics Goes to the Movies

by Burkard Polster and Marty Ross

Evariste Galois (1965)

Galois is practicing shooting the pistol in preparation for a duel next day. Two of his friends are there to help him, a soldier and a civilian.
Soldier: Still doing mathematics? You better practice.

A cadet from the Polytechnic joins them and starts studying some mathematical writings on the wall.
GALOIS: Does this interest you?
He starts wiping equations off the wall.
CADET: Very much. Those are substitutions?
GALOIS: As you can see.
GALOIS: To solve equations.
CADET: Of what order? Even Abel could not solve anything beyond forth order.
GALOIS: Abel was a genius. People like you let him die of hunger at the age of 25. Cauchy didn’t even read his thesis ???? Are you at the Polytechnic?
GALOIS: I failed twice.
CADET: I know. You threw a duster at the examiner. Working on equations?
GALOIS: That problem is solved. I said it’s solved. I’ve discovered the necessary and sufficient conditions for the solvability of general equations by radicals.
CADET: That would be a good result.
GALOIS: Beyond the 4th order this is usually impossible as Abel conjectured. The proof is based on the fact that the group of permutations of the letters ??? there does not exist ??? an intermediate normal subgroup other than the subgroup consisting of the even permutations.
CADET: I don’t see what that has to do with equations.
GALOIS: But it’s obvious. Just substitute the n roots of an nth order equation you get the complete set of possible permutations. Among them is a group of invariants of rational functions formed from the roots and the equation is solvable otherwise not.
CADET: Does this method give an applicable result?
GALOIS: The calculations are not practical. Life is too short.
CADET: So, what is the use of all this.
GALOIS: To solve the problem and to explain a lot of things that at first sight don’t have anything to do with equations.
GALOIS: Why.