Evariste Galois (1965) - full transcript
So my friend, still in mathematics?
You'd better practice
That's better.
Keep going, and you'll
make short work of your rival.
Beware friend ! Wrong target.
He's not the enemy.
Does this interest you?
Very much. Those are substitutions?
As you can see.
What is it for?
To solve equations.
Of what order? None could solve
anything beyond forth order.
Even Abel....
Abel was a genius !
People like you let him die at 25
of hunger and pneumonia
Cauchy didn?t even read his thesis
He found it was written
with an ink too pale...
Are you at the Polytechnic?
I failed.
Twice.
I know. You threw a duster at the examiner.
Working on equations?
That problem is solved.
I said : it?s solved.
I?ve discovered the necessary and sufficient
condition for the solvability...
...of general equations by radicals.
That would be a good result.
Beyond the 4th order this is usually impossible,
as Abel conjectured.
My proof is based on the fact that
in the group of permutations of the letters
we cannot have, for n above 4
any normal subgroup other than
the subgroup of even permutations.
I don?t see what that has to do with equations.
But it?s obvious.
Think.
Instead of letter, simply put
the n roots of an nth order equation
You get the complete set of
possible permutations.
- Does this method give an applicable result?
- Sure it does
The calculations are not practical.
Life is too short.
So, what is the use of all this?
To solve the problem once and for all
and to explain a lot of things that at first sight
don?t have anything to do with equations.
That's what bothers me with your approach.
Why?
You do not calculate,
you speculate.
I try to think.
Using vague evidence, which have nothing
to do with your subject.
Because it?s the same thing!
I could have talked about rotation in space,
series of numbers, or cristals symetry.
The immediate data represented by equations
and fonctions do not matter
What is important is what is behind,
their common structure.
We are not at the botanical garden.
We are not going to worry for centuries
about single problems in little boxes...
Let?s have a little bit of imagination.
Leave that to the poets.
We are talking of algebra.
Not generalities.
Mathematics also have generalities.
The logic of reasoning?
In algebra, the reasoning is calculations.
Where are yours?
Well, I?m listening.
Prove what you have said.
I can follow a proof.
It?s my job, you see.
Go away...
You are unable to understand.
You are just as stupid as the others.
There is nothing to understand, Galois.
You are dreaming.
What you are trying to prove is nonsense.
Get out !
You already have a duel to handle
In tribute to your political bravery,
I came to asssist you...
Just listen to this.
I may not be a genius,
but I am certainly good enough
as a mathematician
to assure you that there isn't in Europe
any single person who can follow your reasoning.
Whether you are a prophet or a fool,
the result is the same.
You'll find none
to convey your thoughts.
What counts in science, Galois,
is its positive aspect.
The misunderstood, the unknown
cannot find any place
You have wasted your time.
Leave me now.
I fight very early in the morning.
I don?t have much time.
What are you doing Evariste?
You are not going to work?
I though I told you to go away
That's suicide...
Have some rest
Your only chance to get away tomorrow
is to practice all night
then have some sleep
Mind your own business please.
Galois!
Don't go to this duel tomorrow
It will be butchery.
Why?
You think I canot handle a gun?
Don't be afraid.
Geometrician have a military mind.
They have great success in artillery.
And the one I'm figthing for
will inspire my hand.
It's not my first duel anyway
I carried out my revolutionary duty
And I even went to jail
Precisely!
They have not forgotten
You now...
A duel may be arranged
What a good opportunity
to get rid of an annoying enemy
I was not that dangerous...
It was so long ago...
It's late now.
Too late to change anything
to my plans.
I fight tomorrow at dawn.
Evariste!
Did you understand what I tried
to explain to that idiot?
You know I'am not smart enough.
Then you can't help me.
Leave me alone.
I still have a lot of work
before tomorrow.
And not much time left.
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.
The only world
he has ever known.
The study room in college,
the dormitory in the university,
and the stinking cell in prison.
Straight from the classroom to the barricades...
and from the barricades to prison.
He has been studying mathematics
for six years only.
He started when he was 15
and now he is 22.
In a few hours he will be dead.
That's sure now.
Don?t be in a hurry Galois.
You?ve got plenty of time.
Your friend the cadet was right.
There isn't in Europe today
one single person who may
understand what you are writing.
In fifty years, maybe.
In a hundred.
You must forgive to Poisson,
to Cauchy, to the Academy,
who rejected your thesis,
They could not understand, that?s all.
You are not the first, Galois.
Remember Abel.
Maybe in fifty years.
You?ve still got plenty of time.
What did you see of life, Evariste?
Nothing.
So few.
Nothing but the pride
in having invented.
This fever of conquering intelligence
that fascinates itself
to know it gave birth
to a new field.
I'm ready, Sir.
Sirs, a duel will start, between
M. Duchatelet and M. Evariste Galois
The distance between the marks
is 30 feets
Between the handkerchiefs,
20 feets
At the starting signal,
each man may go from his place
to the handherchief, and shoot.
But he may also shot
without moving.
After the first shot, the other
party has one minute to shoot.
As agreed, guns will be
drawn by your witnesses.
Sirs, do you agree?
- M. Duchatelet?
- Yes, I agree.
And you, M. Galois?
Do you agree with
what I've just said?
M. Galois?!
Yes, I agree.
Sirs, you may choose
the guns.
You may go.
M. Galois, you have 1 minute
to stand up and shoot.
Here comes the police.
Run.
You too, Sir.
Run.
Help!
Picked up by a farmer,
and brought to Cochin Hospital,
Galois died on May 31, 1832.
The morning after.
It took 14 years to
have a first edition
of Galois work,
in Liouvillle's journal.
40 years for Camille Jordan to dedicate
him his Trait? des substitutions, in 1870.
But nowdays, any student in
Mathematics,
knows the name of fields
containing a finite number of elements.
These fields are named
"Galois fields".
You'd better practice
That's better.
Keep going, and you'll
make short work of your rival.
Beware friend ! Wrong target.
He's not the enemy.
Does this interest you?
Very much. Those are substitutions?
As you can see.
What is it for?
To solve equations.
Of what order? None could solve
anything beyond forth order.
Even Abel....
Abel was a genius !
People like you let him die at 25
of hunger and pneumonia
Cauchy didn?t even read his thesis
He found it was written
with an ink too pale...
Are you at the Polytechnic?
I failed.
Twice.
I know. You threw a duster at the examiner.
Working on equations?
That problem is solved.
I said : it?s solved.
I?ve discovered the necessary and sufficient
condition for the solvability...
...of general equations by radicals.
That would be a good result.
Beyond the 4th order this is usually impossible,
as Abel conjectured.
My proof is based on the fact that
in the group of permutations of the letters
we cannot have, for n above 4
any normal subgroup other than
the subgroup of even permutations.
I don?t see what that has to do with equations.
But it?s obvious.
Think.
Instead of letter, simply put
the n roots of an nth order equation
You get the complete set of
possible permutations.
- Does this method give an applicable result?
- Sure it does
The calculations are not practical.
Life is too short.
So, what is the use of all this?
To solve the problem once and for all
and to explain a lot of things that at first sight
don?t have anything to do with equations.
That's what bothers me with your approach.
Why?
You do not calculate,
you speculate.
I try to think.
Using vague evidence, which have nothing
to do with your subject.
Because it?s the same thing!
I could have talked about rotation in space,
series of numbers, or cristals symetry.
The immediate data represented by equations
and fonctions do not matter
What is important is what is behind,
their common structure.
We are not at the botanical garden.
We are not going to worry for centuries
about single problems in little boxes...
Let?s have a little bit of imagination.
Leave that to the poets.
We are talking of algebra.
Not generalities.
Mathematics also have generalities.
The logic of reasoning?
In algebra, the reasoning is calculations.
Where are yours?
Well, I?m listening.
Prove what you have said.
I can follow a proof.
It?s my job, you see.
Go away...
You are unable to understand.
You are just as stupid as the others.
There is nothing to understand, Galois.
You are dreaming.
What you are trying to prove is nonsense.
Get out !
You already have a duel to handle
In tribute to your political bravery,
I came to asssist you...
Just listen to this.
I may not be a genius,
but I am certainly good enough
as a mathematician
to assure you that there isn't in Europe
any single person who can follow your reasoning.
Whether you are a prophet or a fool,
the result is the same.
You'll find none
to convey your thoughts.
What counts in science, Galois,
is its positive aspect.
The misunderstood, the unknown
cannot find any place
You have wasted your time.
Leave me now.
I fight very early in the morning.
I don?t have much time.
What are you doing Evariste?
You are not going to work?
I though I told you to go away
That's suicide...
Have some rest
Your only chance to get away tomorrow
is to practice all night
then have some sleep
Mind your own business please.
Galois!
Don't go to this duel tomorrow
It will be butchery.
Why?
You think I canot handle a gun?
Don't be afraid.
Geometrician have a military mind.
They have great success in artillery.
And the one I'm figthing for
will inspire my hand.
It's not my first duel anyway
I carried out my revolutionary duty
And I even went to jail
Precisely!
They have not forgotten
You now...
A duel may be arranged
What a good opportunity
to get rid of an annoying enemy
I was not that dangerous...
It was so long ago...
It's late now.
Too late to change anything
to my plans.
I fight tomorrow at dawn.
Evariste!
Did you understand what I tried
to explain to that idiot?
You know I'am not smart enough.
Then you can't help me.
Leave me alone.
I still have a lot of work
before tomorrow.
And not much time left.
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.
The only world
he has ever known.
The study room in college,
the dormitory in the university,
and the stinking cell in prison.
Straight from the classroom to the barricades...
and from the barricades to prison.
He has been studying mathematics
for six years only.
He started when he was 15
and now he is 22.
In a few hours he will be dead.
That's sure now.
Don?t be in a hurry Galois.
You?ve got plenty of time.
Your friend the cadet was right.
There isn't in Europe today
one single person who may
understand what you are writing.
In fifty years, maybe.
In a hundred.
You must forgive to Poisson,
to Cauchy, to the Academy,
who rejected your thesis,
They could not understand, that?s all.
You are not the first, Galois.
Remember Abel.
Maybe in fifty years.
You?ve still got plenty of time.
What did you see of life, Evariste?
Nothing.
So few.
Nothing but the pride
in having invented.
This fever of conquering intelligence
that fascinates itself
to know it gave birth
to a new field.
I'm ready, Sir.
Sirs, a duel will start, between
M. Duchatelet and M. Evariste Galois
The distance between the marks
is 30 feets
Between the handkerchiefs,
20 feets
At the starting signal,
each man may go from his place
to the handherchief, and shoot.
But he may also shot
without moving.
After the first shot, the other
party has one minute to shoot.
As agreed, guns will be
drawn by your witnesses.
Sirs, do you agree?
- M. Duchatelet?
- Yes, I agree.
And you, M. Galois?
Do you agree with
what I've just said?
M. Galois?!
Yes, I agree.
Sirs, you may choose
the guns.
You may go.
M. Galois, you have 1 minute
to stand up and shoot.
Here comes the police.
Run.
You too, Sir.
Run.
Help!
Picked up by a farmer,
and brought to Cochin Hospital,
Galois died on May 31, 1832.
The morning after.
It took 14 years to
have a first edition
of Galois work,
in Liouvillle's journal.
40 years for Camille Jordan to dedicate
him his Trait? des substitutions, in 1870.
But nowdays, any student in
Mathematics,
knows the name of fields
containing a finite number of elements.
These fields are named
"Galois fields".