Math for everyone
Mathematical content accessible to everyone
A math problem taken to court
Should the solution to a mathematical puzzle have to be approved by a judge? If the case reported here is anything to go by, the answer is not so simple.
Loop quantum gravity
What if our universe were actually discrete? If confirmed, a bold theory known as loop quantum gravity could reconcile the physics of macroscopic gravitational fields with quantum physics. Spin plays a fundamental role in this theory.
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.
What if our universe were a hologram? | Tangente
Our universe could be a sphere whose exterior would resemble a black hole. Our world would merely be the reflection of a reality inscribed on the surface of this sphere—a kind of hologram. All information would be encoded on our cosmic horizon. A scenario that may not be so far-fetched after all…
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.
A point charge
A point charge is a source of mystery, like an electron with charge e in a vacuum.
Quantum computers: a threat to encryption | Tangente
Internet communications are currently secured by symmetric encryption systems such as AES, whose keys are transmitted using an asymmetric encryption system such as RSA.
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.
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.
Instruments in the service of music
Marking time, giving music its rhythm by keeping the beat: these are the functions of an object that accompanies many musicians—the metronome. Originally mechanical, it later became electronic, no doubt to keep in tune and move with the times…
Acoustics and computer music: Helmholtz | Tangente
Thanks to the work of Joseph Sauveur and later Hermann von Helmholtz on sound phenomena, we can analyze a sound in terms of its pitch, intensity and timbre. This is the analysis used in computer music, which is so popular with contemporary composers.