Folders

Behind new medical techniques, mathematics hide more than ever. The development of imaging, whose most well-known tools are the scanner or the MRI, has revolutionized practices. Many branches of mathematics were called upon to develop these new technologies: geometry, Fourier analysis, the Radon transform and, more recently, wavelet theory. Furthermore, more and more individuals are testing, via their smartphone, various indicators such as their heart rate, their blood pressure or their weight. This may be useful, but not without risk…

Sociology is a relatively recent field, and yet its links with mathematics are already well established. Thus, statistics, data analysis, and decision theory are widely used tools. But in the era of social networks, modeling interactions between individuals has become essential. To do this, the need for cutting-edge mathematics has exploded: graph theory, linear algebra, and principal component analysis are entering the field of human and social sciences.

Observe the pattern drawn, depending on the time, by the shadow of the parasol on the small wall at the edge of the beach. Try to predict the shape adopted by a pile of sand whose base rests on sinuous contours. Contemplate the movement of the waves or the undulation of the dunes and understand the analogy between these wonders of nature and the equations that govern them. In a word, sunbathe intelligently. That's what Tangente offers its readers this summer.

Fed by concepts that borrow from formal logic as well as probability theory, AI is a vast construction site that is preparing a significant part of our future. Mathematics plays, and will play, a key role in it. All sectors are concerned, from logic to neural networks, from probability to statistics… It even exploits the algebraic properties of rational functions. It falls to the actors in the mathematical world to contribute to enlightening citizens about the issues of this new transformation.

Since Pythagoras, we have known the close links between music and mathematics. In the 20th century, the greatest names such as Boulez, Xenakis or Schaeffer, vied with inventiveness, drawing on probabilities, symmetries and even chaos theory, to create new compositions. Since the advent of synthesizers, the game has been revolutionized and engineers collaborate on musical creations in organizations such as Ircam. Some draw inspiration from rhythms based on simple numerical ratios to revisit popular music such as Argentine tango.

Games and mathematics are intimately linked. By solving problems or imagining theories, are we not playing? Conversely, the various strategies developed by a player and the algorithms for solving situations in board games gave rise to a field of mathematics, game theory. We then understand why games can... "play" a role in school and make education fun. What if every math problem took the form of a game? Puzzles and other recreational pastimes have long been popular with readers, in the press as well as in publishing. Eminent mathematicians have even posed challenges at the boundary between pure play and mathematical problems. Doing math through play means reconciling the useful and the pleasant, it means improving life in society. It is not surprising that the theme of Maths Week 2019 is "Playing together with mathematics".

The now traditional Maths Week will have the theme in 2021 "Mathematics and society". A vast subject, which led the editorial team to choose a "philosophical" perspective that questions the mathematization of life in society and social interactions. From democratic questions - "Does the aggregate of individual rationalities necessarily lead to the general interest?" - to high-performance computing tools needed to process large volumes of data, including the counting of demonstrators or the use of graphs to model social proximity, the subjects are varied. Another approach to the theme will be covered in issue 56 of Tangente Éducation, under the title: "Mathematical mindset, critical thinking".

One might think that a chasm separates mathematics from the practice of sport. However, the optimization of performance in many sporting activities relies on a branch of mathematics. Geometry makes it possible to manage the trajectory of balls, but also of bicycles or Formula 1 cars. Game theory is at the basis of the strategies employed, as are probabilities, which also enable the forecasting of results and therefore the management of sports betting. Discrete mathematics (arithmetic, combinatorics…) is used for the organization of events and the establishment of rankings. Conversely, cheating can be detected through the observation of statistical inconsistencies…

Since the time of Archimedes already, science has been used to detect fraud. Today, the administration uses mathematics, via sophisticated algorithms, to unmask those who hide profits or income. As for the « fallacious proofs », are they swindles? They are closer to magic tricks where the unnoticed error constitutes the « trick » that the game consists of spotting, and are an excellent pedagogical tool to highlight the implicit properties used in certain reasonings.

We readily imagine mathematicians as not very sporty. Yet, calculations have become central to the practice of sport, whether it is helping athletes improve their individual and collective performances, comparing results from different disciplines or building playing fields. Did you know that Big Data entered sport starting from baseball and that penalty shootouts in football can be approached using the Nash equilibrium? Have you ever imagined how to make the decathlon events or the performances of women and men commensurable? Welcome to a world of strongly built figures!