Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
By law, π = 3.2
Well, almost… because the bill did not pass!
It's everywhere!
π turns up almost everywhere, sometimes even in the most fanciful fields. In mathematics, of course, we encounter it in geometry, analysis and number theory… As a result of this omnipresence, it appears throughout the other sciences too!
The spirit of quadratic fields
Why keep adding more and more elements to the set of known numbers? Adjoining just one number to the rationals and combining it with them is already enough to produce many sets with a wealth of wonders to reveal.
New numbers with Richard Dedekind
The real numbers include the rational numbers—the quotients of two integers—and the irrational numbers, of which √2 and π are two well-known examples. This gives us one way of classifying the reals. But another classification is possible, based on numbers known as algebraic numbers.
Transcendental, you say? The history of a term | Tangente
In Latin, the verb transcendere combines trans, "beyond," with scandere, "to climb"; it therefore literally means "to climb beyond," "to cross" or "to surpass."
In search of the universal number: Champernowne and Borel | Tangente
Sometimes, a concept that is relatively simple to define leads us into a world we dare not imagine, where our common sense struggles to find its bearings. Such is the case with universal numbers, which remain today as elusive as they are fascinating.
The story of e
At the beginning of the 17th century, Galileo's telescopes and Newton's theories sparked an explosion in observations of the heavens. New mathematical tools were devised to handle the associated calculations, which were astronomical in every sense. Euler's number emerged naturally from this work.
Liouville, Hermite and Lindemann: paving the way | Tangente
A tribute to the pioneers who blazed the trail for others to follow.
On the road to transcendence
Among irrational numbers, transcendental numbers are not roots of any polynomial equation with integer coefficients. They seem to transcend common sense, hence their name. Cantor showed that they make up the overwhelming majority of the real numbers, without identifying a single one!
Pi, a number beyond reason
Since π is defined as the ratio of a circle's circumference to its diameter, it would be convenient if it were rational—that is, the quotient of two integers. Unfortunately, it is not! Worse still, some might say, it is even transcendental…
It’s quite a story…
The constant π is everywhere in mathematics. It is undoubtedly the best-known irrational number—and even the best-known transcendental number. How is it defined geometrically, and why does it appear in every branch of mathematics?
An exhibition to set up near you | Tangente
"Why do we lean into turns?" is the title of an exhibition accompanying the release of Amandine Aftalion's book.
Sports performance trends: a maths brief | Tangente
Citius, altius, fortius. The Olympic motto ("Faster, higher, stronger") sums up athletes' ambition to push the limits of human capabilities; for more than a century of competition, they have regularly broken records.
Spotlight on skateboarding
Skateboarding became popular in Europe around 1990. Whether tackling a straight line, a flat surface, a curve or an aerial trick, skateboarders must read their surroundings and have spatial and architectural awareness. This is where physics and mathematics come into play…
Nash and penalty shootouts: maths article | Tangente
When a penalty is taken in football, the player wants to put the ball in the net; the goalkeeper has to stop him. Can mathematics help maximize the chances of scoring—or of saving that fateful shot? The affirmative answer illustrates the work of John Nash.
Hungarian tables: mathematics article | Tangente
Combined events in athletics, such as the decathlon, require a way of comparing results across different disciplines. Scoring tables were therefore developed from statistical data and are regularly updated to reflect changes in human physical development.
Statistics, what else? A mathematics article | Tangente
Among the branches of mathematics applied to sport, statistics holds a prominent place. It is used to analyze large datasets—big data—to combat doping, and in media coverage of sport, typically for questions concerning the Olympic Games.
One Saturday a month at "Math Park": Math brief… | Tangente
The "Mathematic Park" series was launched by Xavier Caruso in 2003. Initially aimed at high school students but run on a fairly small scale, it moved to the Institut Henri-Poincaré (Paris, 5th arrondissement) in 2011.
2024 Abel Prize awarded to French mathematician Michel Tal… | Tangente
The fifth French laureate to receive the Abel Prize, mathematics' equivalent of the Nobel Prize, Michel Talagrand was born in 1952 and spent his career at the CNRS, developing an early interest in random processes.
Did you say “Myriogon”? — Mathematics brief | Tangente
Myriogon is a YouTube channel run by a team of mathematics communicators: Stephen Barcelo, Chloé Bouchaour, Robin Jamet, Mickael Launay and Roger Mansuy