Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
Cauchy and the rise of mathematical journals | Tangente
As the press expanded dramatically in the 19th century, advances in science prompted the creation of new publications devoted to scientific research.
Cauchy: A man of contradictions | Tangente
Cauchy's teaching and research left a profound mark on the history of mathematics. Yet both his work and personality were full of contradictions and did not always meet with universal approval.
Cauchy's rigidity theorem and polyhedra | Tangente
Cauchy's earliest work concerned polyhedra, including his foundational rigidity theorem.
Counting by substitution
At barely 25, Cauchy puts the finishing touches to a paper on symmetric functions that is eventually published as two articles. In it, he introduces new concepts, notation and methods, and creates the calculus of substitutions, which will play a central role in the development of group theory.
Cauchy and his rivals: a man of controversy | Tangente
Disputes over the authorship of theorems reflect the bitter controversies that pitted Cauchy against some mathematicians of his time.
The origins of complex analysis
Cauchy is often credited with single-handedly founding complex analysis. The reality is subtler: although Cauchy gave the subject its structure and rigor, he drew on a wealth of earlier research, notably dating back to d’Alembert. Moreover, his involvement was prompted by debates between Laplace and Poisson over whether the use of complex numbers in integral calculations was legitimate. To understand Cauchy’s work, then, we must reconstruct its entire intellectual context.
A train of thought
It took mathematicians a long time to define a convergent sequence without falling into the many logical traps involved. Cauchy's research was among the most important contributions that eventually clarified the matter.
Cauchy’s first discoveries: polyhedra | Tangente
Although Cauchy is widely regarded as a highly abstract thinker, the first chapter of his work is, by contrast, strikingly visual. His study of regular polyhedra marked his entry into the world of mathematical research.
From Arcueil to Sceaux: in Cauchy's footsteps | Tangente
Cauchy had close ties to the southern suburbs of Paris. After growing up in Arcueil, he spent his holidays in Sceaux, where he produced some of his mathematical work. He also died and was buried there.
Cauchy the poet: defending maths in verse | Tangente
Although his name means only one thing to us—that of a mathematician—Cauchy also had a solid classical education. Having won distinction in the literary papers of the Concours général, he even tried his hand at poetry to explain the value of his science.
The other bicentenary: Cauchy commemorated in 1989 | Tangente
In France, 1989 was a year of major celebrations marking the bicentenary of the 1789 Revolution. Yet it was also the bicentenary of Cauchy's birth.
A series of errors
Nobody is perfect—not even the greatest mathematicians in their own field. Take Cauchy, who made a mistake concerning the convergence of series of functions—one that no student would dare make today.
Worth reading: Belhoste's biography of Cauchy | Tangente
Writing a biography of a man like Cauchy is a tour de force.
Editorial
The latest elections were a fiasco for the government, which has faced intense popular opposition and serious economic difficulties for months. Hoping to regain the initiative, the head of state then decides, to everyone’s surprise, to dissolve the National Assembly…
Science podcasts worth listening to | Tangente
Canal Académies is a podcast platform created by the Institut de France in 2004.
Secrets from mathematical archives | Tangente
For its YouTube channel, the Académie des sciences produced a series entitled "Treasures from the archives." Each episode, lasting around five minutes, features a member of the Academy presenting a document from its archives.
Images des mathématiques gets a makeover | Tangente
You can hardly have missed the Images des mathématiques website since its launch in 2009! This online magazine quickly established itself as an essential resource for sharing and popularizing mathematics.
Women in science: where are they? | Tangente
On June 18, 2024, the French Academy of Sciences published a 32-page report highlighting the shortage of women in scientific professions in France.
Markov recommends Avenue Henri-Martin
The well-known board game Monopoly is a fine example of a stochastic process—a situation whose evolution is governed by the laws of probability. So, to find out whether you should buy Gare Saint-Lazare or Rue de Vaugirard, follow the guide…
A (good) Babylonian approximation
The Babylonians have always been renowned as brilliant mathematicians, and the clay tablets that have survived sometimes bear dazzling witness to their skill.