Interview
Interviews with mathematicians and personalities from the scientific world
The mathematics of physics
Mathematical models enable us to understand and master the universe. But how far can this mastery extend? What are its limits? Mathematics allows us to devise models of the world around us and test them against reality.
First black hole photograph: Katie Bouman | Tangente
The first photograph of a black hole was produced using an algorithm tasked with assembling all the data collected by a network of telescopes.
Coloring planar tilings: four colors | Tangente
The proof of the four-color theorem caused quite a stir! Results on colorings using only two or three colors have proved less controversial. By considering how to make a beaded necklace, we can take a fresh look at these coloring questions.
The astrolabe: answers to six practical challenges | Tangente
After reading the article on the planispheric astrolabe, practise using it by answering these questions
The geoid: the Earth's true shape | Tangente
The surface most familiar to us, the one we walk on every day, raises its fair share of questions: what exactly is the shape of the Earth? It is neither quite a sphere nor an ellipsoid. This irregular object, the geoid, has some subtle properties. We spoke with a specialist.
Darboux, the geometer who expanded the study of surfaces | Tangente
The Institut Henri Poincaré hosted an exhibition entitled "The Depth of Surfaces," devoted to the mathematician Gaston Darboux. Its scientific curator was Barnabé Croizat, a specialist in this great French geometer.
High school maths: education's vicious circle | Tangente
On January 24, 2018, the Villani–Torossian report, "21 Measures for the Teaching of Mathematics," was published, generating enthusiasm among the teaching community. That enthusiasm was tempered on February 12 by the announcement of the forthcoming high school reform.
Envelopes, moving points and evolutes
The envelope of a family of lines can be understood in two ways. The second lends itself better to computation, but both give rise to superb geometric questions.
In the press too…
Mathematical games, familiar from the scientific press, are few and far between in the mainstream press. Some newspapers have nevertheless taken the plunge, often with success! There is indeed an audience for recreational mathematics—provided it is not schoolwork in disguise.
Applications of the second derivative
The concept of acceleration corresponds to a second derivative. It therefore seems only natural that a mathematical concept as sophisticated as the derivative should have concrete applications. Such applications arise in questions involving the profiles of roads and railway tracks.
Newton's synthetic method
How does the Earth, of mass m, move around the Sun, of mass M, under gravity alone? To answer this question with something more than philosophical assertions, Newton proposed a synthetic method inspired by the description of motion.
A controversy over gears
What shape should gear teeth have to get the most out of gears? The question preoccupied 17th-century scholars so intensely that tempers sometimes flared. Philippe de La Hire and Gottfried Wilhelm Leibniz were two of the protagonists in this historic scientific dispute.
Combinatorics, past and present: An interview with Pierre Duchet
The study of combinatorial structures is a recent branch of mathematics, rich in counting problems. A journey into a far too little-known realm.
Speaking numbers
Do you speak numbers? Writing numbers is perfectly automatic, but reading them raises several questions.
The story of a geometry unlike any other
A science that is hard to define in a few words, topology has found its way into geometry, analysis and even algebra. How did it emerge in the mathematical world? Where is it useful? And above all, what is topology? Let's look back at the birth of a new way of seeing our space…
Population dynamics: overcoming data scarcity | Tangente
In some fields, data are scarce. Descriptive statistics are out of the question! Mathematics offers other tools: topology and probability help ecologists predict how groups of species will evolve.
How to simulate human behavior | Tangente
In video games, the challenge is to simulate human behavior so that users feel they are facing other players. Designing an artificial character is not simply a matter of optimization.
Ethical driving - mathematics brief | Tangente
Programming self-driving cars raises ethical questions. Unexpected new conundrums have emerged. Some require only minor adjustments, but others remain unsolvable for now.
Computer-assisted proofs | Tangente
Can a machine prove a theorem? Probably not without a human to guide it, but computers are becoming increasingly useful assistants—for example, by turning a human proof into a formal one. Spectacular developments and applications are currently under way.
Reasoning means solving
Reasoning means organizing your thoughts. Yes, but how? Are there methods for keeping our thoughts from descending into anarchy and confusion? Mathematics is, by its very nature, the discipline that has enabled us to answer these questions over the centuries. And it works!