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

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 Beauty of Ellipses, Parabolas and Hyperbolas

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 Amazing Physics of Water in Trees

As explained by Derek Muller on Veritasium, the flow of water in trees involves complex physical phenomena including pressure, osmosis, negative pressure, capillarity and evapotranspiration. What seems simple will blow your mind!

## Shannon’s Information Theory

Claude Shannon may be considered one of the most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Yet, unfortunately, he is virtually unknown to the public. This article is a tribute to him. And the best way I’ve found is to explain some of the brilliant ideas he had.

## Entropy and the Second Law of Thermodynamics

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!

## Primal and Dual Simplex Methods

The simplex method is one of the major algorithm of the 20th century, as it enables the resolution of linear problems with millions of variables. An intuitive approach is given. But that’s not all. We present an important variant called the dual simplex. Finally, we’ll explain its main default, that is, when facing degeneracy.

## Duality in Linear Programming

Duality in linear programming yields plenty of amazing results that help understand and improve algorithms of resolution. This article shows the construction of the dual and its interpretation, as well as major results. In particular, matching of primal and dual bases will be dealt, before presenting the issue of degeneracy and its dual interpretation.

## The Addictive Mathematics of the 2048 Tile Game

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!

## The Revolutionary Galois Theory

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!

## The Tortuous Geometry of the Flat Torus

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!

### All Other Articles…

Euler’s Formula and the Utilities Problem

Spacetime of General Relativity

Type Theory: A Modern Computable Paradigm for Math

Fourier Analysis: Signals and Frequencies

The Harmonious Mathematics of Music

Column Generation and Dantzig-Wolfe Decomposition

Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse

Homotopy Type Theory and Higher Inductive Types

Poincaré Conjecture and Homotopy

Santa Routing and Heuristics in Operations Research

A Model of Football Games

Bayesian Games: Math Models for Poker

Differential Calculus and the Geometry of Derivatives

P versus NP: A Crucial Open Problem

Euclidean Geometry and Navigation

Imaginary and Complex Numbers

Logarithms and Age Counting

Linear Algebra and Higher Dimensions

Advanced Game Theory Overview

Mechanism Design and the Revelation Principle

Self-Reference, Math Foundations and Gödel’s Incompleteness

Hypothesis Test with Statistics: Get it Right!

From Britain’s coast to Julia set: an introduction to fractals

Dynamics, Chaos, Fractals (pt 1)

Symmetries and Group Theory

The Massive Puzzles of Gravity

Univalent Foundations of Mathematics

The Magic of Algebra

The Limitless Vertigo of Cantor’s Infinite

Geometry and General Relativity

Temperature Misconception: Heat is Not How it Feels

Multicriteria with MACBETH

Geological Wonders of Iceland

The Most Troubling Experiments on Human Behavior

The Frontier of Cold: The Quest for Absolute Zero

The Magic of Analysis

From Divide and Conquer to Parallelization

Does God play dice?

Glaciers: Retreat, Moraines, Valleys, Fjörds

Dual Variable Stabilization

What Makes a Published Result Believable?

The New Big Fish Called Mean-Field Game Theory

Cryptography and Number Theory

Game Theory and the Nash Equilibrium

The Essence of Quantum Mechanics

The Surprising Flavor of Infinite Series

Non-Euclidean Geometry and Map-Making

The Triangle of Power

Optimization by Integer Programming

The Cubic Ball of the 2014 FIFA World Cup

Optimization by Linear Programming

Numbers and Constructibility

Construction and Definition of Numbers

Topology: from the Basics to Connectedness

The Unlikely Correctness of Newton’s Laws

HDI: a measure of human capabilities

Proof by Mathematical Induction

Marriage Assignment Problem and Variants

Fair Division and Cake-Cutting

Colors: It’s not just about Wavelengths!

Evolutionary Game Theory

Conditional Probabilities: Know what you Learn

A Mathematical Guide to Selling

Model-Dependent Realism

The Secretary/Toilet Problem and Online Optimization

Web Programming: From HTML to AJAX

The Biology Civil War Opposing Kin to Group Selection

High Dynamic Range and Tone Mapping

Colours and Dimensions

Spacetime of Special Relativity

Pluto is NOT (not?) a Planet

The forces of Nature: from Newton to String Theory

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

Space Deformation and Group Representation

Cryptography and Quantum Physics

Dynamics, Chaos, Fractals (pt 2)

Regulation of Electricity Markets

Probabilistic Algorithms, Probably Better

Beauty, the Driving Force of our Quest for Truth

The coach’s dilemma.

Computing Hunger worldwide: the Global Hunger Index (GHI)