Famous figures
Portraits of famous mathematicians, historical and contemporary
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!
Dust in the corners
The beauty of fractal curves fascinates amateurs and seasoned mathematicians alike. The latter, however, know that these objects also give rise to subtle problems in measure theory. Here we illustrate an apparently paradoxical situation and a delicate theorem.
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.
A well-deserved medal – Mathematics news | Tangente
The MATh.en.JEANS association has won the CNRS science outreach medal
Newton's method
Do you know how your calculator—or your smartphone's calculator—computes the square root of a number a > 0?
Évarhistoire: a forum about Galois's life | Tangente
Far from it—there is still much to be said about Galois! New communication tools, online discussion forums, and the documents digitized and made available online each day are enabling the investigation into this fascinating figure to continue.
Galois manuscript mystery solved | Tangente
A contributor to the les-mathematiques.net forum, known by the username anqian, recently solved a small mystery that successive editors of Galois's works had puzzled over in vain.
Fibonacci for rabbits | Tangente
These numbers are named after the 13th-century Italian mathematician Leonardo Fibonacci (c. 1175–c. 1250).
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.
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".
Catalan numbers
Eugène Charles Catalan (1814–1894), the son of a Parisian jeweler, was born in Bruges, Belgium. A brilliant student, he entered the École polytechnique in 1833, where he befriended a teaching assistant who would later become famous: Joseph Liouville.
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.
Making counting easier | Tangente
Counting the elements of certain sets is not always straightforward. In the last century, William Burnside, a mathematician specializing in group theory, established a result that simplifies the calculation of the number of objects in certain finite sets.
Cauchy–Schwarz in graph theory | Tangente
Take ten points and join some of them with line segments, but never form a triangle (that is, a triangle whose vertices are among the original ten points). What is the maximum number of segments you can draw?
The birth of thermodynamics and Clausius | Tangente
The study of heat transformed our view of the world by prompting us to consider whether a physical "arrow of time" exists. It all comes down to one remarkably simple relation: the Clausius inequality.
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.
Five variants of the Cauchy–Schwarz inequality | Tangente
The Cauchy–Schwarz inequality appears in several branches of mathematics: analysis, arithmetic, geometry, probability... It is so important that many widely differing proofs have been devised!
A history of ordered means: AM, GM, HM | Tangente
“The” mean of two numbers is defined “naturally” according to the context. It is not always the familiar arithmetic mean! Several different notions coexist and are closely interconnected, as Liouville, Cauchy and Jensen clearly understood.