# Make it simple. Make it cool.

Science4All is a website of *Quality Popular Science*.

I believe that the greatest challenge in education is to make science and math appealing.

This is why I aim at bringing enthusiasm and excitement to the readers’ learning experience.

The Secretary/Toilet Problem and Online Optimization The Secretary/Toilet Problem and Online Optimization

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 1158

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Harmonious Mathematics of Music The Harmonious Mathematics of Music

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1472

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Limitless Vertigo of Cantor’s Infinite The Limitless Vertigo of Cantor’s Infinite

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1301

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Cryptography and Number Theory Cryptography and Number Theory

By Scott McKinney | **Updated:**2012-12 | **Views**: 4156

Over 300 years ago, a mathematician named Fermat discovered a subtle property about prime numbers. In the 1970’s, three mathematicians at MIT showed that his discovery could be used to formulate a remarkably powerful method for encrypting information to be sent online. The RSA algorithm, as it is known, is used to secure ATM transactions, online business, banking, and even electronic voting. Surprisingly, it’s not too difficult to understand, so let’s see how it works., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

Regulation of Electricity Markets Regulation of Electricity Markets

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1216

Electricity markets are not like any markets. In particular, they cannot be liberalized without regulation. In the article, I list the reasons why this market is specific and I conclude by giving you important features of a good regulation., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Conditional Probabilities: Know what you Learn Conditional Probabilities: Know what you Learn

By Lê Nguyên Hoang | **Updated:**2014-02 | **Views**: 2545

Suppose a man has two children, one of them being a boy. What’s the probability of the other one being a boy too? This complex question has intrigued thinkers for long until mathematics eventually provided a great framework to better understanding of what’s known as conditional probabilities. In this article, we present the ideas through the two-children problem and other fun examples., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Secretary/Toilet Problem and Online Optimization The Secretary/Toilet Problem and Online Optimization

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 1158

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

P versus NP: A Crucial Open Problem P versus NP: A Crucial Open Problem

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 4677

P=NP is probably today’s most crucial open problem. Not only is it a very theoretical question in computer science and mathematics, but it also has major implications to real world. Its resolution could revolutionize the world. This article gives the definition and major results of P=NP., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Magic of Analysis The Magic of Analysis

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 1005

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Shannon’s Information Theory Shannon’s Information Theory

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 12337

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Euler’s Formula and the Utilities Problem Euler’s Formula and the Utilities Problem

By Lê Nguyên Hoang | **Updated:**2014-06 | **Views**: 6349

I was a kid when I was first introduced to the deceptively simple utilities problem. It’s only lately that I’ve discovered its solution! And it’s an amazing one! Indeed, it provides a wonderful insight into some fundamental mathematics, including Euler’s formula! This is nothing less than the gateway to the wonderful world of algebraic topology!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Game Theory and the Nash Equilibrium Game Theory and the Nash Equilibrium

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 7572

In the movie “A Beautiful Mind”, the character is John Nash. He is one of the founders of a large and important field of applied mathematics called game theory. Game Theory is the study of human interactions. Its fallouts in economy, politics or biology are countless. This article gives you an introduction to the concepts of this amazing way of thinking., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Topology: from the Basics to Connectedness Topology: from the Basics to Connectedness

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 2910

Topology was my favorite course in pure maths. I love it because it’s a powerful abstract theory to describe intuitive and visual ideas about space. This article gives you an introduction to this amazing field. We’ll introduce graph topology, metric spaces, continuity and connectedness., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Addictive Mathematics of the 2048 Tile Game The Addictive Mathematics of the 2048 Tile Game

By Lê Nguyên Hoang | **Updated:**2014-06 | **Views**: 6945

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Entropy and the Second Law of Thermodynamics Entropy and the Second Law of Thermodynamics

By Lê Nguyên Hoang | **Updated:**2014-11 | **Views**: 18062

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Euclidean Geometry and Navigation Euclidean Geometry and Navigation

By Scott McKinney | **Updated:**2013-01 | **Views**: 1731

This is the first of a series of three posts. In this post we’ll see how the Greeks developed a system of geometry – literally “Earth measure” – to assist with planetary navigation. We then will see why their assumption that the Earth is flat means that Euclidean geometry is insufficient for studying the Earth. The Earth’s spherical surface looks flat from our perspective, but is actually qualitatively different from a flat surface. In the ensuing posts, we’ll see why this implies that it is impossible to make a perfectly accurate map of the Earth, and build on this idea to get a glimpse into Einstein’s revolutionary theories regarding the geometry of the space-time universe., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

The Surprising Flavor of Infinite Series The Surprising Flavor of Infinite Series

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 5280

1+2+4+8+16+…=-1, as proven by Henry Reich on Minute Physics! Now, as a mathematician, I must say that his proof is far from being rigorous. In fact, anyone familiar with the surprising flavor of infinite series should not find it convincing. Surprisingly though, his proof can be rigorously and naturally justified! Find out how!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Thrilling Physics of Resonance The Thrilling Physics of Resonance

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 8647

From the destruction of bridges and buildings to the foundations of electromagnetism and quantum mechanics, through their uses by radios or our ears,resonance is a counter-intuitive underlying phenomenon which shapes our reality. But amazingly, they can be made amazingly visual by playing with head massagers!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Biology Civil War Opposing Kin to Group Selection The Biology Civil War Opposing Kin to Group Selection

By Lê Nguyên Hoang | **Updated:**2014-03 | **Views**: 1630

In 2010, a controversial article published in Nature violently criticized the last 40 years of developments in evolutionary biology, triggering an ongoing war within the scientific community. This article explains the essence of the controversy!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

A Model of Football Games A Model of Football Games

By Lê Nguyên Hoang | **Updated:**2014-10 | **Views**: 3885

Back then, I simulated the outcome of the 2006 World Cup, based on a modelling of football games. This article explains this model and presents its results., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Santa Routing and Heuristics in Operations Research Santa Routing and Heuristics in Operations Research

By Lê Nguyên Hoang | **Updated:**2014-05 | **Views**: 4105

Designing routes to visit customers has become one of applied mathematicians’ favorite optimization problems, as companies offer millions to solve them! This article discusses the clever technics they have come up with, and use them to help Santa deliver toys to kids all over the world!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Multicriteria with MACBETH Multicriteria with MACBETH

By Lê Nguyên Hoang | **Updated:**2013-07 | **Views**: 1539

As more and more complex problems are dealt with in our societies, developing models such as multi-criteria analysis is crucial to better understand these problems. MACBETH is a state-of-the-art method to do just that. Its functioning is described in this article., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

From Divide and Conquer to Parallelization From Divide and Conquer to Parallelization

By Lê Nguyên Hoang | **Updated:**2013-04 | **Views**: 1265

Divide and conquer is a extremely powerful concept that is being used a lot in computer science, and that can also be applied in real life. We present its application to sorting algorithms. Then we’ll talk about a major fundamental open mathematical problem, called P=NC., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Fourier Analysis: Signals and Frequencies Fourier Analysis: Signals and Frequencies

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 4129

Fourier analysis is a fundamental theory in mathematics with an impressive field of applications. From creating radio to hearing sounds, this concept is a translation between two mathematical worlds: Signals and Frequencies. Here is an introduction to the theory., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Computing Hunger worldwide: the Global Hunger Index (GHI) Computing Hunger worldwide: the Global Hunger Index (GHI)

By Estève Giraud | **Updated:**2014-04 | **Views**: 383

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. , by Estève Giraud Estève Giraud

I hold a MSc in Management from Toulouse Business School (France). I currently work as a MRes/PhD student in University Pompeu Fabra (Barcelona, Spain) and research on ethical mindsets in business.

Dynamics, Chaos, Fractals (pt 2) Dynamics, Chaos, Fractals (pt 2)

By Scott McKinney | **Updated:**2013-04 | **Views**: 955

Dynamical systems such as a system of 3 planetary bodies can exhibit surprisingly complicated behavior. If the initial state of the system is slightly varied, the resulting system behaves in a radically different manner. This “sensitivity to initial conditions” is a key element of what’s become (perhaps disproportionately) well-known as chaos. Using the mathematical notion of iterative systems, we can model such systems and understand how chaos arises out of deceptively simple foundations., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

Non-Euclidean Geometry and Map-Making Non-Euclidean Geometry and Map-Making

By Scott McKinney | **Updated:**2013-01 | **Views**: 2113

Geometry literally means “the measurement of the Earth”, and more generally means the study of measurements of different kinds of space. Geometry on a flat surface, and geometry on the surface of a sphere, for example, are fundamentally different. A consequence of this disparity is the fact that it is impossible to create a perfectly accurate (flat) map of the Earth’s (spherical) surface. Every map of the Earth necessarily has distortions. In this post we look at a few different methods of map-making and evaluate their distortions as well as their respective advantages., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

Univalent Foundations of Mathematics Univalent Foundations of Mathematics

By Lê Nguyên Hoang | **Updated:**2015-01 | **Prerequisites: **Type Theory: A Modern Computable Paradigm for Math, Homotopy Type Theory and Higher Inductive Types | **Views**: 1735

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Self-Reference, Math Foundations and Gödel’s Incompleteness Self-Reference, Math Foundations and Gödel’s Incompleteness

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2525

Although highly appreciated by artists, self-reference has been a nightmare for mathematicians. It took one of the greatest, Kurt Gödel, to provide a better understanding of it. This article deals with paradoxes, recursion, fractals and Gödel’s incompleteness theorems., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Linear Algebra and Higher Dimensions Linear Algebra and Higher Dimensions

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2630

Linear algebra is a one of the most useful pieces of mathematics and the gateway to higher dimensions. Using Barney Stinson’s crazy-hot scale, we introduce its key concepts., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Mechanism Design and the Revelation Principle Mechanism Design and the Revelation Principle

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2379

Whenever you need to make a group of people interact, you are designing a mechanism. If you want to achieve a good interaction, you need to make sure your mechanism is well designed. In this article, I’ll show you main features of mechanisms through various examples. I’ll also talk about a great mathematical tool for mechanism design: the revelation principle., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The forces of Nature: from Newton to String Theory The forces of Nature: from Newton to String Theory

By Thibault_Lehouillier | **Updated:**2012-10 | **Views**: 1199

, by Thibault_Lehouillier Thibault_Lehouillier

PhD candidate at Ecole Polytechnique of Montréal (Canada)

Engineer of the ENSIMAG (France)

Homotopy Type Theory and Higher Inductive Types Homotopy Type Theory and Higher Inductive Types

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 1258

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Cubic Ball of the 2014 FIFA World Cup The Cubic Ball of the 2014 FIFA World Cup

By Lê Nguyên Hoang | **Updated:**2014-07 | **Views**: 3566

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Hypothesis Test with Statistics: Get it Right! Hypothesis Test with Statistics: Get it Right!

By Lê Nguyên Hoang | **Updated:**2013-11 | **Views**: 3220

Statistician Johnson recently claimed that up to 25% of published scientific experimental results were just wrong! To see why, let’s get to the bottom of the scientific method! And it’s probably more complicated than you think. In this article, we apply it rigorously to “prove” $\pi=3$. This will highlight the actually mechanism of the scientific method, its limits, and how much messages of experiments are often deformed!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

A Mathematical Guide to Selling A Mathematical Guide to Selling

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1352

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Magic of Algebra The Magic of Algebra

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 1886

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Duality in Linear Programming Duality in Linear Programming

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Optimization by Linear Programming, Linear Algebra and Higher Dimensions | **Views**: 8703

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Space Deformation and Group Representation Space Deformation and Group Representation

By Lê Nguyên Hoang | **Updated:**2014-03 | **Views**: 1486

All along the 20th century, pure algebraists have dug deep into the fundamental structures of mathematics. In this extremely abstract effort, they were greatly help by the possibility of representing these structures by space deformations, which could then be understood much better. This has led to breakthroughs, including the proof of Fermat’s las theorem. This article introduces the ideas of group representations., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Proof by Mathematical Induction Proof by Mathematical Induction

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 4338

This article explores the potency of proofs by induction with 4 different stunning puzzles, from a lock puzzle and a lion issue, to the monk problem and the pencil conundrum!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Column Generation and Dantzig-Wolfe Decomposition Column Generation and Dantzig-Wolfe Decomposition

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Linear Algebra and Higher Dimensions, Optimization by Linear Programming | **Views**: 2865

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., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The New Big Fish Called Mean-Field Game Theory The New Big Fish Called Mean-Field Game Theory

By Lê Nguyên Hoang | **Updated:**2014-06 | **Views**: 5195

In recent years, at the interface of game theory, control theory and statistical mechanics, a new baby of applied mathematics was given birth. Now named mean-field game theory, this new model represents a new active field of research with a huge range of applications! This is mathematics in the making!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Geological Wonders of Iceland Geological Wonders of Iceland

By Lê Nguyên Hoang | **Updated:**2013-06 | **Views**: 1061

Iceland is at an amazingly active volcanic location, yielding extreme geological phenomenons. Iceland is therefore a giant laboratory for geologists. It’s also an awesome place for visitors, especially hikers. This article introduces some of Iceland’s wonders., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Dual Variable Stabilization Dual Variable Stabilization

By Lê Nguyên Hoang | **Updated:**2012-07 | **Prerequisites: **Optimization by Linear Programming, Duality in Linear Programming, Primal and Dual Simplex Methods | **Views**: 375

Simplex methods face issues in case of degeneracy. The dual variable stabilization is a very recent state-of-the-art way to deal with degeneracy. An intuitive understanding is given in this article., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Advanced Game Theory Overview Advanced Game Theory Overview

By Lê Nguyên Hoang | **Updated:**2015-01 | **Prerequisites: **Game Theory and the Nash Equilibrium | **Views**: 3533

This article gives an overview of recent developments in game theory, including evolutionary game theory, extensive form games, mechanism design, bayesian games and mean field games., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Marriage Assignment Problem and Variants Marriage Assignment Problem and Variants

By Lê Nguyên Hoang | **Updated:**2014-01 | **Views**: 3234

Marriage problems consist in matching boys and girls. They are a very interesting class of problems that include assignment problems, which have a very large range of applications. Additional results have been found for variants which include the introduction of boys and girls’ preferences, and cases where people cannot be categorized into two groups., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Cryptography and Quantum Physics Cryptography and Quantum Physics

By Scott McKinney | **Updated:**2012-12 | **Views**: 1486

Recent discoveries in the branch of physics known as quantum mechanics have powerful applications in the field of network security – they have the potential to break forms of internet security based on mathematics such as the RSA algorithm, and also present new ways to safely send information. In this article we’ll see how a physics-based method can be used to secure online information., by Scott McKinney Scott McKinney

Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.

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

By Thomas C | **Updated:**2013-05 | **Views**: 1959

, by Thomas C Thomas C

I studied applied mathematics at Ecole Polytechnique and I am currently working as a consultant in information and communications technologies.

The Revolutionary Galois Theory The Revolutionary Galois Theory

By Lê Nguyên Hoang | **Updated:**2014-12 | **Prerequisites: **Linear Algebra and Higher Dimensions, Imaginary and Complex Numbers, Symmetries and Group Theory | **Views**: 9960

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Spacetime of Special Relativity Spacetime of Special Relativity

By Lê Nguyên Hoang | **Updated:**2014-03 | **Views**: 1913

Einstein’s theory of relativity is the best-known breakthrough of the History of science. The reason for that isn’t only the accuracy of the theory, but also and mainly its beauty. As Einstein once said: “Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone.” This is what the article aims at showing Einstein’s simple ideas of special relativity and their beauty., by Lê Nguyên Hoang Lê Nguyên Hoang

Math and science popularizer. Postdoc at MIT in Applied Maths.

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

## Here’s what they say about Science4All…

Looking for substance behind popular science? This is a great resource! http://t.co/jE1aHvac

— SciAfterSchool (@SciAfterSchool) January 28, 2013

Fair division in Game Theory modelled using Friends. pretty awesome @helpatz http://t.co/yVCCS887

— Emma Alexander (@emmaaaaa8) November 27, 2012

Lê Nguyên Hoang (el promotor science4all) es uno de los jóvenes matemáticos más brillantes de la actualidad (y una gran persona)

— IMUVA (@IMUVA_) March 7, 2013

Really nice article with great visuals covering Stable Marriage algorithms and variants. http://t.co/rSHnDKCyxa #GraphNerds

— David W. Allen (@DataRiot) March 24, 2013

#Marriage Problem and Variants: http://t.co/XLMGMcIO98 #FF @science__4__all (he's a #genius)

— Berlanda Mauro (@mauroberlanda) April 12, 2013

This post almost makes me want to teach science again http://t.co/d6csaIRgra Almost.

— Fawn Nguyen (@fawnpnguyen) April 18, 2013

Great article on tree physics by @science__4__all: http://t.co/uiftTXyh3G

— Derek Muller (@veritasium) April 18, 2013

This really is a great article: Hypothesis Testing http://t.co/KVVKayG84K Well done @science__4__all (cc @DrTonyPadilla @numberphile)

— James Grime (@jamesgrime) May 17, 2013

AMAZING! Indeed I was talking about http://t.co/DqHJ4kkcxI articles. @science__4__all More scientists should contribute – @benstill !!!???

— Jennifer Crouch (@JenniferCrouch) May 30, 2013

why do I end up reading poincare conjecture? http://t.co/R2hdy1Xgh8 :).

— Avivah Yamani (@ivie97) June 5, 2013

So good. Love how Le takes the Euler formula (and utilities problem) and kicks it up a bunch of notches. http://t.co/KVoxCjvsQI

— Fawn Nguyen (@fawnpnguyen) June 20, 2013

Masterful exposition of topology made accessible: Euler's Formula and the Utilities Problem http://t.co/uL4Aw9VAnC HT @fawnpnguyen

— Joshua Bowman (@Thalesdisciple) June 21, 2013

Enjoy #math with @republicofmath @jamestanton @maanow @MrHonner @wilderlab @earlsamuelson @WWMGT @daveinstpaul @science__4__all #ff

— Alexander Bogomolny (@CutTheKnotMath) June 21, 2013

I would like to do a #ff for @science__4__all who are doing an excellent job with their maths articles http://t.co/R7G1EhMcg7

— James Grime (@jamesgrime) June 21, 2013

Just RIDICULOUS HOW GOOD this is, "The Beauty of Ellipses, Parabolas and Hyperbolas" by @science__4__all
http://t.co/eBCazmcxVi

— Fawn Nguyen (@fawnpnguyen) July 22, 2013

Bravo! Lê Nguyên Hoang Founder Science4All Your Papers are Brilliant!
http://t.co/AvCQPZcwPB What Does this Mean!

— David Valin (@gbdavid1) July 22, 2013

@science__4__all Your document it's all beauty! Thanks for sharing it!

— Margarita Parra (@BMPM1) September 9, 2013

Shannon's Information Theory: lucid, illustrated thorough introduction, keep it as a reference, share it as a gift! http://t.co/tqR8xKqDBA

— Arthur Doohan (@artied) September 29, 2013

#shannon <3<3<3 #enmettrepartout <3<3<3 #dansmaface “@MathUpdate: Shannon's Information Theory http://t.co/XdLEL7JUj7”

— Dr. Bisounours (@BisounoursJp) September 29, 2013

Muy bueno el blog Science4all Le Nguyen Hoang http://t.co/3VfpY7QZ7o esfuerzo para divulgar conceptos de forma sencilla y divertida

— Luis A. Núñez (@nunezluis) October 27, 2013

Always a great blog "@science__4__all: Discover irrational, constructible, transcendental and computable numbers! http://t.co/BRBIf5PrDM"

— James Grime (@jamesgrime) November 7, 2013

Simple, well-explained, well-written article about evolution of science philosophy, from Ptolemy to Stephen Hawking http://t.co/Njf3auyAtP

— Cloud-Big Data-EDD (@Ediscoverycloud) November 12, 2013

How can one not love #math? RT @centerofmath The Beauty of Ellipses, Parabolas and Hyperbolas – http://t.co/SSmmLMhj1B #math

— MathDaily (@MathDaily) November 28, 2013

Barney Stinson's theories to explain linear algebra. It's legen(wait-for-it)dary and awesome.
By @science__4__all
http://t.co/X9SVtDFyHr

— Helene Sarah Becotte (@hbecotte) November 28, 2013

Not just the Traveling Santa Problem. See a discussion of SC's route as a vehicle routing problem http://t.co/iBRQqsDCJS

— AmericanMathSociety (@amermathsoc) December 23, 2013

Wishing everyone a geeky mary christmas. http://t.co/TaAZQ2ZI2P

— InTheNext10Years (@inthenext10year) December 25, 2013

This is a fantastic explanation of Quantum Mechanics http://t.co/FZl9OFQqaH

— Nick Gotch (@pszNicx) December 30, 2013

Wow, really good overview! (The Essence of Quantum Mechanics – S4A) http://t.co/rtr8LeRIXn

— Xavi (@nymiro) December 30, 2013

For no reason, do you know @science__4__all http://t.co/R7G1EhMcg7 They're very good.

— James Grime (@jamesgrime) January 10, 2014

Looks cool! RT @science__4__all: NEW ARTICLE!!! Get an intimate feel of The Greatest Feat of Mathematics: http://t.co/qsb5lAA9IP

— Danica McKellar (@danicamckellar) February 21, 2014

@science__4__all I really like your web site! Great work…I am telling any friends interested in science and mathematics about it.

— Joe Dayton ☮ (@JoeDaytonMN) February 22, 2014

"The Most Amazing Thing About Trees" is, frankly, amazing. http://t.co/amaHMkwSX1 HT: @highlyanne

— Adam Mandelman (@amandelman) February 25, 2014

This is so damn cool! "The Tortuous Geometry of the Flat Torus" http://t.co/gybXXnZP2z – last image = new wallpaper!

— LucasVB (@LucasVB) March 16, 2014

Incredible cool way to visualize imaginary numbers: http://t.co/ZPEDz5yN6e #math #mathchat #mathtip #mathed #edchat #edtech

— Rimwe (@RimweLLC) April 27, 2014

This is the first truly convincing argument I've seen that the 131072 tile is the largest possible for the #2048game. http://t.co/ez0JCxjbTs

— Dave Radcliffe (@daveinstpaul) June 20, 2014

To all students of data, this is a must-read > Shannon’s Information Theory: http://t.co/3fHla3HWl0 by @science__4__all #DataScience

— Kirk Borne (@KirkDBorne) July 8, 2014

http://t.co/YNd1CFXPnd Follow
Lê Nguyên Hoang @science__4__all to read and contribute to "popular" science #Interesting

— anbudan BALA|எஅ.பாலா (@AmmU_MaanU) July 13, 2014

I enjoyed this engaging read by LN Hoang about some #Maths research: The New Big Fish Called Mean-Field Game Theory: http://t.co/OiemfWnT7y

— Anita Hall (@ani2tall) September 24, 2014

@science__4__all Thank you for your articles. Just amazing! Wonder how you compile and relate so many things…

— Prasad Gokhale (@Prasad_Gokhale) September 28, 2014

This is GREAT! Even non-math people will enjoy this. The Tortuous Geometry of the Flat Torus: http://t.co/9eZamXiB5o

— Kim Langen (@KimLangen) October 2, 2014

arguably #ComputerScience owes more to #Shannon than anyone else. An excellent article on Shannon's Info Theory: http://t.co/u5AI6qjbKO

— Numan Sheikh (@numansheikh) October 13, 2014

Good one for interested ones, Puzzles, science, methodologies and manymore: http://t.co/NN31T9JNMe

— Pankaj Saraf (@saraf_pankaj) December 21, 2014

Santa's optimization for Christmas visits! A wonderful explanation to Vehicle Routing Problem. http://t.co/pBfq7wW0aP #OperationsResearch

— Vandana Narasimhan (@vandy_ie) December 25, 2014

@science__4__all Great! Primary colours, wavelengths, cones, vectors and spaces, matrices,…this article is really multidimensional.

— Prasad Gokhale (@Prasad_Gokhale) January 10, 2015

@science__4__all hey, you have a great blog! I'm enjoying reading through your articles

— Cam Davidson-Pilon (@Cmrn_DP) January 25, 2015

Another amazing read! #math http://t.co/04oImebBaT

— Cassie Lynn Holmes (@CassiHolmes) March 1, 2015

실시간으로 결정을 해야하고 한번 결정하면 되돌릴 수 없을때, 수학으로 전략 만들기
“@MathbloggingAll:The Secretary/Toilet Problem and Online Optimization http://t.co/G4nMBhTdIG”

— 상일 (@sioum) April 2, 2015