Category Archives: Article

The Triangle of Power

September 18, 2016Article813 vuesEdit
Notations do not matter to the essence of mathematics. But poor notations can be misleading. Notations based on exponents, radicals and logarithms definitely are. They are very distinct, even though they are supposed to describe very similar relations between numbers. The triangle of power is a recently proposed alternative. In short, I am convinced!

Can we measure peace ? The Global Peace Index (GPI)

April 10, 2016Article346 vuesEdit
When you look at these pictures, what do you think about? Each of these pictures is a symbol of peace, and it is likely that this word will pop up in your mind by looking at one of these pictures – at least. That is true… But beside the word itself, I barely see what […]

The Secretary/Toilet Problem and Online Optimization

April 02, 2015Article2311 vuesEdit
A large chunk of applied mathematics has focused on optimizing something with respect to all relevant data. However, in practice, especially in the online world, the data is not available to us, and, yet, we're still expected to make nearly optimal decisions. This problem is exemplified by the famous secretary problem, where a manager needs to decide to hire candidates right after interviews, even though he has not yet met all the candidates. In this article, we review this classic as well as many very recent developments.

The Harmonious Mathematics of Music

February 10, 2015Article2719 vuesEdit
It was when hearing the sounds of hammers that Pythagoras realized the ubiquity of numbers in mathematical harmony. He would go on laying down the mathematical foundations of music, based on octaves, perfect fifths and major thirds. This mathematics of music would then become the favourite playground of all musicians, from Beethoven to Gangnam Style.

The Limitless Vertigo of Cantor’s Infinite

January 29, 2015Article2126 vuesEdit
No one believed him. Not even fellow mathematicians. They thought he was wrong. They thought he was crazy. Even he ended up doubting himself and went crazy. And yet, he had mathematically proved it all. Georg Cantor had figured out how to manipulate the infinite. Even more remarkable, he showed that there were actually several infinities; and some are bigger than others!

A Mathematical Guide to Selling

January 19, 2015Article2696 vuesEdit
How to best sell a good? Should we auction it like in movies? Since the 1960s, economists have addressed this question mathematically and found surprising results. Most notably, in 1981, Nobel prize winner Roger Myerson proved that most auctions you could think of would win you just as much as any basic auction, but that, as well, you could do better using his approach. Since, today, billions of dollars are at play in online auctions, you can imagine how hot a topic it has now become!

Colours and Dimensions

January 08, 2015Article1695 vuesEdit
You've probably learned early on that there are three primary colours. But why three? And why these three? Surprisingly, the answer lies in the beautiful mathematics of linear algebra and (high) dimension spaces!

The Massive Puzzles of Gravity

December 11, 2014Article2698 vuesEdit
This article follows the footsteps of the giants of physics that have moulded our current understanding of gravity. It is a series of brilliant inspirations, usually accompanied by deceiving misconceptions. After all, even today, gravity is still a slippery concept.

The Magic of Analysis

December 05, 2014Article1399 vuesEdit
This article retraces the endless pursuit of the infinite that is at the basis of mathematical analysis. From the first approximations of pi to the shape of our limitless universe, from the essential usefulness of differential equations to the troubles with infinite sums, we present the great ideas of mathematical geniuses all along History.

Temperature Misconception: Heat is Not How it Feels

October 03, 2014Article1851 vuesEdit
In the last FIFA football world cup, many players complain about Manaus' unbearable heat condition. Yet, the thermometer only went up to 30°C (86°F). Why is that? Well, as it turns out, how you feel is not really the outside temperature. This article unveils many of our deep misconceptions about heat.

The Magic of Algebra

September 23, 2014Article2478 vuesEdit
The power of algebra lies in abstraction, and abstraction is basically forgetting. By retracing the History of algebra from its roots to more recent advancements, this article unveils the numerous breakthrough in our understanding of the world, by abusing of the power of forgetting.

The Cubic Ball of the 2014 FIFA World Cup

June 24, 2014Article5121 vuesEdit
I know this sounds crazy. Even stupid. But Adidas did design a cubic ball, called brazuca, for the 2014 World Cup. And, yet, this cubic ball is rounder than any previous ball in football History. How is it possible? This article explains it.

The Addictive Mathematics of the 2048 Tile Game

June 04, 2014Article11677 vuesEdit
2048 is the Internet sensation of the year. This very addictive game has been downloaded hundred of millions of times. Interestingly, this game raises plenty of intriguing mathematical questions. This article unveils some of them!

Column Generation and Dantzig-Wolfe Decomposition

May 24, 2014Article4698 vuesEdit
Column generation and the Dantzig-Wolfe decomposition are powerful tricks which have revolutionized optimization addressed to industrial problems, and generated millions and millions of dollars. My PhD supervisor effectively took great advantage of these tricks and founded companies with it. This article explains the tricks.

The Unlikely Correctness of Newton’s Laws

April 30, 2014Article3657 vuesEdit
Do moving objects exhaust? Does the Moon accelerate? How strong is the gravity pull of the Moon on the Earth compared to that of the Earth on the Moon? While we've all learned Newton's laws of motion, many of us would get several answers of these questions wrong. That's not so surprising, as Newton's laws are deeply counter-intuitive. By stressing their weirdness with Veritasium videos, this article dives into a deep understanding of classical mechanics.

Univalent Foundations of Mathematics

April 21, 2014Article2342 vuesEdit
In an effort to make mathematics more computable, a consortium of today's greatest mathematicians have laid out new foundations. Amazingly, they all lie upon one single axiom, called univalence. The goal of this axiom is to make formal mathematics more similar to informal mathematics. With univalence, our Arabic numbers aren't just like natural numbers; They are natural numbers. Univalence also has unforeseen and mesmerizing consequences.

Computing Hunger worldwide: the Global Hunger Index (GHI)

April 17, 2014Article477 vuesEdit
The Global Hunger Index was first published in 2006 by the International Food Policy Research Institute and the NGO Welthungerhilfe. In 2007, Concern worldwide joined them. Since then, the Index reports every year the evolution of the hunger situation worldwide and focus on a given topic. How is it calculated? And what is hunger? How are we connected ? What can be done? To learn more, read the article below.

Homotopy Type Theory and Higher Inductive Types

April 06, 2014Article2003 vuesEdit
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) circle and sphere.

Type Theory: A Modern Computable Paradigm for Math

March 20, 2014Article8264 vuesEdit
In 2013, three dozens of today's brightest minds have just laid out new foundation of mathematics after a year of collective effort. This new paradigm better fits both informal and computationally-checkable mathematics. There is little doubt that it will fundamentally change our perspective on rigorous knowledge, and it could be that, in a few decades, the book they published turns out to be the bedrock of all mathematics, and, by extension, all human knowledge! Have a primer of this upcoming revolution, with this article on type theory, the theory that the book builds upon!

The Tortuous Geometry of the Flat Torus

March 09, 2014Article10429 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!