Mathematical Themes
Explore the major mathematical themes: geometry, algebra, analysis, arithmetic, logic, and many other fascinating fields.
Autonomous vehicles: life-or-death maths | Tangente
How can morality be programmed into autonomous vehicles? The question, worthy of science-fiction novels, is topical today.
Mathematical economics
Economists have often used percentages in their models
In economics too: maths at the heart of the system | Tangente
In economics, as in everyday life, rates are everywhere. Let's see how.
Deus ex machina: in mathematics too!
Looking for a simple, unexpected solution to a difficult problem? A deus ex machina can sometimes provide a surprise resolution to a desperate mathematical situation. Combinatorics, arithmetic and geometry are fertile ground for such an "aha!" moment.
Roger Godement: an extraordinary mathematician | Tangente
Who has not had Roger Godement's monumental Cours d'algèbre on their shelves—the textbook that introduced generations of budding mathematicians to linear algebra and undoubtedly taught them to love it?
The pitfalls of rates
Our thinking seems naturally additive. If we add 10% and then another 10%, we expect the total to be 20%. Yet that is wrong! Rates are not added; they are multiplied. How can we avoid the pitfalls of percentages? How can we work out the cost of a loan?
They are among us: everyday mathematics | Tangente
Percentages are everywhere. Learn how to avoid their pitfalls.
The multiplier: a tool for every citizen
Everyone encounters rates of change sooner or later. Handling them is often a source of error, although one simple, effective tool can solve many such problems: the multiplier.
Percentages, for better or worse
Since antiquity, data have been compared by scaling the total to 100. The introduction of Arabic numerals gave percentages an important role, offering a clear, quick view of a wealth of statistical data... provided, of course, that one understands how they work and can count!
The "happy ending" problem
In 1933, Hungarian mathematician Eszter Klein posed an apparently elementary geometry problem to a group of young colleagues. It would lead to the birth of a new field of mathematics, discrete geometry, and... a marriage.
A practical protractor at last: measuring tools | Tangente
What could be more commonplace in geometry than a protractor?
This polyhedron is dangerous: the geometry of the Zika virus | Tangente
Behind this polyhedron, a virus
Cancer: maths to beat the disease | Tangente
"At a time when medicine can join forces with mathematics to predict how a cancer develops, it is high time we rethought our prejudices about maths — and, while we're at it, about women mathematicians…"
Solar System stability: the KAM theorem | Tangente
Jürgen Moser belongs to the long line of mathematicians who have tackled the problem of the Solar System's stability. He is the "M" in the KAM theorem's trinity—Kolmogorov, Arnold and Moser—which links number theory and celestial mechanics.
Approximating a function and following its curve
Assuming that a function is a polynomial yields useful approximation formulas. A complicated function can thus be replaced by a polynomial, simplifying most calculations. More surprisingly, interpolation lies at the heart of a secret-sharing technique.
In search of asymptotes
Euclidean division of polynomials is very useful in analysis! The proof, with three examples
Sphere packing:
We live in extraordinary times! Not a month goes by without a new mathematical breakthrough. The latest? A young researcher has solved the problem of the optimal packing of identical spheres in dimensions 8 and 24.
Between algebra and analysis: an indispensable world
Polynomials belong to both algebra and analysis, which can lead to all kinds of confusion! This dual nature offers a simple way to explain the subtle differences between variables, unknowns and indeterminates.
Have you heard of Yakazu, a Japanese logic game? | Tangente
There are dozens of number-grid puzzles, often hugely popular. Yakazu, created in 2015 by hobbyist Patrick Tirone, is perhaps a little less so.
Crocodile tears
So many tears shed in Scotland over this famous crocodile problem!