Famous figures
Portraits of famous mathematicians, historical and contemporary
Ptolemy's little-known inequality explained | Tangente
The Greek mathematician, geographer and astronomer Claudius Ptolemy discovered a theorem about quadrilaterals inscribed in a circle in the second century CE. His result is certainly far less famous than that of his compatriot Pythagoras, but it is every bit as beautiful.
Maryna Viazovska on CultureMATH | Tangente
The CultureMath website, produced by the École normale supérieure, features an interview well worth reading. Mathematics teacher Nathalie Braun interviews Maryna Viazovska.
2023 Abel Prize: Luis Caffarelli | Tangente
The 2023 Abel Prize was awarded to Luis Caffarelli
A tribute to Pierre Audin | Tangente
Pierre was rigorous, dependable, compassionate, attentive, determined and funny… and he seemed tireless. He slept very little, sending a great many emails at night—often at 3:14 a.m.
Charlotte Angas Scott, a pioneer | Tangente
A pioneer of algebraic geometry and a specialist in curves and surfaces, British mathematician Charlotte Angas Scott was forced to move to the United States to find an academic post. Her chief claim to fame is an elegant proof she devised for a difficult theorem by Max Noether.
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: blogging and learning | Tangente
Terence Tao has created a professional blog featuring "updates on his research and expository papers, discussion of open problems, and other maths-related topics." What can his posts on learning mathematics teach us?
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.
Generating the famous Pythagorean triples
Characterizing all right triangles in the plane with integer side lengths amounts to finding all Pythagorean triples. The geometric problem thus appears to become purely arithmetic! How did mathematicians go about completing this quest?
The Pythagorean theorem before Pythagoras | Tangente
Pythagoras would never have accepted this result being named after him: he knew perfectly well that he had learned it on his journeys of study. As we shall see, it already existed in Babylon and India!
From an Erdős conjecture to Tao’s theorem
The prolific Hungarian mathematician Paul Erdős (1913–1996), along with many number theorists and combinatorialists who followed him, studied the "discrepancy problem." In 1932, Erdős formulated a deep conjecture. In 2015, Tao proved it.
Catherine Com-Nougué and biostatistics | Tangente
Many biostatisticians in academia and the private sector were trained by Catherine Com-Nougué (1944–2017) and impressed by her gifts as a teacher.
Karl Pearson and the Birth of Correlation | Tangente
The British mathematician Karl Pearson (1857–1936) was a socialist-leaning freethinker and feminist.
Artists’ visions: knots in art and maths | Tangente
Three artists share their visions of knots.
Stereographic projection
Since 2021, the Bourse de commerce in Paris has been open to the public, showcasing contemporary art from the Pinault Collection. Its superbly renovated interior offers mathematicians an opportunity to explore… stereographic projections!
Vaughan Jones, a "pure genius" of knot theory
If ever there was a knot theorist, it was Vaughan Jones. This New Zealand-American mathematician, a 1990 Fields Medalist, is now renowned worldwide for his contributions to knot theory. French mathematician Alain Connes (born in 1947 and himself a Fields Medalist) described his discoveries as "work of pure genius".
Terence Tao: Académie des sciences medal | Tangente
On March 21 in Paris, the mathematics world was abuzz: Terence Tao, a true "star" in the field to whom Tangente will devote a special feature in its next issue, was awarded a particularly prestigious honor for a researcher—the Grand Medal of the Académie des sciences.
A stamp honoring Blaise Pascal | Tangente
To mark the 400th anniversary of his birth, La Poste will issue a stamp bearing the likeness of Blaise Pascal (1623–1662) on June 19, 2023.
Optimal control and Zermelo problems | Tangente
A particularly important class of optimal control problems consists of Zermelo-type problems: their applications have proved rich and fruitful in mathematics… and beyond. They are studied using a combination of geometric and numerical methods.
The sphere effect
The sphere came to be seen as a model of the world because of its perfection. Greek mathematicians soon sought to measure its properties, laying the groundwork for calculation techniques that would not bear fruit until centuries later.