(quoted from Evariste Galois)
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.
CADET: What is it for?
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?
CADET nods.
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.
CADET: That is what I find wrong with your result.
GALOIS: Why.
CADET: It's all speculation.
GALOIS: Thinking.
CADET: Using vague evidence which have nothing to do with your subject.
GALOIS: Because it's the same thing! I could have talked about series
of numbers or space. The way in which equations are represented is not important.
What is important is what is behind these representations, their common structure.
We are not going to worry for centuries about which answers we tick. Let's
have a little bit of imagination.
CADET: Leave that to the poets.
GALOIS: Mathematics also has generalities. The logic of reasoning…
CADET: Algebra is calculation. Where is yours? Well, I'm listening. Prove
what you have said. I can follow. It's my job.
GALOIS: Go away, you are not able to understand, you are just as stupid as the
others.
CADET: There is nothing to understand, Galois. You are dreaming. What you are
trying to prove is nonsense.
GALOIS: Get out!
…
CADET: Listen. I may not be a genius, but I am certainly good enough a mathematician
to be able to assure you that in Europe that is not a single person who can
follow your reasoning. Whether you are a prophet or a fool, the result is the
same. Nobody can understand your thoughts. What counts in science, Galois, is
its positive aspect. You have wasted your time.
GALOIS: Leave me now. I've got to work. I don't have much time.
STORYTELLER: So, in the silence of the night Galois set to work one more time.
How many nights like this has he spent in different rooms? The table, the four
walls are all that he has ever known. The study at school, the room at college
and the stinking cell in prison. Straight from the classroom to the barricades
and prison. He has been studying mathematics for six years. He started when
he was 15 and now he is 22. In a few hours he will certainly be dead. Don't
be in a hurry Galois, you've got plenty of time. Your friend the cadet
was right. Nobody in Europe is able to understand what you are writing. Maybe
in fifty years, maybe in a hundred. You must forgive those at the Academy who
rejected your thesis, they did not understand, that's all. You are not
the first, Galois. Remember Abel. Maybe in fifty years. You've still got
plenty of time.
