History of mathematics' didactic
What is the mental representation?
Matematical mental representation
Recording interview: René Thom, Dominique, Rosine...
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 Another loosely grouped set of statements included

Q16:- In mathematics there is no place for personality; all that you do has been done before, everything has been seen already.

 Q18:- Mathematics sometimes risks bringing destruction, you only have to think of the atomic bomb.

 Q23:- When one is deep in maths work, it's difficult to get out of it, that's why it doesn't do to get involved with it.

 Q24:- Doing maths oversimplifies everything, it takes the poetry out of things.

 Q25:- Those who do too much mathematics some times risk not having your feet on the ground.


 The negative characteristics attributed here to mathematics present it as something dangerous where there is "no place for personality".

This feeling of danger can only come from a projection of the self onto mathernatics which in itself is neither dangerous nor reassuring.


The danger is inside the individual.

To protect yourself you project the danger outward onto an object, in this case mathematics.


The statements include suggestions of danger for the individual arising when personal expression is not a possibility.

There is also the danger of losing your own physical boundaries: notions like "being deep in" or "having difficult getting out of" express the risk of leaving your element, of losing one's way, of being on the verge of "destruction".

The danger of no longer "havîng your feet on the ground" can lead as far as the idea of going mad. That mathematics provokes a state of madness is a theme often taken up by student


A 17-year-old boy from the arts


stream helps us understand how far mathematics can take on this aspect:

<<I know a shepherd. I don't know how he found himself faced with some mathematical tables. He started to write down the numbers, to do calculations; eventually he reached the point of gaining his doctorate in mathematics.

And so now he does calculations ...

He could have had a little farm and lived quite comfortably while still living with nature...he would have been happy.

Ali, well! Now he is with his numbers. He is no longer concerned with sheep. He no longer knows anything about life,

In fact, it would astonish me if he were still to know anything of the outside world.

He studies, I don't know what after all; I no longer know what he does now.


In the end, he abandoned his down-to-earth job, something natural that gave him a certain amount of physical exercise and kept him alive and breathing.

Whereas here he is now, enclosed in a laboratory doing calculations. He suffocates in figures ... He thinks mathematically.

Well, I don't know, ultimately ... we are mad ... we are mad.


In the end, we have little chance of getting to that level. That's how it is, A well!

Lunatics in the end ... People say that certain children who know how to calculate roots to what ever power were mentally deficient ... oh, well! Fortunately, there's little chance of our going mad, because not many of us become top mathematicians.>>


Note during this passage how the student is gradually taken by his story.

From the opening "I knew a shepherd" to the final "I don't know" he moves on to a more impersonal "we" when it comes to the subject of madness.

This fear of madness, or more plainly this "risk of no longer having your feet on the ground" may surely be explained by the fact that for certain individuals, the need to invest energy in abstract representations, which have not yet been incorporated into their psychic reality and into their own mental mechanisms, seems to constitute a traumatic experience.

It breaks relationship with reality, and cuts off a channel of instinctive discharge - that of the flow of sadism sublimated into an activity of mental control of the outside world.

The ego finds itself somewhat disconnected, in danger of a loss of meaningfulness and of depersonalisation



Various mental representations


History of mathematics' didactic
What is the mental representation?
Matematical mental representation
Recording interview: René Thom, Dominique, Rosine...
Write to me