Topology
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Topology, deforming without tearing
When an elastic object can, when it is deformed continuously without tearing, take the shape of another object, they have the same topological structure: they are said to be homeomorphic. A sphere and a cube (both hollow) are homeomorphic, but they are not with a torus. Topology provides a fundamental complement to analysis and to the definitions of limit or continuity by introducing new notions such as compactness. Welcome to this geometry "unlike any other"…
Numbering systems
Civilizations have doubled their ingenuity to estimate quantities. They created systems based on new alphabets or symbols. The natural reaction was to use the decimal system, but other bases were invented, such as base 60, still thriving today to define time. Coming from India, positional notation made it possible to use algorithms to perform operations. More recently, the binary system proved essential in the explosion of computer science and data science.
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Tangente awards 2018
Ever since Napoleon's coronation in 1804, 2 December has been a day for coronations. Here are the many winners of Club Tangente's 2018 competitions and prizes, honoured at the Musée des Arts et Métiers.
The SCM–FFJM competition
Each year, the SCM, in partnership with the FFJM, organizes a research competition based on a mathematical problem drawn from "real life." This time, participants have until April 30 to study traffic congestion in Houston.
180 seconds of popular science
Three minutes flat is not long to sum up a thesis—especially when the presentation has to be accessible to a wide audience. That is the daunting challenge faced each year by a number of French-speaking doctoral students in "My Thesis in 180 Seconds," modelled on the English-language Three Minute Thesis competition.
Breakthrough Prize awarded to Vincent Lafforgue
French mathematician Vincent Lafforgue, brother of 2002 Fields Medalist Laurent Lafforgue, has won the 2019 Breakthrough Prize in Mathematics, worth $3 million, "for his fundamental and elegant contributions to the Langlands program in the function field case."
The campylograph
At the end of the 19th century, Father Dechevrens, director of the Jersey observatory, devised a curve-drawing machine. Originally designed to plot the paths of the planets as seen from Earth, it could produce many other curves besides epicycles!
Christian Lavigne
Visual artist Christian Lavigne's work achieves a beautiful alchemy of mathematics, art, poetry and, above all, digital sculpture, a field in which he is a leading figure. He created the first French digital sculpture produced using additive manufacturing.
Pierre Duchet: research in action
Mathematician Pierre Duchet died on October 27 last year at his home in Mexico City. A friend of the editorial team at Tangente, this specialist in combinatorics, discrete mathematics and especially graph theory was always eager to share his work with younger generations.
Michel Serfati: a passion for the history of mathematical ideas
Mathematician, philosopher and historian of science, Michel Serfati, who died on September 30 last year, was all three.
South America: Fondation Cartier's ode to geometry
Until 24 February 2019, Fondation Cartier is exploring the presence of geometry in art across South America, from Mexico to Tierra del Fuego, spanning pre-Columbian and contemporary art as well as Indigenous American cultures.
Combinatorics, past and present: An interview with Pierre Duchet
The study of combinatorial structures is a recent branch of mathematics, rich in counting problems. A journey into a far too little-known realm.