## The Tortuous Geometry of the Flat Torus

March 09, 2014Article16101 vuesEdit
Take a square sheet of paper. Can you glue opposite sides without ever folding the paper? This is a conundrum that many of the greatest modern mathematicians, like Gauss, Riemann, and Mandelbrot, couldn't figure out. While John Nash did answer yes, he couldn't say how. After 160 years of research, Vincent Borrelli and his collaborators have finally provided a revolutionary and breathtaking example of a bending of a square sheet of paper! And it is spectacularly beautiful!

## The Thrilling Physics of Resonance

March 03, 2014Article15797 vuesEdit
From the destruction of bridges and buildings to the foundations of electromagnetism and quantum mechanics, through their uses by radios or our ears,resonance is a counter-intuitive underlying phenomenon which shapes our reality. But amazingly, they can be made amazingly visual by playing with head massagers!

## The Most Beautiful Equation of Math: Euler’s Identity

February 18, 2014Article78392 vuesEdit
In 1988, Euler's identity was elected most beautiful theorem of mathematics. It has been widely taught worldwide. But have you ever stopped to really sense the meaning of this incredible formula? This article does.

## The New Big Fish Called Mean-Field Game Theory

February 05, 2014Article12827 vuesEdit
In recent years, at the interface of game theory, control theory and statistical mechanics, a new baby of applied mathematics was given birth. Now named mean-field game theory, this new model represents a new active field of research with a huge range of applications! This is mathematics in the making!

## Pluto is NOT (not?) a Planet

January 29, 2014Article2919 vuesEdit
In 2006, Pluto was officially demoted from its planetary status. When we dig a little bit, this isn't much of the surprise. What's more interesting is rather why it ever was regarded as a planet, as the History of Pluto highlights a magic enterprise that science is!

## The Most Troubling Experiments on Human Behavior

January 13, 2014Article2358 vuesEdit
We all intuitively think of ourselves as independent creatures with strong free will. However, many disturbing experiments about fashion, conformity, obedience, environment, choice and opinions have been troubling this idea we make of ourselves. These ought to be lessons of humility for all of us.

## The Revolutionary Galois Theory

January 05, 2014Article18163 vuesEdit
In 1832, Évariste Galois died. He was 20. The night before his death, he wrote a legendary letter to his friend, in which he claims to have found a mathematical treasure! Sadly, this treasure had long been buried in total indifference! It took nearly a century to rediscover it! Since then, Galois' legacy has become some of the finest pure mathematics, which represents a hugely active field of research today with crucial applications to cryptography. Galois' work is now known as Galois theory. In essence, it unveils the hidden symmetries of numbers!

## Santa Routing and Heuristics in Operations Research

December 19, 2013Article7112 vuesEdit
Designing routes to visit customers has become one of applied mathematicians' favorite optimization problems, as companies offer millions to solve them! This article discusses the clever technics they have come up with, and use them to help Santa deliver toys to kids all over the world!

## The Biology Civil War Opposing Kin to Group Selection

December 09, 2013Article3651 vuesEdit
In 2010, a controversial article published in Nature violently criticized the last 40 years of developments in evolutionary biology, triggering an ongoing war within the scientific community. This article explains the essence of the controversy!

## Linear Algebra and Higher Dimensions

November 27, 2013Article5538 vuesEdit
Linear algebra is a one of the most useful pieces of mathematics and the gateway to higher dimensions. Using Barney Stinson's crazy-hot scale, we introduce its key concepts.

## Numbers and Constructibility

November 05, 2013Article6829 vuesEdit
Last summer, I got to discover Morellet's artwork on inclined grids. Amazingly, this artwork is a display of the irrationality of $\sqrt{2}$! It's also a strong argument for the existence of this number. In this article, after discussing that, I take readers further by discussing what numbers can be constructed geometrically, algebraically, analytically or set theoretically using the power of mathematics!

## Entropy and the Second Law of Thermodynamics

October 15, 2013Article23492 vuesEdit
The second law of thermodynamics is my favorite law in physics, mainly because of the troubling puzzles it raises! Indeed, what your professors may have forgotten to tell you is that this law connects today's world to its first instant, the Big Bang! Find out why!

## Logarithms and Age Counting

October 09, 2013Article5662 vuesEdit
Amusingly, the age difference between a 45-year-old man and a 25-year-old woman doesn't seem as big as the age difference between them 20 years earlier, when the woman was a little 5-year-old girl. This remark was the insight the late science popularizer Albert Jacquart liked to give to his readers to explain logarithms. This article pays tribute to the great scientist by introducing age difference as he liked to tell it.

## Optimization by Integer Programming

September 24, 2013Article7449 vuesEdit
Integer programming is arguably the greatest achievement of applied mathematics. Half of the time, it's what's used to solve real-world problems!

## Imaginary and Complex Numbers

August 29, 2013Article6129 vuesEdit
My first reaction to imaginary numbers was... What the hell is that? Even now, I have trouble getting my head around these mathematical objects. Fortunately, I have a secret weapon: Geometry! This article proposes constructing complex numbers with a very geometrical and intuitive approach, which is probably very different from what you've learned (or will learn).

## Beauty, the Driving Force of our Quest for Truth

August 19, 2013Article1441 vuesEdit
According to Matthew Colless, the most important aspect of science is beauty. Not only is it what inspires scientists and their quests, I'd even claim that it's also the compass that guide them in their quests, in a deeper and more surprising way that one can imagine!

## High Dynamic Range and Tone Mapping

August 05, 2013Article3493 vuesEdit
Our eyes are amazing! Even today's cameras are nowhere near competing with them. However, the recent development of high dynamic range (HDR) and tone mapping technologies creates new possibilities to get images nearly as awesome as what our eyes really see!

## The Beauty of Ellipses, Parabolas and Hyperbolas

July 22, 2013Article51226 vuesEdit
The conic sections, that is, ellipses, parabolas and hyperbolas, are too often presented analytically. Yet, their amazing beauty is actually their spectacular geometry, as well as their omnipresence! This article presents plenty of illustrative descriptions of their uncountable applications!

## The Surprising Flavor of Infinite Series

July 01, 2013Article9606 vuesEdit
1+2+4+8+16+...=-1, as proven by Henry Reich on Minute Physics! Now, as a mathematician, I must say that his proof is far from being rigorous. In fact, anyone familiar with the surprising flavor of infinite series should not find it convincing. Surprisingly though, his proof can be rigorously and naturally justified! Find out how!

## Euler’s Formula and the Utilities Problem

June 20, 2013Article13103 vuesEdit
I was a kid when I was first introduced to the deceptively simple utilities problem. It's only lately that I've discovered its solution! And it's an amazing one! Indeed, it provides a wonderful insight into some fundamental mathematics, including Euler's formula! This is nothing less than the gateway to the wonderful world of algebraic topology!