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.
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!
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!
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.
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 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!
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 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.
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!
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
Darwin’s Theory of Evolution
Spacetime of General Relativity
Column Generation and Dantzig-Wolfe Decomposition
Type Theory: A Modern Computable Paradigm for Math
The Surprising Flavor of Infinite Series
Non-Euclidean Geometry and Map-Making
The Cubic Ball of the 2014 FIFA World Cup
Construction and Definition of Numbers
Poincaré Conjecture and Homotopy
Logarithms and Age Counting
Homotopy Type Theory and Higher Inductive Types
Santa Routing and Heuristics in Operations Research
Differential Calculus and the Geometry of Derivatives
A Model of Football Games
Linear Algebra and Higher Dimensions
Marriage Assignment Problem and Variants
HDI: a measure of human capabilities
Proof by Mathematical Induction
Fair Division and Cake-Cutting
Evolutionary Game Theory
Symmetries and Group Theory
Conditional Probabilities: Know what you Learn
Colours and Dimensions
Hypothesis Test with Statistics: Get it Right!
The Biology Civil War Opposing Kin to Group Selection
The Massive Puzzles of Gravity
The Limitless Vertigo of Cantor’s Infinite
The Magic of Algebra
Pluto is NOT (not?) a Planet
Can we measure peace ? The Global Peace Index (GPI)
Temperature Misconception: Heat is Not How it Feels
Cryptography and Quantum Physics
The Most Troubling Experiments on Human Behavior
The Frontier of Cold: The Quest for Absolute Zero
Regulation of Electricity Markets
The Magic of Analysis
Beauty, the Driving Force of our Quest for Truth
Glaciers: Retreat, Moraines, Valleys, Fjörds
Dual Variable Stabilization
Computing Hunger worldwide: the Global Hunger Index (GHI)
The New Big Fish Called Mean-Field Game Theory
The Harmonious Mathematics of Music
Fourier Analysis: Signals and Frequencies
Game Theory and the Nash Equilibrium
The Essence of Quantum Mechanics
The Triangle of Power
Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse
Numbers and Constructibility
The Unlikely Correctness of Newton’s Laws
Optimization by Integer Programming
Euclidean Geometry and Navigation
Topology: from the Basics to Connectedness
Bayesian Games: Math Models for Poker
Optimization by Linear Programming
P versus NP: A Crucial Open Problem
Colors: It’s not just about Wavelengths!
Mechanism Design and the Revelation Principle
Imaginary and Complex Numbers
Self-Reference, Math Foundations and Gödel’s Incompleteness
Advanced Game Theory Overview
The Secretary/Toilet Problem and Online Optimization
A Mathematical Guide to Selling
From Britain’s coast to Julia set: an introduction to fractals
Dynamics, Chaos, Fractals (pt 1)
Univalent Foundations of Mathematics
Web Programming: From HTML to AJAX
High Dynamic Range and Tone Mapping
Geometry and General Relativity
Spacetime of Special Relativity
The forces of Nature: from Newton to String Theory
Multicriteria with MACBETH
Space Deformation and Group Representation
Geological Wonders of Iceland
Dynamics, Chaos, Fractals (pt 2)
Probabilistic Algorithms, Probably Better
From Divide and Conquer to Parallelization
Does God play dice?
The coach’s dilemma.
What Makes a Published Result Believable?