Emancipatory Aspects of Learning
(and Teaching) Mathematics

Mathematics, like the martial arts, provides us both with a technique to face the world and to face ourselves. I will explore a view of mathematics which has its testified origins in Greek philosphy, Roman engineering and Arabic science. It is the basis of the Renaissance views of man, of the ethos of the autonomous individual and the underlying assumption of secularism. Here are some of its major points which should play a vital role when we ask ourselves why we teach mathematics.

• Mathematics deals with a controled virtual reality, a landscape of mental images. Virtual, because we create it unless we are die--hard platonists, controled, because once we look at it, it does not change.
• The mathematical challenge is to explore this landscape, to map it out and to conquer it for exploitation (applications). We are allowed and encouraged to use landmarks of our predecessors, but we pride ourselves on being able to remap and reconquer this landscape using our own capacities and ingenuity if needed.
• The personal challenge of a mathematician is to control his/her hopes, feelings, weaknesses and fears in the face of the mathematical terra incognita. We want to know what it looks like there, and from there further on with the only goal to see.
• Each mathematical victory consists also in a victory over ones weaknesses. We reach a point on our own and the sole reward is to be there and to be able to generously and humbly share our view with our fellow travellers.
• Competitiveness among mathematicians tries to turn the other's weakness into our own strength. It makes us mean, petty and greedy. We should always remember to serve Mathematics humbly rather than use Her for our own purposes.
• Even in teaching mathematics we can at least attempt to teach the students the flavour of freedom and critical thought, and to get them used to the idea of being treated as humans empowered with the ability of understanding. Roger Godement, Cours d'Alg`ebre, Hermann, Paris 1966.