History and Culture
History of mathematics and cultural connections
Tchebychev's inequalities for sequences | Tangente
Elementary results can sometimes prove astonishingly fertile, opening the way to a host of developments and applications. Chebyshev's inequality is a case in point.
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.
Dido's problem and isoperimetry | Tangente
For a given perimeter, the disk is the figure with the greatest area. This result, popularized by a trick attributed to Dido, the founder and first queen of Carthage, is the "isoperimetric theorem." It gave rise to many more general inequalities.
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.
Research
Singmaster's conjecture, the Polymath projects, the Green–Tao theorem…
Annette and André Parent's legacy | Tangente
Annette Parent passed away on April 26, 2023. Her death was a source of immense sadness for everyone who knew her; Annette had a generosity and warmth that no one could forget.
Enter the Trophées Tangente | Tangente
Every summer, Club Tangente presents its awards. Alongside its literary prizes—the Tangente Book Prize and the Tangente High School Students' Prize—which recognize books devoted to mathematical culture, two competitions invite our readers to get creative. Don't hesitate to enter!
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!
Some results
Terence Tao has successfully tackled many mathematical conjectures. Here are a few examples.
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.
Alain Desrosières: numbers are not neutral | Tangente
A graduate of the École polytechnique (class of 1960) who was deeply engaged with political and civic issues, Alain Desrosières (1940–2013) chose the École nationale de la statistique et de l’administration économique and became an Insee administrator in 1965.
How many tanks? Statistical estimation | Tangente
During the Second World War, the Allies used statistics to estimate German tank production.