Amazing Math
Surprising or counterintuitive mathematical results and proofs
Laplace: philosopher of chance and determinism | Tangente
The chief architect of determinism, Laplace marked a crucial milestone in the transformation of probability theory into a fully fledged branch of mathematics. Is that a paradox, or a coherent intellectual approach? Let's return to his writings to find out!
The hidden riches of the multiplication table
Think you know your multiplication tables? Think again! A surprising property emerges when a regular polygon is drawn on the multiplication table: the mean of the values at its vertices is the value at the polygon's center!
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.
Marguerite at the ENS | Tangente
Le Théorème de Marguerite, screened last June at the La Baule Festival, received a standing ovation!
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!
Egon Balas | Tangente
Egon Balas's life story reads like an adventure novel. Discover the remarkable story of this mathematician from communist Romania, who managed to escape the turmoil brought upon him by his love of freedom and whose name is associated with numerous discoveries, particularly in operations research.
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.
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.
How is life expectancy calculated? | Tangente
Life expectancy is undoubtedly one of the most widely used statistical indicators. Yet how it is calculated sometimes remains a mystery.
Identifying knots with Gauss codes | Tangente
A visual encoding introduced by Gauss to make knots easier to recognize and manipulate leads to surprising developments in combinatorics, algebra and topology. Armed with paper, pencil and a few pieces of string, let's explore this world.