Over 300 years ago, a mathematician named Fermat discovered a subtle property about prime numbers. In the 1970's, three mathematicians at MIT showed that his discovery could be used to formulate a remarkably powerful method for encrypting information to be sent online. The RSA algorithm, as it is known, is used to secure ATM transactions, online business, banking, and even electronic voting. Surprisingly, it's not too difficult to understand, so let's see how it works.

Although they have been used for thousands of years, an actual definition of numbers was given less than a century ago! From the most fundamental level of set theory, this article takes you to the journey of the construction of natural, integer, rational, real and complex numbers.

Although highly appreciated by artists, self-reference has been a nightmare for mathematicians. It took one of the greatest, Kurt Gödel, to provide a better understanding of it. This article deals with paradoxes, recursion, fractals and Gödel's incompleteness theorems.

While mountaineers aim at tops of mountains, some scientists have sought the bottom of temperature scale with frequent surprising wonders at different scales. This article takes you through these scientists' journey!

Differential calculus is one of the most important concept of mathematics for science and engineering. This article focuses on its fundamental meaning.

How to better understand Poker and card games in general? Bayesian games provide the right mathematical model just for that! These correspond to games with incomplete information and include probabilistic reasonings.

Darwin's theory of evolution is one of the greatest of all time. It's also one of the most controversial. This article presents the most fundamental concepts of the theory. We'll also provide results of modern science and discuss to which extend to they confirm Darwin's postulates.

Beauty is extremely hard to define. Yet, physicists and artists seem to agree on an important feature of beauty, created by mathematicians: Symmetries. This article aims at introducing the beauty and the concepts on symmetries, from the basic geometrical symmetries to the more abstract fundamental automorphisms.

Einstein's theory of relativity is the best-known breakthrough of the History of science. The reason for that isn't only the accuracy of the theory, but also and mainly its beauty. As Einstein once said: "Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone." This is what the article aims at showing Einstein's simple ideas of special relativity and their beauty.

Fourier analysis is a fundamental theory in mathematics with an impressive field of applications. From creating radio to hearing sounds, this concept is a translation between two mathematical worlds: Signals and Frequencies. Here is an introduction to the theory.

As more and more complex problems are dealt with in our societies, developing models such as multi-criteria analysis is crucial to better understand these problems. MACBETH is a state-of-the-art method to do just that. Its functioning is described in this article.

We live in a very complex universe, and as far as one can remember, men have always wanted to know everything about it: where do we come from? what is our world made of? To answer these questions, sciences were developped, and among them, theoretical physics: using mathematics to describe certain aspects of Nature. From […]

Iceland is at an amazingly active volcanic location, yielding extreme geological phenomenons. Iceland is therefore a giant laboratory for geologists. It's also an awesome place for visitors, especially hikers. This article introduces some of Iceland's wonders.

INTRODUCTION What is HDI? A chemical? A Peugeot Citroën engine type? A video connector? Well, it might be. But here – and as in most of economics, sociology, international relations or politics references since 1990 – HDI stands for Human Development Index. Easyyyy, I know what it is. “Human” – I get it – that’s […]

This article gives an overview of recent developments in game theory, including evolutionary game theory, extensive form games, mechanism design, bayesian games and mean field games.

Introduced by the two renowned theoretical physicists Stephen Hawking and Leonard Mlodinov in their book The Grand Design in 2010, model-dependent realism is a new controversial understanding of the universe. Based on solid logical reasonings and recent developments in physics, this concept may well be an incredible breakthrough for philosophy and science, as well as metaphysics.

Probabilities have been proven to be a great tool to understand some features of the world, such as what can happen in a dice game. Applied to programming, it has enabled plenty of amazing algorithms. In this article, we discuss its application to the primality test as well as to face detection. We'll also deal with quantum computers, as well as fundamental computer science open problems P=BPP and NP=BQP.

In the movie "A Beautiful Mind", the character is John Nash. He is one of the founders of a large and important field of applied mathematics called game theory. Game Theory is the study of human interactions. Its fallouts in economy, politics or biology are countless. This article gives you an introduction to the concepts of this amazing way of thinking.

Evolutionary Game Theory is a relatively recent branch of game theory which studies the dynamics of games. Originally used to describe populations of species in biology, and more particularly, the consequences of their interactions to the evolution of their populations, this field now produces interesting results for economic and environmental modelings.

The Internet is an unavoidable component of today's life, and will only become more and more important in the future. In this article, we"ll have an overview of its development in terms of coding languages. This article explains how webpages actually work. In particular, we'll discuss HTML, CSS, PHP, WordPress, MySQL, Javascript, XML and JSON, as well as their competitors.