Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
André Antibi: A tribute to an educator | Tangente
Holding two doctoral degrees, André Antibi was professor emeritus at Université Toulouse-III-Paul-Sabatier and Sup-Aéro. He became best known for his original ideas on mathematics education, but his work ranged far more widely.
Bertrand Russell: A century of passionate living | Tangente
Bertrand Russell was no ordinary mathematician. His Nobel Prize in Literature attests to the breadth of his talents. His advocacy of sexual freedom and his campaigning for peace gave this exceptional man his full stature.
A genius off the beaten track
In the scientific world, Bertrand Russell is known first and foremost as a logician and philosopher. His contribution cannot be understood without grasping the major shift then taking place in the development of mathematics: this was the era of the "foundational crisis."
Alfred Whitehead, Russell's collaborator | Tangente
Russell's fame has overshadowed Whitehead's immense contribution to the development of logicist theories. The two men wrote the Principia Mathematica together.
From intuition to rigor
In Euclid’s geometry, a line already divided the plane into two distinct regions, but negative lengths were not accepted. How can the algebraic notions of direction and measurement be brought into geometry?
Russell: logic, faith and reason | Tangente
A free thinker, Bertrand Russell made no secret of his agnosticism and did not hesitate to criticize religion. He deplored the fact that people's reasons for embracing faith had little to do with rational argument. In his view, hatred of reason seems to be a constant throughout human history.
Wittgenstein and Russell at Cambridge | Tangente
Born in Vienna in 1889, Ludwig Wittgenstein began studying mechanical engineering in 1906. Drawn to mathematics, he initially explored its applications before becoming fascinated by Russell's writings.
A mathematical critique of liberalism | Tangente
In our "modern" and "civilized" societies, some workers are overwhelmed with work while a whole section of the population is shut out of employment. Is this situation inevitable? Bertrand Russell dismantled certain dogmas of economic liberalism point by point and showed that other models of society are possible.
Bertrand Russell's politically engaged writings | Tangente
Bertrand Russell's literary writings range widely; they are tinged with philosophy, politics, and sociology. What unites them is that they all have a message to convey.
A graphic novel on the foundational crisis | Tangente
Logicomix is a graphic novel centered on Bertrand Russell.
Why do clocks turn clockwise? | Tangente
Clock hands turn clockwise, rather than counterclockwise. Why?
Bertrand Russell: a man of letters and numbers | Tangente
At 78, too old for a Fields Medal, and with no prize specifically devoted to philosophy, the mathematician and philosopher Bertrand Russell was awarded the 1950 Nobel Prize in Literature, much to his surprise.
The Möbius strip in art | Tangente
The legendary Möbius strip—a two-dimensional, non-orientable surface with only one side, easily made from a strip of paper—has inspired several artists.
The etymology and history of orientation | Tangente
Do you know where the words "orientation" and "orient" come from?
Hilbert's thirteenth problem
At the second Congress of Mathematicians, held in Paris in the summer of 1900, David Hilbert presented a list of research questions that he considered important. The list contains twenty-three problems spanning every field: algebra, geometry and analysis.
The building blocks of Galois theory
Although inspired by Galois's work, "his" theory developed long after his death and did not take off until algebraic structures were introduced.
Beyond Lagrange's memoir
As a teenager, Galois read Legendre and Lagrange, followed by Gauss and Cauchy. He often cites the latter two, but rarely Lagrange. Galois was clearly influenced by Lagrange's ideas; he would, however, go much further, benefiting from all the advances made since 1771.
Tales of roots
The roots of unity form an abelian group. A quick refresher...
The school system in Galois's time | Tangente
In Évariste Galois's day, the school system was still somewhat different from ours. For example, students could choose to skip certain grades depending on their intended course of study.
Galois, an artistic inspiration: opera and maths | Tangente
Évariste Galois's eventful life has inspired many artists. He appears in several plays, a film and even... an opera!