Jacques Bair
56 articles published in Tangente
History and CultureN°91Aug 25, 2024The battle over infinity
For more than two centuries, scholars and mathematicians debated infinitesimals: could they be handled safely, or were the paradoxes they generated insoluble? Amid this debate, Cauchy ushered analysis into the modern era while maintaining a nuanced position.
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History and CultureN°212Jun 27, 2023Learning:
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?
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History and CultureN°212Jun 21, 2023From 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.
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Games and ChallengesN°210Feb 22, 2023Converging to a number: is there only one way?
Traditional mathematics provides a precise definition of convergence for a numerical series, explored in the main body of this article. But this should not rule out less conventional approaches, discussed in the box and in several articles in this special issue.
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History and CultureN°210Feb 20, 2023A brief history of Grandi's series
Grandi's series is the infinite sum 1 – 1 + 1 – 1 + 1 – 1 + … Mathematicians have studied it for more than three hundred years. Its history can be divided into three stages.
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Math for everyoneN°84Nov 18, 2022Different types of tangency in microeconomics
In microeconomics, certain arguments rely on a graphical representation and call upon different types of tangency. This is the case with basic consumer theory, the Edgeworth box, and a firm's long-run average cost.
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Math for everyoneN°84Nov 18, 2022Deviation of a curve from a tangent
Newton and Leibniz, the founders of differential and integral calculus, studied how a curve deviates from a tangent. To this end, they drew on the notion of curvature. The fundamental ideas of these two scholars gave rise to contemporary mathematical analysis.
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Math for everyoneN°84Nov 18, 2022Observing curves with magnifying glasses
Used appropriately, extremely powerful magnifying glasses make most curves appear to coincide locally with a tangent line or an osculating circle.
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History and CultureN°208Oct 21, 2022Hervé Lehning (1948–2022)
Tireless in his work, Hervé Lehning devoted his life to sharing the mathematics he loved so deeply and making it accessible without sacrificing quality, driven above all by a desire to pass on his passion. But he was much more besides.
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Math for everyoneN°207Aug 19, 2022Axiomatizing versus de-axiomatizing
The French mathematician Maurice Fréchet distinguished two types of researchers. Some work essentially in an abstract manner, while others are concerned with experimentally verifying the predictions that their mathematical approach leads them to.
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History and CultureN°206Jun 21, 2022André Antibi (1944–2022)
Holding two doctoral degrees, André Antibi was professor emeritus at Université Toulouse-III-Paul-Sabatier and Sup-Aéro. He became best known for his original ideas on mathematics education, but his work ranged far more widely.
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KnowledgeN°204Feb 17, 2022Beyond convexity
The intuitive idea behind convexity seems entirely natural. Yet one cannot help wondering whether slightly altering the formal definition might lead to other interesting ideas… Here too, convexity is just as fruitful!
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