Knowledge
In-depth articles on mathematical knowledge and theories
Major mathematical concepts in computational form... | Tangente
Will machines replace human beings? Will artificial intelligence prove better than us in every field? Gérard Berry reassures us on at least one point: computers are nowhere near supplanting mathematical ingenuity…
The birth of artificial intelligence | Tangente
The conjecture that all cognitive functions can be described precisely enough to be reproduced on computers has never been proved or disproved. It forms the basis of artificial intelligence as a scientific discipline.
Misuse and security | Tangente
While AI makes large-scale data collection and analysis easier, it also enables greater surveillance of the population. Every coin has two sides...
Computer-assisted proofs | Tangente
Can a machine prove a theorem? Probably not without a human to guide it, but computers are becoming increasingly useful assistants—for example, by turning a human proof into a formal one. Spectacular developments and applications are currently under way.
Bridge opens up a promising future for AI
Bridge is one of the few games to have resisted advances in computing. To crack it, a French academic is preparing to overturn received wisdom about AI development and take it to a new level, opening the way to fresh challenges.
False "proofs"
Although fallacious proofs are not scams, they remain a teaching tool that often amuses math buffs… and everyone else!
Calculators in entrance exams: end of an era | Tangente
For several years now, some written papers in the competitive entrance examinations for France's engineering grandes écoles have prohibited calculators. But this was not a blanket rule.
Learn to calculate with a calculator | Tangente
Machines generally calculate faster than people. But exactly how does a machine perform a simple addition? Revisiting the methods taught to children reveals two main techniques, which we can compare using CASIO's Graph 90+E calculator.
The magic of domino divisibility tests
You know the divisibility tests for 2, 3, 4, 5, 10, 20… and perhaps others as well. But are you familiar with "domino tests"? Variants of a famous divisibility test for 11, they make for a wonderful mathematical playground!
Geometric “tricks” for arithmetic
The human mind often needs concrete representations of abstract concepts. Geometry can thus serve as an aid to calculation, as Descartes was among the first to show.
Mental arithmetic: a vital skill | Tangente
There is unanimous agreement: mental arithmetic is fundamental both to mathematics education and to citizens of tomorrow. What lies behind this remarkable consensus, and where does mental arithmetic stand in schools today? Let's take stock.
Rio Congress:
Algebraic geometry featured in the research of three of the four Fields medalists. Although the French took home no awards, they nevertheless played a prominent role. There was one disappointment, however: St Petersburg was chosen over Paris to host the next ICM, in 2022.
The techniques of the prodigious Terence Tao
Terence Tao is one of the greatest mathematicians of our time. He solves formidable mathematical problems himself. Nor does he hesitate to share his working methods on his widely read blog and offer advice that anyone can put to use.
Reasoning means solving
Reasoning means organizing your thoughts. Yes, but how? Are there methods for keeping our thoughts from descending into anarchy and confusion? Mathematics is, by its very nature, the discipline that has enabled us to answer these questions over the centuries. And it works!
Animals do math too! Polya and heuristics | Tangente
To solve mathematical problems, we can sometimes draw inspiration from the way certain animals solve theirs. You read that right! Chimpanzees and mice, for example, display remarkable ingenuity in reaching their favorite treat…
Elementary yet powerful: the pigeonhole principle
If your chest of drawers has two drawers and you put three items of clothing in them, at least two items—possibly all three—must end up in the same drawer. This seemingly trivial observation is actually the basis of a powerful reasoning tool!
A deep connection with determinism
Many physical and economic phenomena are described by differential equations. This implies, in particular, that the functions we seek are differentiable, but also that the phenomena concerned are locally deterministic.
From intuition to rigor
Studying derivatives of functions sometimes leaves only a distant memory of applying somewhat esoteric formulas. Yet the underlying idea is as simple and concrete as it is effective. What if we went back to basics to gain a better grasp of the concept's power?
The mysterious crystal
For a change, beneath its polyhedral exterior, the subject of this instalment in our mathematical objects saga is a puzzle. You will find everything you need to build it on the Tangente website.
Journalists and scientists join forces | Tangente
In an unprecedented initiative, journalists and scientists joined forces for an entire day to make sense of the news