Curiosity
Patterns, crafts, magic squares and fun mathematical content not part of the school curriculum
Marguerite's Theorem – Article | Tangente
Anna Novion's film Marguerite's Theorem had already won numerous prizes and awards before it even reached cinemas. Anna Novion, the director, and Ariane Mézard, the mathematician who advised her, agreed to answer Tangente's questions.
Tête-à-tête chercheuse(s): maths brief | Tangente
Nathalie Ayi, a researcher and associate professor at Sorbonne Université, also created and hosts the podcast Tête-à-tête chercheuse(s).
How many stars are there in our galaxy? | Tangente
The first map of the Milky Way was drawn by William Herschel (1738–1822) in 1785. Unable to count every star, he used a statistical method.
Marie Crous's two books digitized | Tangente
And soon Marie Crous, a pioneer of decimal arithmetic in France, will no longer be forgotten!
Marguerite at the ENS | Tangente
Le Théorème de Marguerite, screened last June at the La Baule Festival, received a standing ovation!
Vauban… for the pigs | Tangente
Sébastien Le Prestre (1633–1707), Marquis de Vauban, better known simply as Vauban, was an eighteenth-century man of many talents: engineer, military architect, urban planner, encyclopedist… Louis XIV appointed him Marshal of France near the end of his life. He was responsible for numerous military fortresses throughout France.
Perrin's test for primes… almost! | Tangente
The Perrin numbers are named after Raoul Perrin, a French engineer (1841–1910) who served as president of the Société mathématique de France in 1908.
Carmichael numbers | Tangente
Does Fermat's little theorem characterize prime numbers? Far from it! Yet few composite numbers satisfy the theorem's conclusion, making them all the more intriguing to number-theory enthusiasts and specialists alike.
Great names for great numbers
Many mathematicians have lent their names to numbers in common use. "Very large" numbers have names too: a way had to be found to represent them as well, since they come up in several fields, from combinatorics to mathematical logic!
Adrien-Marie Legendre, in search of integer solutions
The search for integer or rational solutions to algebraic equations has left its mark on the history of mathematics. The law of quadratic reciprocity, stated by Legendre, which determines whether a number is a square "modulo a given integer," advanced this field.
Theatre and maths with Compagnie Terraquée | Tangente
François Perrin, an actor, director and mathematician, and Meriem Zoghlami, a creator of unconventional cultural formats, lead Compagnie Terraquée. Exactly ten years ago, they founded its Mathéâtre lab. In 2017, the company devised a major festival, "Maths en ville".
Sophie Germain primes | Tangente
From Fermat's Last Theorem to cryptography, Sophie Germain primes have played a part in many scientific adventures over the past two centuries. These prime numbers have earned their place in the pantheon of arithmetic, yet we still do not know whether infinitely many exist.
Cauchy–Schwarz inequality: proofs | Tangente
The Cauchy–Schwarz inequality takes many forms: arithmetic, integral and geometric; it even appears in probability theory. Let us trace its development, from Cauchy's numerical formulation around 1820 to its general form a century later.
Tchebychev's inequalities for sequences | Tangente
Elementary results can sometimes prove astonishingly fertile, opening the way to a host of developments and applications. Chebyshev's inequality is a case in point.
Fermat's infinite descent explained | Tangente
Pierre de Fermat wrote that he had succeeded in proving that the area of a right triangle can never be an integer that is a perfect square. To do so, he introduced a method of reasoning that would go down in history: infinite descent.
Terence Tao: the rise of a prodigy | Tangente
Given his life story and exceptional intellectual abilities, mathematician Terence Tao—born in Australia in 1975 and now a professor at the University of California, Los Angeles (UCLA), in the United States—has been dubbed the "Mozart of mathematics" by many.
Research
Singmaster's conjecture, the Polymath projects, the Green–Tao theorem…
Some questions about sums of integers…
You might think that everything has already been said and done about adding two integers. Think again! That mischievous carry, which can ripple from one step of the calculation to the next, gives rise to difficult questions. This elementary algorithm still raises formidable problems.
Enter the Trophées Tangente | Tangente
Every summer, Club Tangente presents its awards. Alongside its literary prizes—the Tangente Book Prize and the Tangente High School Students' Prize—which recognize books devoted to mathematical culture, two competitions invite our readers to get creative. Don't hesitate to enter!
Some results
Terence Tao has successfully tackled many mathematical conjectures. Here are a few examples.