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Les Mathématiques sont bien souvent sur le devant de la scène lorsqu’il s’agit de leur enseignement au collège et au lycée, voire dans le primaire. A intervalles réguliers, un ministre, parfois interpellé par les résultats des enquêtes Pisa menées par l’OCDE, s’inquiète du désamour des élèves pour les mathématiques. Doit-on ou ne doit-on pas aimer les mathématiques ? Question bien étrange alors qu’il faudrait plutôt s’interroger sur le sens et le rôle des mathématiques, et en quoi leur enseignement est indispensable.

Les mathématiques de nos jours sont souvent perçues comme un domaine ingrat, plus ou moins incompréhensible et intimidant. Certains s’attachent à les rendre plus attrayantes par la BD, la simplification extrême, par un ensemble de procédés qui n’a rien à voir avec les mathématiques en tant que telles. Or, loin d’être cet objet dont on ne sait que faire en dehors de quelques applications calculatoires, les mathématiques sont au cœur de la construction de ce qui fait l’humanité. Cette affirmation peut paraître obscure et surprenante, elle ne l’était pas il y a encore peu de temps.

De nos jours, parce qu’on confond, science et technoscience, la science et ses applications, la connaissance s’évanouit dans le productivisme et l’utilitaire et, corrélativement, l’enseignement des mathématiques se réduit au calcul mental et à l’apprentissage de quelques compétences finalisées ne pouvant que susciter ennui et désaffection. Or, les mathématiques sont loin de n’être que cela. Leur histoire est une aventure intellectuelle passionnante où l’on voit se dessiner à travers la constitution de l’espace démonstratif des mathématiques une science comprise comme visée de vérité et de connaissance, appartenant à tous au sens où chacun est en droit d’exercer sa pensée dans la liberté et que cette pensée s’inscrit dans l’histoire de l’humanité.

Cette aventure prend son origine et construit ses premiers objets avec le langage, les gestes quotidiens, l’abstraction des opérations techniques et les nécessités comptables, agraires ou astronomiques des premières communautés humaines. Dans ce cadre complexe, les chiffres, les calculs, la numération et les figures surgissent comme autant de procédures maîtrisées mais gardées par certains.

C’est le temps des prêtres et du mystère des calculs, calculs intimidants parce que servant à des prédictions, voire à des sacrifices et dont tout un chacun ignore les simples raisons et les modalités opératoires ; des secrets bien gardés au fond des temples, des secrets pour construire et nourrir des cultes et établir des pouvoirs. De ces multiples calculs, procédures et règles mystérieuses associés aux jeux des pouvoirs et aux règles des cultes, ne peut-on faire un tout, un enchevêtrement ordonné de raisons partagées ?

Ne peut-on vouloir faire de ce qui est dit et proclamé un corps de savoir où le dit et le proclamé doivent être démontrés, c’est-à-dire que soient exhibés en toute clarté les concepts, notions, principes et procédures logiques afin que chacun, par lui-même, puisse comprendre et s’approprier ce savoir ? Question éminemment philosophique à laquelle les mathématiques, en tant que réponse, vont s’instituer en instituant une liberté et une autonomie pour la pensée, c’est-à-dire une autonomie pour chacun et donc un nouvel horizon de liberté pour l’humanité. Moment principalement euclidien, prolongé en terre d’islam et renforcé à partir de la fin du XVIe siècle, où les mathématiques naissent vraiment en affirmant que chacun peut les comprendre s’il fait l’effort requis. Il n’y a plus de mystère. La démonstration règne et par elle s’accomplit la visée de vérité, la satisfaction de la raison et finalement l’obligation pour chacun de prouver et de démontrer ce qu’il avance. Les mathématiques, par cette exigence, deviennent une école de la pensée par laquelle celle-ci apprend à conquérir sa liberté ; un fondement pour une éthique.

J’ai voulu renouer, parce qu’il y va de l’exercice même de la pensée, les fils essentiels qui lient les mathématiques au travail de liberté de l’humanité. Une pensée solide et profonde resurgit alors derrière l’image frelatée de mathématiques intimidantes et incompréhensibles qui semble régner de nos jours. Il convient de revenir, dans l’enseignement, à ce qui constitue depuis des siècles le principal apport des mathématiques : enseigner que toute affirmation doit être démontrée pour être partagée. C’est à cette condition que peuvent s’instaurer, dans l’histoire, la liberté de chacun et l’émancipation de tous. Il ne suffit pas de critiquer, de dire que l’on n’est pas d’accord, encore faut-il prouver et démontrer. Les mathématiques apprennent à viser la connaissance et la vérité dans le partage par l’exigence démonstrative. En cela, elles indiquent le sens d’une certaine ascèse intellectuelle et républicaine bien éloignée du jeu des beaux parleurs remplissant les médias et la politique.

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