Interview
Interviews with mathematicians and personalities from the scientific world
No derivatives required: optimization for everyone!
Optimization and differentiation are linked—but in both algebra and geometry, derivatives can sometimes be avoided. A few elementary algebraic examples will show us that quadratics are often subtler than they look…
TIMSS and PISA: The latest developments in mathematics assessments
The recent publication of the PISA and TIMSS results unleashed a media storm, so poor were the scores of young people in France. But rather than settling for a few simplistic figures and reductive statistics, what if we took a closer look at what these assessments actually measure?
In search of friends
Integers never cease to fascinate us: divisibility raises some formidable questions, as several conjectures about perfect numbers attest. Here, experimenting with a computer is a valuable aid in the hunt for counterexamples.
Deduction, induction, abduction: three forms of logic | Tangente
A host of tiny clues leads the detective Sherlock Holmes to formulate a theory, moving from the particular to the general. He is well aware that his method leads to the truth only if it is confirmed by the facts—that is, by observation!
Potato diagrams: a chipper idea
When considering several subsets of the same set, it can be difficult to distinguish their various intersections. Representing these subsets as "potato-shaped blobs" often makes things clearer—and keeps us from looking like potatoes when faced with questions that are simpler than they seem.
What if it were false?
Is Pythagoras' theorem really true? The question may seem strange, but in fact it all depends on the setting in which we wish to apply this geometric result.
Autonomous vehicles: life-or-death maths | Tangente
How can morality be programmed into autonomous vehicles? The question, worthy of science-fiction novels, is topical today.
The multiplier: a tool for every citizen
Everyone encounters rates of change sooner or later. Handling them is often a source of error, although one simple, effective tool can solve many such problems: the multiplier.
Plaque in memory of Évariste Galois in Paris | Tangente
Passersby on the rue des Bernardins will now be able to pause and wonder at this plaque, which was missing from the capital.
Rolle: a cascade of theorems!
Rolle's theorem, like the celebrated mean value theorem, has been dropped from the secondary-school curriculum. Yet these two major results in analysis are of far more than historical importance. They can be used to solve a great many mathematical problems!
From Euclid to Bourbaki: perpetual reform
Mathematics has undergone waves of reform in the past, is undergoing them now, and will continue to do so. This applies to schools of mathematical thought and major research movements, but also to elementary mathematics—the mathematics taught in secondary schools in most countries around the world.
The projective line: a fruitful new perspective
The line is the simplest geometric figure imaginable. The variety of situations encountered in geometry may seem more complicated, and yet… might there be a special perspective from which the plane could be understood as a line? That is precisely what projective geometry is about!
Equations of a line
What defines a line, and in what geometric setting? Each possible answer leads to a representation from which the corresponding equations follow.
Historical math challenges: the Renaissance | Tangente
Throughout history, one of the driving forces behind mathematical research has been intellectual battles fought through challenges. Some of them have remained famous.
Percentage tennis: the maths that make you win | Tangente
Everyone talks about them, but few enthusiasts know what they really mean: probabilities play a major role in tennis, and players are best off adapting to them. Although the same issue arises in every sport, it has been studied most thoroughly in tennis.