Interview
Interviews with mathematicians and personalities from the scientific world
Would you like a slice of a sphere? | Tangente
John Conway passed away this year, but the profound questions he raised across many fields remain as relevant as ever (see Tangente 194).
Mathematical models and measurement | Tangente
When direct measurements are impossible, we must rely on mathematical models, which need to be validated. The results then depend on the precision of the available direct measurements and on how well suited the chosen model is.
An elusive geometric concept
Almost two thousand years of geometry! That is how long it took, with Descartes, to develop the first tools for studying those mathematical objects we all think we know: curves. How far we have come since the tentative explorations of ancient Greek scholars!
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?
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.
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.
Mathematical innovation days | Tangente
Businesses and academic research laboratories have every reason to collaborate—but for that to happen, they must first be brought together!
Academia and industry: a dialogue | Tangente
What matters most is not so much that academia tackles problems faced by industry, but that there is an open, ongoing exchange through which academia can make its advances known.
The mathematics of 5G | Tangente
Large companies are beginning to understand that they cannot survive in the long term without funding fundamental research. A career as a mathematician in the private sector is therefore possible, provided you have some understanding of technological challenges.
Stories of successful maths–industry collaborations | Tangente
On November 26, 2019, AMIES invited a number of speakers to describe successful collaborations between companies and mathematical research laboratories. It was an opportunity to discover sometimes unexpected partnerships, suggesting that mathematics will play an increasingly prominent role in business operations.
Heilbronn triangles
How should points be placed in a region of the plane to maximize the smallest area determined by any three of them? Despite the elementary nature of this geometry problem, no general solution is known even today!
Good divisions
Beautiful problems are like delicious dishes: we love to share them. Sometimes the question of how to share them out becomes interesting in its own right, especially when we are generous by nature and want to be able to let as many people as possible enjoy them.
Coloring problems for all ages
Assigning colors—and their associated sets of constraints—to the vertices of a graph opens up the fascinating world of graph-coloring problems.
On persistence
Apply the same algorithm to the digits of a number, then repeat the process with the digits of the result, and you encounter the notion of persistence… and the questions it raises.
The art of avoiding crossings
Artists using mathematics: nothing new there. But artists posing optimization problems that mathematicians still cannot solve: now that is surprising! One seemingly innocuous conjecture about drawing graphs has resisted all attempts at proof for fifty years.
Graph vertex degree constraints | Tangente
What is the smallest graph with a given set of degrees? Forty years ago, an article provided an elegant, constructive answer to this question.
Dendrochronology
How was a harbor built in Roman times? When was this violin made? When was a mine's infrastructure built? Dendrochronologists seek to answer all these questions by precisely dating objects, structures, or remains containing wood.
A math problem taken to court
Should the solution to a mathematical puzzle have to be approved by a judge? If the case reported here is anything to go by, the answer is not so simple.
Shuffling an infinite deck of cards
Shuffling a fifty-two-card deck is easy enough. But suppose the deck contained infinitely many cards: could it still be "shuffled"? The answer is entirely up to you! Welcome to the world of paradoxes that play with infinity…
The unforgettable Emmy Noether
A strong-willed woman and visionary mathematician, Emmy Noether defied many restrictions throughout her life and opened up new fields in mathematics and physics.