Duality

At the beginning of the 19th century, mathematician Joseph Gergonne thought he had discovered a new world when he understood that one theorem was born from another by interchanging the terms 'point' and 'line' in a statement. In a broader sense, this analogy had already been highlighted, particularly within the framework of Platonic solids. Later named duality, it allows, by 'reversing' two 'dual' concepts, to achieve strikingly quick proofs. Duality was the cradle of projective geometry. It is found today in many fields: set theory, logic, linear algebra... Analysis has also taken hold of it within the framework of functional spaces.

Literature and mathematics, is this an oxymoron? This year again, for the eleventh edition of the Tangente book prize, the selected works prove the opposite. This is the occasion to vote for your favorite. Also take advantage of summer to make new discoveries and make a wise choice of books about mathematics, thanks to the many reading notes published in our various issues, particularly in this feature. Writing and popularization enthusiasts are even invited to take up the pen as part of the Tangente best article prize.

It's summer time, time for vacations and games, all sorts of games. • Video games? Math (vectors, matrices and even quaternions) is everywhere to manage the animation. • Card games? Shuffling well is not so simple, especially if the deck is infinite… • Program a mathematical game? Creativity is on display for all young talents who want to try their hand at it within the framework of the Bernard-Novelli prize. • Warming up your brain at the beach or on the banks of the Seine? The usual games and problems sections are always there, with the addition (mystery, of course) of two new pages of cryptarithms. Tangente wishes everyone a wonderful summer.