Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
Persian tilings and Islamic geometry | Tangente
A highly debatable approach to Persian pentagonal patterns has been repeated so indiscriminately in scientific journals that it has become received wisdom. It is high time to offer another perspective.
From Baghdad to Toledo: legendary places | Tangente
A great many works from ancient Greece survived and reached a wider audience thanks to their translation into Arabic or Latin. This legacy was made possible by the determination of a handful of rulers who understood the universality of knowledge and the importance of passing it on.
Greek mathematical texts in translation | Tangente
Greek mathematical texts influenced the entire history of mathematics around the Mediterranean. Yet Greek was not always spoken by every scholar. Ancient texts therefore had to be translated to make them accessible to as many people as possible.
How Europe made Arabic mathematics its own | Tangente
With a passion for mathematics and history, Marc Moyon studies how scientific knowledge and practices travelled from the Greco-Roman world and the lands of Islam to Europe. A skilled translator of mathematical texts, he shares his experience with us.
Approximating functions efficiently
Most physical phenomena involve transcendental functions such as the exponential and trigonometric functions. To minimize computation times, we try to replace them with polynomials.
When numbers awoke to wonder
Ancient peoples used numbers for purely practical purposes: to count and enumerate. Five centuries before the Common Era, after travelling the world, a Greek scholar named Pythagoras returned certain that the original order of the World was Number, thereby turning it into a philosophical concept.
Whether or not to choose the mathematics specialization | Tangente
Parents of tenth-grade students who do not have a high-school mathematics teacher among their close acquaintances often wonder which specializations their children should choose in 11th grade. In particular, is taking mathematics a wise choice?
Self-reference at every level | Tangente
We do not always pay attention to them, but self-referential sentences and turns of phrase surround us every day!
Words and mathematics | Tangente
Symbols and formulas emerged only gradually from mathematics that was initially expressed entirely in words. Ever since, the relationship between formalism and ordinary language has continued to fascinate.
Wanted: a missing abacus | Tangente
An ancient Roman ivory abacus has been missing for several years.
Laure Saint-Raymond: 2020 Bôcher Prize | Tangente
The American Mathematical Society (AMS) has just awarded the 2020 Bôcher Prize to French mathematician Laure Saint-Raymond, a professor at ENS Lyon and a member of the Académie des sciences, for her "transformative contributions to kinetic theory, fluid dynamics and Hilbert's sixth problem."
An aberration: the discontinuity in mathematics educ... | Tangente
In France, every reform reduces the opportunities for students on non-science tracks to study mathematics.
Pure and impure self-reference | Tangente
Self-reference is not "pure". It must be tied to an object, a situation or a concept—here, for instance, artistic creation, and photography in particular.
Gödel's incompleteness theorems
In mathematics, although there are many conjectures and hypotheses, it is generally assumed that any well-formed statement must have either a proof or a refutation. Kurt Gödel showed that this is not so. His proof uses self-reference.
Distributions:
The idea of discontinuity is epitomized by two “functions” named after the physicists Heaviside and Dirac. An economic problem offers an opportunity to introduce the fundamentals of the underlying mathematical theory intuitively.
Welcome to 2020! | Tangente
As usual, the new year inspired the Tangente team and their friends, who all vied with one another to tease out the number 2020's astonishing properties.
The Gibbs phenomenon
When an image is compressed, it not only becomes slightly blurred: wherever there is strong contrast, its discontinuities are accentuated. This is known as the Gibbs phenomenon, and understanding it requires knowing how a wave can be decomposed into harmonics.
When works speak for themselves | Tangente
Advertising regularly makes use of it, as do graphic designers and artists. Self-reference has become a genre in its own right, appealing not only to our eyes but to all our senses! Let's take a wild tour of this seemingly limitless creativity.
Disputes and paradoxes | Tangente
Even the greatest mathematicians have fallen into the traps laid by logic and its paradoxes.
The paradoxes that shook mathematics
What a devilish theory Georg Cantor created with set theory! So thought some mathematicians at the turn of the 20th century, when a series of paradoxes seemed to threaten the foundations of mathematics. This prompted a reassessment of the role of logic.