#### 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.

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**: 889Glaciers 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.

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**: 5391Over 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**: 3105Linear 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.

Construction and Definition of Numbers Construction and Definition of Numbers

By Lê Nguyên Hoang |

Although they have been used for thousands of years, an actual definition of numbers was given less than a century ago! From the most fundamental level of set theory, this article takes you to the journey of the construction of natural, integer, rational, real and complex numbers.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 4232Although they have been used for thousands of years, an actual definition of numbers was given less than a century ago! From the most fundamental level of set theory, this article takes you to the journey of the construction of natural, integer, rational, real and complex 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**: 1534You’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**: 1876No 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!

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**: 1985As 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.

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**: 4397How 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.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 3022Although 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.

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**: 9572Most 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 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**: 9984From 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!

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**: 3162Suppose 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 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**: 19974As 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!

HDI: a measure of human capabilities HDI: a measure of human capabilities

By Estève Giraud |

By Estève Giraud |

**Updated:**2016-02 |**Views**: 4093The 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**: 97272048 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!

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**: 1355Divide 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.

Dual Variable Stabilization Dual Variable Stabilization

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**Optimization by Linear Programming, Duality in Linear Programming, Primal and Dual Simplex Methods |**Views**: 458Simplex 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.

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**: 4379Operations 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 4955Designing 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!

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**: 12166Duality 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.

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**: 62631+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!

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**: 2833Introduced 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.

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**: 1725All 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.

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**: 2470Pluto 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**: 1748In 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!

Marriage Assignment Problem and Variants Marriage Assignment Problem and Variants

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 3998Marriage 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.

The Magic of Algebra The Magic of Algebra

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 2338The 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.

Differential Calculus and the Geometry of Derivatives Differential Calculus and the Geometry of Derivatives

By Lê Nguyên Hoang |

Differential calculus is one of the most important concept of mathematics for science and engineering. This article focuses on its fundamental meaning.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 4008Differential calculus is one of the most important concept of mathematics for science and engineering. This article focuses on its fundamental meaning.

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**: 5089Fourier 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.

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**: 1371We 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.

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**: 3528Statistician 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!

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

By Thibault_Lehouillier |

By Thibault_Lehouillier |

**Updated:**2016-02 |**Views**: 1449Can we measure peace ? The Global Peace Index (GPI) Can we measure peace ? The Global Peace Index (GPI)

By Estève Giraud |

By Estève Giraud |

**Updated:**2016-04 |**Views**: 92Fair 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**: 3451Cutting 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.

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**: 1604Our 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 3622Topology 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.

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**: 7573In 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!

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

By Scott McKinney |

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 |

**Updated:**2016-02 |**Views**: 3091Geometry 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.

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**: 4706I 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.

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**: 3022Do 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.

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**: 4595Integer programming is arguably the greatest achievement of applied mathematics. Half of the time, it’s what’s used to solve real-world problems!

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!

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**: 2403Amusingly, 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 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**: 1322This 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.

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**: 7572I 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!

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**: 1743While 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!

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.

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**: 8614In 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.

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**: 17631Claude 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.

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**: 10227Darwin’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.