History and Culture
History of mathematics and cultural connections
Grothendieck archives: an enigmatic treasure | Tangente
One hundred thousand pages of archives is no small matter! That is the scale of the legacy left by Alexandre Grothendieck, who withdrew from the world in 1991 to live in a remote village in Ariège, where he died in 2014.
Michel Serres: tribute to a learned philosopher | Tangente
Michel Serres, philosopher and member of the Académie française, died on June 1 at the age of 88.
The unification of physics through mathematics | Tangente
Physicists have two dreams. The first is to find a beautiful equation. The second is for that beautiful equation to describe all of physics. The Standard Model, string theory and loop quantum gravity are all candidates for a "theory of everything."
Dirac and distributions
Distributions generalize the concept of a function to account for discontinuous phenomena in physics.
Rattlebacks: when motion reverses | Tangente
Among the unusual objects that inspire both wonder and scientific curiosity, few are more astonishing than the rattleback. When spun, it has the remarkable ability to reverse its direction of rotation "by itself."
Shuffling an infinite deck of cards
Shuffling a fifty-two-card deck is easy enough. But suppose the deck contained infinitely many cards: could it still be "shuffled"? The answer is entirely up to you! Welcome to the world of paradoxes that play with infinity…
How mathematics powers video animation
Three-dimensional digital works, such as video games and animated films, unsurprisingly rely on mathematics to immerse us in their worlds. Angles, linear algebra, vectors and matrices play a particularly important role.
When polyhedra come in pairs
Swapping the faces and vertices of a polyhedron produces a new one, which can be built using elementary geometric constructions. This phenomenon once again demonstrates the close connection between arithmetic and geometry.
Mathematical controversy over duality | Tangente
The word "duality" comes from the Late Latin dualitas, which had displaced the classical term duales, used to describe something associated with two (duo in Cicero's Latin).
Partner-swapping in geometry
Duality has appeared in many branches of mathematics, from the Platonic solids of antiquity onward. It came into its own in projective geometry in the early 19th century, emerged soon afterward in logic with George Boole and Augustus De Morgan, and later flourished in linear algebra.
Let’s multiply in quasi-linear time!
The news broke in late March: mathematicians David Harvey and Joris van der Hoeven showed that large integers can be multiplied in "quasi-linear" time, confirming a conjecture that dates back to 1971, when Volker Strassen first suggested it. Let's revisit one of arithmetic's basic operations!
Hilbert, the twenty-three problems and physics
In his plenary address at the second International Congress of Mathematicians in 1900, David Hilbert presented the world with his famous "twenty-three problems." Some relate directly to physics; others have driven advances in both physics and mathematics.
The unforgettable Emmy Noether
A strong-willed woman and visionary mathematician, Emmy Noether defied many restrictions throughout her life and opened up new fields in mathematics and physics.
Cosmology and polyhedra: Plato to Kepler | Tangente
Regular polyhedra appear in many theories. These five solids fascinate us with their remarkable symmetries.
Erwin Schrödinger's cat
In its century of existence, quantum physics has proved extraordinarily effective and has never been found wanting. Yet many difficulties remain when it comes to interpreting it. One emblematic example of its strangeness is a famous feline thought experiment.
France at the forefront of music research | Tangente
It took many a political battle, but today France can pride itself on having world-class centers dedicated to music research.
Oumupo: The workshop of potential music | Tangente
In 1960, François Le Lionnais and Raymond Queneau founded a collective dedicated to renewing literary forms: Oulipo (the Workshop of Potential Literature). From the outset, Le Lionnais considered extending this approach to other forms of expression.
When mathematics enters musical composition | Tangente
The deep connections between mathematics and music in the process of composition grew richer during the twentieth century.
Atonal music: a rearguard debate | Tangente
In 2013, Karol Beffa, a composer and improvising pianist who held a chair at the Collège de France, organized a lecture. Drawing on examples, he set out to demonstrate the continued existence of the tonal—or neo-tonal—system and the failings of an atonal system that he considered dogmatic, inaccessible to the ear and obsolete.
Jean Bourgain, exceptional Fields medallist | Tangente
The prodigious Belgian mathematician Jean Bourgain (1954–2018) worked in many fields of mathematics, forging wholly unexpected links between seemingly separate areas. His outstanding results earned him numerous awards.