#### Welcome to Science4All

My name is Lê and 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.

Science4All is also available in French.

Evolutionary Game Theory Evolutionary Game Theory

By Lê Nguyên Hoang |

Evolutionary Game Theory is a relatively recent branch of game theory which studies the dynamics of games. Originally used to describe populations of species in biology, and more particularly, the consequences of their interactions to the evolution of their populations, this field now produces interesting results for economic and environmental modelings.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 3030Evolutionary Game Theory is a relatively recent branch of game theory which studies the dynamics of games. Originally used to describe populations of species in biology, and more particularly, the consequences of their interactions to the evolution of their populations, this field now produces interesting results for economic and environmental modelings.

Cryptography and Number Theory Cryptography and Number Theory

By Scott McKinney |

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 |

**Updated:**2016-01 |**Views**: 5543Over 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.

Type Theory: A Modern Computable Paradigm for Math Type Theory: A Modern Computable Paradigm for Math

By Lê Nguyên Hoang |

In 2013, three dozens of today’s brightest minds have just laid out new foundation of mathematics after a year of collective effort. This new paradigm better fits both informal and computationally-checkable mathematics. There is little doubt that it will fundamentally change our perspective on rigorous knowledge, and it could be that, in a few decades, the book they published turns out to be the bedrock of all mathematics, and, by extension, all human knowledge! Have a primer of this upcoming revolution, with this article on type theory, the theory that the book builds upon!

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 7694In 2013, three dozens of today’s brightest minds have just laid out new foundation of mathematics after a year of collective effort. This new paradigm better fits both informal and computationally-checkable mathematics. There is little doubt that it will fundamentally change our perspective on rigorous knowledge, and it could be that, in a few decades, the book they published turns out to be the bedrock of all mathematics, and, by extension, all human knowledge! Have a primer of this upcoming revolution, with this article on type theory, the theory that the book builds upon!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 3253Suppose 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.

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

By Lê Nguyên Hoang |

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.

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 39523In 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.

Temperature Misconception: Heat is Not How it Feels Temperature Misconception: Heat is Not How it Feels

By Lê Nguyên Hoang |

In the last FIFA football world cup, many players complain about Manaus’ unbearable heat condition. Yet, the thermometer only went up to 30°C (86°F). Why is that? Well, as it turns out, how you feel is not really the outside temperature. This article unveils many of our deep misconceptions about heat.

By Lê Nguyên Hoang |

**Updated:**2015-12 |**Views**: 1717In the last FIFA football world cup, many players complain about Manaus’ unbearable heat condition. Yet, the thermometer only went up to 30°C (86°F). Why is that? Well, as it turns out, how you feel is not really the outside temperature. This article unveils many of our deep misconceptions about heat.

The Harmonious Mathematics of Music The Harmonious Mathematics of Music

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 2226It 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.

Univalent Foundations of Mathematics Univalent Foundations of Mathematics

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Prerequisites:**Type Theory: A Modern Computable Paradigm for Math, Homotopy Type Theory and Higher Inductive Types |**Views**: 2142In 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.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 64671+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!

The Revolutionary Galois Theory The Revolutionary Galois Theory

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**Linear Algebra and Higher Dimensions, Imaginary and Complex Numbers, Symmetries and Group Theory |**Views**: 11455In 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!

Beauty, the Driving Force of our Quest for Truth Beauty, the Driving Force of our Quest for Truth

By Lê Nguyên Hoang |

According to Matthew Colless, the most important aspect of science is beauty. Not only is it what inspires scientists and their quests, I’d even claim that it’s also the compass that guide them in their quests, in a deeper and more surprising way that one can imagine!

By Lê Nguyên Hoang |

**Updated:**2015-12 |**Views**: 1075According to Matthew Colless, the most important aspect of science is beauty. Not only is it what inspires scientists and their quests, I’d even claim that it’s also the compass that guide them in their quests, in a deeper and more surprising way that one can imagine!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 2413In 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 3562Statistician 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 19116The 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!

Optimization by Linear Programming Optimization by Linear Programming

By Lê Nguyên Hoang |

Operations Research deals with optimizing industrial systems. Those systems can be very complex and their modeling may require the use of hundreds, thousands or even millions of variables. Optimizing over millions of variables may seem impossible, but it can be done if the optimization problem has a linear structure. Learn more on this linear structure and optimization solutions!

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 4498Operations Research deals with optimizing industrial systems. Those systems can be very complex and their modeling may require the use of hundreds, thousands or even millions of variables. Optimizing over millions of variables may seem impossible, but it can be done if the optimization problem has a linear structure. Learn more on this linear structure and optimization solutions!

Multicriteria with MACBETH Multicriteria with MACBETH

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 2037As 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.

Shannon’s Information Theory Shannon’s Information Theory

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 18714Claude 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.

High Dynamic Range and Tone Mapping High Dynamic Range and Tone Mapping

By Lê Nguyên Hoang |

Our eyes are amazing! Even today’s cameras are nowhere near competing with them. However, the recent development of high dynamic range (HDR) and tone mapping technologies creates new possibilities to get images nearly as awesome as what our eyes really see!

By Lê Nguyên Hoang |

**Updated:**2015-12 |**Views**: 1699Our eyes are amazing! Even today’s cameras are nowhere near competing with them. However, the recent development of high dynamic range (HDR) and tone mapping technologies creates new possibilities to get images nearly as awesome as what our eyes really see!

A Model of Football Games A Model of Football Games

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 4780Back 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.

Colours and Dimensions Colours and Dimensions

By Lê Nguyên Hoang |

You’ve probably learned early on that there are three primary colours. But why three? And why these three? Surprisingly, the answer lies in the beautiful mathematics of linear algebra and (high) dimension spaces!

By Lê Nguyên Hoang |

**Updated:**2015-12 |**Views**: 1600You’ve probably learned early on that there are three primary colours. But why three? And why these three? Surprisingly, the answer lies in the beautiful mathematics of linear algebra and (high) dimension spaces!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 1920No 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!

Poincaré Conjecture and Homotopy Poincaré Conjecture and Homotopy

By Lê Nguyên Hoang |

Poincaré conjecture is the most recent major proven theorem. Posited a century ago by Henri Poincaré, this major conjecture of topology was solved by Gregori Perelman. It has revolutionized our understanding of space and raised intriguing questions regarding the global structure of our Universe.

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 5475Poincaré conjecture is the most recent major proven theorem. Posited a century ago by Henri Poincaré, this major conjecture of topology was solved by Gregori Perelman. It has revolutionized our understanding of space and raised intriguing questions regarding the global structure of our Universe.

Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse

By Lê Nguyên Hoang |

On one hand, the dynamics of the wave function can follow Schrödinger equation and satisfy simple properties like Heisenberg uncertainty principle. But on the other hand, it can be probabilistic. This doesn’t mean that it’s totally unpredictable, since the unpredictability is amazingly predictable. Find out how these two dynamics work!

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Prerequisites:**The Essence of Quantum Mechanics, Imaginary and Complex Numbers, Linear Algebra and Higher Dimensions |**Views**: 5141On one hand, the dynamics of the wave function can follow Schrödinger equation and satisfy simple properties like Heisenberg uncertainty principle. But on the other hand, it can be probabilistic. This doesn’t mean that it’s totally unpredictable, since the unpredictability is amazingly predictable. Find out how these two dynamics work!

A Mathematical Guide to Selling A Mathematical Guide to Selling

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 2441How 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 1374Divide 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.

The Most Troubling Experiments on Human Behavior The Most Troubling Experiments on Human Behavior

By Lê Nguyên Hoang |

We all intuitively think of ourselves as independent creatures with strong free will. However, many disturbing experiments about fashion, conformity, obedience, environment, choice and opinions have been troubling this idea we make of ourselves. These ought to be lessons of humility for all of us.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 1413We all intuitively think of ourselves as independent creatures with strong free will. However, many disturbing experiments about fashion, conformity, obedience, environment, choice and opinions have been troubling this idea we make of ourselves. These ought to be lessons of humility for all of us.

The Unlikely Correctness of Newton’s Laws The Unlikely Correctness of Newton’s Laws

By Lê Nguyên Hoang |

Do moving objects exhaust? Does the Moon accelerate? How strong is the gravity pull of the Moon on the Earth compared to that of the Earth on the Moon? While we’ve all learned Newton’s laws of motion, many of us would get several answers of these questions wrong. That’s not so surprising, as Newton’s laws are deeply counter-intuitive. By stressing their weirdness with Veritasium videos, this article dives into a deep understanding of classical mechanics.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 3182Do moving objects exhaust? Does the Moon accelerate? How strong is the gravity pull of the Moon on the Earth compared to that of the Earth on the Moon? While we’ve all learned Newton’s laws of motion, many of us would get several answers of these questions wrong. That’s not so surprising, as Newton’s laws are deeply counter-intuitive. By stressing their weirdness with Veritasium videos, this article dives into a deep understanding of classical mechanics.

Darwin’s Theory of Evolution Darwin’s Theory of Evolution

By Lê Nguyên Hoang |

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.

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 10530Darwin’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.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 7736I 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!

Primal and Dual Simplex Methods Primal and Dual Simplex Methods

By Lê Nguyên Hoang |

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.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Prerequisites:**Optimization by Linear Programming, Duality in Linear Programming |**Views**: 8270The 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.

Spacetime of General Relativity Spacetime of General Relativity

By Lê Nguyên Hoang |

Most popular science explanations of the theory of general relativity are very nice-looking. But they are also deeply misleading. This article presents you a more accurate picture of the spacetime envisioned by Albert Einstein.

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 9776Most popular science explanations of the theory of general relativity are very nice-looking. But they are also deeply misleading. This article presents you a more accurate picture of the spacetime envisioned by Albert Einstein.

The Triangle of Power The Triangle of Power

By Lê Nguyên Hoang |

Notations do not matter to the essence of mathematics. But poor notations can be misleading. Notations based on exponents, radicals and logarithms definitely are. They are very distinct, even though they are supposed to describe very similar relations between numbers. The triangle of power is a recently proposed alternative. In short, I am convinced!

By Lê Nguyên Hoang |

**Updated:**2016-10 |**Views**: 206Notations do not matter to the essence of mathematics. But poor notations can be misleading. Notations based on exponents, radicals and logarithms definitely are. They are very distinct, even though they are supposed to describe very similar relations between numbers. The triangle of power is a recently proposed alternative. In short, I am convinced!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 5218Fourier 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.

Dynamics, Chaos, Fractals (pt 1) Dynamics, Chaos, Fractals (pt 1)

By Scott McKinney |

The study of dynamical systems, natural or abstract systems that evolve at each instance in time according to a specific rule, is an active and fruitful area of research in mathematics. Its study has yielded insights into the nature of social networks such as Facebook, the spread of diseases such as influenza, and the behavior of the financial markets. In this series of posts, we’ll look in depth at dynamical systems, as well as at the related subjects of chaos theory and fractals, all of which are both interesting and useful for understanding our world.

By Scott McKinney |

**Updated:**2016-02 |**Views**: 2803The study of dynamical systems, natural or abstract systems that evolve at each instance in time according to a specific rule, is an active and fruitful area of research in mathematics. Its study has yielded insights into the nature of social networks such as Facebook, the spread of diseases such as influenza, and the behavior of the financial markets. In this series of posts, we’ll look in depth at dynamical systems, as well as at the related subjects of chaos theory and fractals, all of which are both interesting and useful for understanding our world.

Bayesian Games: Math Models for Poker Bayesian Games: Math Models for Poker

By Lê Nguyên Hoang |

How to better understand Poker and card games in general? Bayesian games provide the right mathematical model just for that! These correspond to games with incomplete information and include probabilistic reasonings.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 4581How to better understand Poker and card games in general? Bayesian games provide the right mathematical model just for that! These correspond to games with incomplete information and include probabilistic reasonings.

The Massive Puzzles of Gravity The Massive Puzzles of Gravity

By Lê Nguyên Hoang |

This article follows the footsteps of the giants of physics that have moulded our current understanding of gravity. It is a series of brilliant inspirations, usually accompanied by deceiving misconceptions. After all, even today, gravity is still a slippery concept.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 2515This article follows the footsteps of the giants of physics that have moulded our current understanding of gravity. It is a series of brilliant inspirations, usually accompanied by deceiving misconceptions. After all, even today, gravity is still a slippery concept.

Logarithms and Age Counting Logarithms and Age Counting

By Lê Nguyên Hoang |

Amusingly, the age difference between a 45-year-old man and a 25-year-old woman doesn’t seem as big as the age difference between them 20 years earlier, when the woman was a little 5-year-old girl. This remark was the insight the late science popularizer Albert Jacquart liked to give to his readers to explain logarithms. This article pays tribute to the great scientist by introducing age difference as he liked to tell it.

By Lê Nguyên Hoang |

**Updated:**2015-12 |**Views**: 2520Amusingly, the age difference between a 45-year-old man and a 25-year-old woman doesn’t seem as big as the age difference between them 20 years earlier, when the woman was a little 5-year-old girl. This remark was the insight the late science popularizer Albert Jacquart liked to give to his readers to explain logarithms. This article pays tribute to the great scientist by introducing age difference as he liked to tell it.

Does God play dice? Does God play dice?

By Arthur Marronnier |

For Albert Einstein, the answer is no. But what did he mean? Has the greatest theoretical physicist of all time really missed the bandwagon of quantum physics? What are the real issues of the controversy that has opposed him to the Copenhagen School (Bohr, Heisenberg …)? Back to the physics of the early twentieth century, its history, philosophy and ideas.

By Arthur Marronnier |

**Updated:**2016-02 |**Views**: 900For Albert Einstein, the answer is no. But what did he mean? Has the greatest theoretical physicist of all time really missed the bandwagon of quantum physics? What are the real issues of the controversy that has opposed him to the Copenhagen School (Bohr, Heisenberg …)? Back to the physics of the early twentieth century, its history, philosophy and ideas.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 103452048 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 Essence of Quantum Mechanics The Essence of Quantum Mechanics

By Lê Nguyên Hoang |

Quantum mechanics is the most accurate and tested scientific theory, Its applications to real life are countless, as all new technologies are based on its principles. Yet, it’s also probably the most misunderstood theory, because it constantly contradicts common sense. This article presents the most important features of the theory.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 7472Quantum mechanics is the most accurate and tested scientific theory, Its applications to real life are countless, as all new technologies are based on its principles. Yet, it’s also probably the most misunderstood theory, because it constantly contradicts common sense. This article presents the most important features of the theory.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 8743In 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.

Fair Division and Cake-Cutting Fair Division and Cake-Cutting

By Lê Nguyên Hoang |

Cutting a cake to satisfy everyone is no piece of cake! In the article, we focus on classical definitions of fair divisions. I’ll criticize those definitions and conclude by extrapolating them to fairness in society.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 3544Cutting a cake to satisfy everyone is no piece of cake! In the article, we focus on classical definitions of fair divisions. I’ll criticize those definitions and conclude by extrapolating them to fairness in society.

Imaginary and Complex Numbers Imaginary and Complex Numbers

By Lê Nguyên Hoang |

My first reaction to imaginary numbers was… What the hell is that? Even now, I have trouble getting my head around these mathematical objects. Fortunately, I have a secret weapon: Geometry! This article proposes constructing complex numbers with a very geometrical and intuitive approach, which is probably very different from what you’ve learned (or will learn).

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 4434My first reaction to imaginary numbers was… What the hell is that? Even now, I have trouble getting my head around these mathematical objects. Fortunately, I have a secret weapon: Geometry! This article proposes constructing complex numbers with a very geometrical and intuitive approach, which is probably very different from what you’ve learned (or will learn).

The Magic of Analysis The Magic of Analysis

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 1336This 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.

The Amazing Physics of Water in Trees The Amazing Physics of Water in Trees

By Lê Nguyên Hoang |

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!

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 21487As 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!

Proof by Mathematical Induction Proof by Mathematical Induction

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 4887This 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!

The coach’s dilemma. The coach’s dilemma.

By Herminio López |

By Herminio López |

**Updated:**2016-02 |**Views**: 634Pluto is NOT (not?) a Planet Pluto is NOT (not?) a Planet

By Lê Nguyên Hoang |

In 2006, Pluto was officially demoted from its planetary status. When we dig a little bit, this isn’t much of the surprise. What’s more interesting is rather why it ever was regarded as a planet, as the History of Pluto highlights a magic enterprise that science is!

By Lê Nguyên Hoang |

**Updated:**2015-12 |**Views**: 1786In 2006, Pluto was officially demoted from its planetary status. When we dig a little bit, this isn’t much of the surprise. What’s more interesting is rather why it ever was regarded as a planet, as the History of Pluto highlights a magic enterprise that science is!

Web Programming: From HTML to AJAX Web Programming: From HTML to AJAX

By Lê Nguyên Hoang |

The Internet is an unavoidable component of today’s life, and will only become more and more important in the future. In this article, we”ll have an overview of its development in terms of coding languages. This article explains how webpages actually work. In particular, we’ll discuss HTML, CSS, PHP, WordPress, MySQL, Javascript, XML and JSON, as well as their competitors.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 2740The Internet is an unavoidable component of today’s life, and will only become more and more important in the future. In this article, we”ll have an overview of its development in terms of coding languages. This article explains how webpages actually work. In particular, we’ll discuss HTML, CSS, PHP, WordPress, MySQL, Javascript, XML and JSON, as well as their competitors.

The Thrilling Physics of Resonance The Thrilling Physics of Resonance

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 10336From 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!