Hervé Lehning
90 articles published in Tangente
Math for everyoneNov 25, 2019Self-reference and fixed points
Self-reference is paradoxical and connected with the mathematical notion of a fixed point, the method of successive approximations, and recursive definitions. Together, these connections make this fundamental idea a natural subject for mathematics enthusiasts.
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Math for everyoneNov 21, 2019Pascal's ribbons
In the past, arithmetic mattered as much to merchants and accountants as it did to scholars. In the 17th century, Blaise Pascal devised a method for automatically testing whether one integer is divisible by another.
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Math for everyoneN°72Oct 10, 2019Gradient descent: skiing your way to a minimum
You are on a ski slope, surrounded by fog. Which route should you take to get all the way down? One approach is to follow the steepest slope—that is, the gradient. This idea yields both a numerical method and a way of finding optima.
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History and CultureN°189Jul 16, 2019Michel Serres, philosopher with a passion for science, dies
Michel Serres, philosopher and member of the Académie française, died on June 1 at the age of 88.
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History and CultureN°189Jul 13, 2019Let’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!
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Math for everyoneN°71Jul 10, 2019Quantum computers: a threat to security?
Internet communications are currently secured by symmetric encryption systems such as AES, whose keys are transmitted using an asymmetric encryption system such as RSA.
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N°71Jul 09, 2019Indispensable symmetry groups
Since Galileo and Newton, symmetries have played an important role in the development of physical theories. A symmetry can be identified with the invariance of a structure under a transformation.
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Math for everyoneN°188May 13, 2019Multiplying in quasi-linear time
Multiplying two integers dates back several thousand years. In 2019, at last, the algorithm was improved!
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Math for everyoneN°188May 10, 2019The theorems of Menelaus and Ceva
Menelaus's and Ceva's theorems, two classics of plane geometry, are similar in form. This resemblance becomes clearer when the notion of cross-ratio is introduced.
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KnowledgeN°70Apr 11, 2019Exquisite minimal surfaces
A surface is minimal when, for a fixed boundary, its area is as small as possible. Soap bubbles provide a physical model of minimal surfaces.
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KnowledgeN°70Apr 11, 2019Measuring areas
As soon as we move beyond elementary figures, calculating area brings us up against the concept of infinity. After Archimedes and his skilful use of potential infinity, it was not until the Renaissance that this obstacle was finally overcome.
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Amazing MathN°70Apr 11, 2019Ruled surfaces
How can a surface made up of straight lines be curved? That is the paradox of ruled surfaces!
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