Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
Recognized amateurs
What is an amateur mathematician? Defining one is no easy task, especially since the concept has undoubtedly evolved over time. Nevertheless, we will look at a few examples, both past and present.
Clairaut's pedagogical Éléments d'algèbre | Tangente
Clairaut's Élemens d'algèbre (Elements of Algebra) was long a standard reference for teaching algebra.
Clairaut.com: a complete online biography | Tangente
As its name suggests, clairaut.com is devoted entirely to Alexis Clairaut. It provides a comprehensive inventory of his works, with links to them, along with his correspondence, academic reports, and the principal tributes and portraits devoted to him by his contemporaries.
Clairaut: a mathematical child prodigy | Tangente
The engraving by Delafosse below was made from a portrait drawn by L. C. de Carmontelle in 1763.
The geometry of curves
Alexis Claude Clairaut first came to the attention of learned circles through his book on curves of double curvature, presented to the Académie in 1729. He was only 16 at the time. The book was published in 1731, earning him election to the Académie des sciences at the age of 18.
In Clairaut’s footsteps
Alexis Clairaut is probably little known today. Yet his writings inspired many scientists. A compilation of 19th-century publications reveals a fame that has since faded.
Alexis Clairaut: A forgotten light of mathematics | Tangente
Alongside Leonhard Euler and Jean Le Rond d’Alembert, Alexis Clairaut was one of the greatest mathematicians of the Enlightenment. Though little known today, he played a fundamental role in validating Newton's theory of universal gravitation.
2025: a very square number!
What better way to celebrate the new year than with some delightful mathematical properties of the number 2025? Tangente wishes all its readers a wonderful 2025.
Curious stories of mathematics on video | Tangente
For almost a year, Noëlle Krajcman has been running a TikTok and Instagram channel devoted to mathematical anecdotes.
Sylvie Méléard wins the Irène-Joliot-Curie Prize | Tangente
A specialist in probability theory, particularly stochastic processes, Sylvie Méléard has spent the past twenty years applying mathematical models to living systems: changes in population size over time (such as bacterial growth), the proportion of an allele in a population, and genetic evolution (such as antibiotic resistance).
Jacques Roubaud: tribute to a poet-mathematician | Tangente
Following Oulipo's time-honored formula, Jacques Roubaud is now excused from its meetings on account of his death, which occurred this past December 5, his 92nd birthday.
Kepler, or the defeat of the circle
Kepler's first law states that planets follow elliptical orbits around the Sun. How can this be proved with the bare minimum of theory? To answer this question, physicist Richard Feynman produced a little gem of classical geometry applied to celestial mechanics.
Ellipse snippets
There are several ways to construct an ellipse. Here are a few.
A question of circumference
You might expect calculating the perimeter of an ellipse—a fairly ordinary shape—to be straightforward. Yet it is a problem on which mathematicians have displayed extraordinary ingenuity. And in the formula contest, Ramanujan wins!
A little something missing
The term "ellipse" differs from the names of the other two conics, the parabola and the hyperbola. In fact, it means "something missing". Behind this surprising etymology lies a mathematical revolution: Apollonius of Perga's theory of conics.
Condorcet and physiocratic political economy | Tangente
Condorcet's ideas were influenced by the Physiocrats, who championed free trade and restricted voting rights to property owners.
Condorcet’s Enlightenment fight against slavery | Tangente
In his Réflexions sur l’esclavage des nègres (Reflections on Black Slavery), published in 1781 under the pseudonym Pastor Joachim Schwartz ("black" in German), Condorcet opposed slavery, which he regarded as a fundamental violation of human rights, and denounced the contradictions and injustices bound up with the enslavement of Black people.
Condorcet, champion of women's suffrage | Tangente
A few years before the Revolution began, Condorcet was the first French writer to make the case for women's voting rights in his Lettres d’un bourgeois de New-Haven (1787).
Condorcet's paradox explained | Tangente
From Lewis Carroll to Kenneth Arrow, the famous Condorcet paradox has generated a great deal of discussion.
Condorcet, theorist of electoral procedures | Tangente
Condorcet is recognized as one of the pioneers in the theory of electoral systems, alongside his contemporary, the Chevalier de Borda. Both thinkers brought a fundamental idea to light: the method used to elect a candidate has a decisive influence on the outcome.