## 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

The New Big Fish Called Mean-Field Game Theory

Type Theory: A Modern Computable Paradigm for Math

Fourier Analysis: Signals and Frequencies

The Surprising Flavor of Infinite Series

Column Generation and Dantzig-Wolfe Decomposition

Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse

Optimization by Integer Programming

Poincaré Conjecture and Homotopy

Optimization by Linear Programming

A Model of Football Games

Bayesian Games: Math Models for Poker

P versus NP: A Crucial Open Problem

Topology: from the Basics to Connectedness

HDI: a measure of human capabilities

Euclidean Geometry and Navigation

Marriage Assignment Problem and Variants

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!

A Mathematical Guide to Selling

Web Programming: From HTML to AJAX

Univalent Foundations of Mathematics

The Massive Puzzles of Gravity

Symmetries and Group Theory

The Magic of Algebra

Spacetime of Special Relativity

Geometry and General Relativity

The forces of Nature: from Newton to String Theory

Multicriteria with MACBETH

Space Deformation and Group Representation

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

The Frontier of Cold: The Quest for Absolute Zero

Regulation of Electricity Markets

From Divide and Conquer to Parallelization

Probabilistic Algorithms, Probably Better

Glaciers: Retreat, Moraines, Valleys, Fjörds

Dual Variable Stabilization

What Makes a Published Result Believable?

Spacetime of General Relativity

Cryptography and Number Theory

Game Theory and the Nash Equilibrium

The Essence of Quantum Mechanics

The Harmonious Mathematics of Music

Non-Euclidean Geometry and Map-Making

Homotopy Type Theory and Higher Inductive Types

The Triangle of Power

Santa Routing and Heuristics in Operations Research

The Cubic Ball of the 2014 FIFA World Cup

Numbers and Constructibility

Differential Calculus and the Geometry of Derivatives

Construction and Definition of Numbers

The Unlikely Correctness of Newton’s Laws

Imaginary and Complex Numbers

Proof by Mathematical Induction

Fair Division and Cake-Cutting

Logarithms and Age Counting

Evolutionary Game Theory

Colors: It’s not just about Wavelengths!

Conditional Probabilities: Know what you Learn

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

Model-Dependent Realism

Dynamics, Chaos, Fractals (pt 1)

The Biology Civil War Opposing Kin to Group Selection

The Secretary/Toilet Problem and Online Optimization

High Dynamic Range and Tone Mapping

Colours and Dimensions

The Limitless Vertigo of Cantor’s Infinite

Pluto is NOT (not?) a Planet

Temperature Misconception: Heat is Not How it Feels

Geological Wonders of Iceland

The Most Troubling Experiments on Human Behavior

Cryptography and Quantum Physics

The Magic of Analysis

Dynamics, Chaos, Fractals (pt 2)

Does God play dice?

Beauty, the Driving Force of our Quest for Truth

The coach’s dilemma.

Computing Hunger worldwide: the Global Hunger Index (GHI)