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