#### 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.

Probabilistic Algorithms, Probably Better Probabilistic Algorithms, Probably Better

By Lê Nguyên Hoang |

Probabilities have been proven to be a great tool to understand some features of the world, such as what can happen in a dice game. Applied to programming, it has enabled plenty of amazing algorithms. In this article, we discuss its application to the primality test as well as to face detection. We’ll also deal with quantum computers, as well as fundamental computer science open problems P=BPP and NP=BQP.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 1239Probabilities have been proven to be a great tool to understand some features of the world, such as what can happen in a dice game. Applied to programming, it has enabled plenty of amazing algorithms. In this article, we discuss its application to the primality test as well as to face detection. We’ll also deal with quantum computers, as well as fundamental computer science open problems P=BPP and NP=BQP.

Spacetime of Special Relativity Spacetime of Special Relativity

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 2267Einstein’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.

Optimization by Integer Programming Optimization by Integer Programming

By Lê Nguyên Hoang |

Integer programming is arguably the greatest achievement of applied mathematics. Half of the time, it’s what’s used to solve real-world problems!

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Prerequisites:**Optimization by Linear Programming |**Views**: 4602Integer programming is arguably the greatest achievement of applied mathematics. Half of the time, it’s what’s used to solve real-world problems!

Advanced Game Theory Overview Advanced Game Theory Overview

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**Game Theory and the Nash Equilibrium |**Views**: 4154This 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.

Symmetries and Group Theory Symmetries and Group Theory

By Lê Nguyên Hoang |

Beauty is extremely hard to define. Yet, physicists and artists seem to agree on an important feature of beauty, created by mathematicians: Symmetries. This article aims at introducing the beauty and the concepts on symmetries, from the basic geometrical symmetries to the more abstract fundamental automorphisms.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 1822Beauty is extremely hard to define. Yet, physicists and artists seem to agree on an important feature of beauty, created by mathematicians: Symmetries. This article aims at introducing the beauty and the concepts on symmetries, from the basic geometrical symmetries to the more abstract fundamental automorphisms.

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 |

By Thomas C |

**Updated:**2016-02 |**Views**: 2471Darwin’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**: 10241Darwin’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.

Geological Wonders of Iceland Geological Wonders of Iceland

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 1301Iceland 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.

Duality in Linear Programming Duality in Linear Programming

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Prerequisites:**Optimization by Linear Programming, Linear Algebra and Higher Dimensions |**Views**: 12187Duality 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.

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**: 7576In 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!

Regulation of Electricity Markets Regulation of Electricity Markets

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 1378Electricity 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.

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**: 11339In 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!

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**: 1536You’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!

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**: 4682Back 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.

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**: 1878No 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!

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**: 1064According 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!

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**: 2366How 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!

Geometry and General Relativity Geometry and General Relativity

By Scott McKinney |

From our “intrinsic” point-of-view on the surface of the Earth, it appears to be flat, but if we examine the Earth from the “extrinsic” point of view, somewhere off the Earth’s surface, we can see that it is clearly a curved surface. Amazingly, it is possible to determine that the Earth is spherical simply by taking measurements on its surface, and it is possible to generalize these measurements in order to study the shape of the universe. Mathematicians such as Riemann did just this, and Einstein was able to apply these geometric ideas to his “general theory of relativity”, which describes the relation between gravitation, space, and time.

By Scott McKinney |

**Updated:**2015-12 |**Views**: 1596From our “intrinsic” point-of-view on the surface of the Earth, it appears to be flat, but if we examine the Earth from the “extrinsic” point of view, somewhere off the Earth’s surface, we can see that it is clearly a curved surface. Amazingly, it is possible to determine that the Earth is spherical simply by taking measurements on its surface, and it is possible to generalize these measurements in order to study the shape of the universe. Mathematicians such as Riemann did just this, and Einstein was able to apply these geometric ideas to his “general theory of relativity”, which describes the relation between gravitation, space, and time.

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**: 2637The 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 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**: 7299Quantum 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.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 7272In 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!

Model-Dependent Realism Model-Dependent Realism

By Lê Nguyên Hoang |

Introduced by the two renowned theoretical physicists Stephen Hawking and Leonard Mlodinov in their book The Grand Design in 2010, model-dependent realism is a new controversial understanding of the universe. Based on solid logical reasonings and recent developments in physics, this concept may well be an incredible breakthrough for philosophy and science, as well as metaphysics.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 2834Introduced by the two renowned theoretical physicists Stephen Hawking and Leonard Mlodinov in their book The Grand Design in 2010, model-dependent realism is a new controversial understanding of the universe. Based on solid logical reasonings and recent developments in physics, this concept may well be an incredible breakthrough for philosophy and science, as well as metaphysics.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 3071Whenever 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.

Pluto 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**: 1749In 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!

Colors: It’s not just about Wavelengths! Colors: It’s not just about Wavelengths!

By Lê Nguyên Hoang |

Colours… What are they really? Are there the same for all of us? And for other animals? How does color addition or subtraction work? How do they work on computers? And on printers? The mysterious (but not dark) world of colors is actually very colourful!

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 2545Colours… What are they really? Are there the same for all of us? And for other animals? How does color addition or subtraction work? How do they work on computers? And on printers? The mysterious (but not dark) world of colors is actually very colourful!

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**: 5386Poincaré 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.

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**: 5399Over 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.

Linear Algebra and Higher Dimensions Linear Algebra and Higher Dimensions

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 3107Linear 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.

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**: 4383Operations 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 4711I 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.

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**: 2745The 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.

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**: 4925On 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!

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**: 4735This 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!

Euclidean Geometry and Navigation Euclidean Geometry and Navigation

By Scott McKinney |

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 |

**Updated:**2016-02 |**Views**: 2429This 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.

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**: 8622In 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.

Space Deformation and Group Representation Space Deformation and Group Representation

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 1728All 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.

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**: 4399How 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.

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

By Scott McKinney |

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 |

**Updated:**2015-12 |**Views**: 1176Dynamical 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.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 2018A 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.

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**: 4317My 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).

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**: 17676Claude 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 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**: 62681+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!

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**: 1617Our 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!

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**: 894For 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.

Glaciers: Retreat, Moraines, Valleys, Fjörds Glaciers: Retreat, Moraines, Valleys, Fjörds

By Lê Nguyên Hoang |

Glaciers are spectacular phenomenons of nature. The physics they are based on is surprising, while the geological role they have is essential. In this article, we discuss these facts, as well as their retreats and their dangers.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 896Glaciers are spectacular phenomenons of nature. The physics they are based on is surprising, while the geological role they have is essential. In this article, we discuss these facts, as well as their retreats and their dangers.

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**: 2325In 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!

Cryptography and Quantum Physics Cryptography and Quantum Physics

By Scott McKinney |

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 |

**Updated:**2016-02 |**Views**: 1656Recent 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.

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**: 2410Amusingly, 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.

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**: 1372We 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 Frontier of Cold: The Quest for Absolute Zero The Frontier of Cold: The Quest for Absolute Zero

By Lê Nguyên Hoang |

While mountaineers aim at tops of mountains, some scientists have sought the bottom of temperature scale with frequent surprising wonders at different scales. This article takes you through these scientists’ journey!

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 1744While mountaineers aim at tops of mountains, some scientists have sought the bottom of temperature scale with frequent surprising wonders at different scales. This article takes you through these scientists’ journey!