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.
The Unlikely Correctness of Newton’s Laws
The Unlikely Correctness of Newton’s Laws
By Lê Nguyên Hoang | Updated:2016-02 | Views: 3104
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.
The Unlikely Correctness of Newton’s LawsBy Lê Nguyên Hoang | Updated:2016-02 | Views: 3104
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.
Bayesian Games: Math Models for Poker Bayesian Games: Math Models for Poker
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4480
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.
Bayesian Games: Math Models for PokerBy Lê Nguyên Hoang | Updated:2016-02 | Views: 4480
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.
Glaciers: Retreat, Moraines, Valleys, Fjörds Glaciers: Retreat, Moraines, Valleys, Fjörds
By Lê Nguyên Hoang | Updated:2016-02 | Views: 908
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.
Glaciers: Retreat, Moraines, Valleys, FjördsBy Lê Nguyên Hoang | Updated:2016-02 | Views: 908
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.
The Frontier of Cold: The Quest for Absolute Zero The Frontier of Cold: The Quest for Absolute Zero
By Lê Nguyên Hoang | Updated:2016-02 | Views: 1765
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!
The Frontier of Cold: The Quest for Absolute ZeroBy Lê Nguyên Hoang | Updated:2016-02 | Views: 1765
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!
A Model of Football Games A Model of Football Games
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4715
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.
A Model of Football GamesBy Lê Nguyên Hoang | Updated:2016-02 | Views: 4715
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.
Shannon’s Information Theory Shannon’s Information Theory
By Lê Nguyên Hoang | Updated:2016-01 | Views: 18140
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.
Shannon’s Information TheoryBy Lê Nguyên Hoang | Updated:2016-01 | Views: 18140
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.
Column Generation and Dantzig-Wolfe Decomposition Column Generation and Dantzig-Wolfe Decomposition
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Linear Algebra and Higher Dimensions, Optimization by Linear Programming | Views: 4201
Column generation and the Dantzig-Wolfe decomposition are powerful tricks which have revolutionized optimization addressed to industrial problems, and generated millions and millions of dollars. My PhD supervisor effectively took great advantage of these tricks and founded companies with it. This article explains the tricks.
Column Generation and Dantzig-Wolfe DecompositionBy Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Linear Algebra and Higher Dimensions, Optimization by Linear Programming | Views: 4201
Column generation and the Dantzig-Wolfe decomposition are powerful tricks which have revolutionized optimization addressed to industrial problems, and generated millions and millions of dollars. My PhD supervisor effectively took great advantage of these tricks and founded companies with it. This article explains the tricks.
Space Deformation and Group Representation Space Deformation and Group Representation
By Lê Nguyên Hoang | Updated:2015-12 | Views: 1774
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.
Space Deformation and Group RepresentationBy Lê Nguyên Hoang | Updated:2015-12 | Views: 1774
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.
Santa Routing and Heuristics in Operations Research Santa Routing and Heuristics in Operations Research
By Lê Nguyên Hoang | Updated:2016-01 | Views: 4994
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!
Santa Routing and Heuristics in Operations ResearchBy Lê Nguyên Hoang | Updated:2016-01 | Views: 4994
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!
The Addictive Mathematics of the 2048 Tile Game The Addictive Mathematics of the 2048 Tile Game
By Lê Nguyên Hoang | Updated:2016-01 | Views: 9959
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!
The Addictive Mathematics of the 2048 Tile GameBy Lê Nguyên Hoang | Updated:2016-01 | Views: 9959
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!
High Dynamic Range and Tone Mapping High Dynamic Range and Tone Mapping
By Lê Nguyên Hoang | Updated:2015-12 | Views: 1655
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!
High Dynamic Range and Tone MappingBy Lê Nguyên Hoang | Updated:2015-12 | Views: 1655
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!
Poincaré Conjecture and Homotopy Poincaré Conjecture and Homotopy
By Lê Nguyên Hoang | Updated:2016-01 | Views: 5429
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.
Poincaré Conjecture and HomotopyBy Lê Nguyên Hoang | Updated:2016-01 | Views: 5429
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.
Homotopy Type Theory and Higher Inductive Types Homotopy Type Theory and Higher Inductive Types
By Lê Nguyên Hoang | Updated:2015-12 | Views: 1734
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) circle and sphere.
Homotopy Type Theory and Higher Inductive TypesBy Lê Nguyên Hoang | Updated:2015-12 | Views: 1734
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) circle and sphere.
Can we measure peace ? The Global Peace Index (GPI)
Can we measure peace ? The Global Peace Index (GPI)
By Estève Giraud | Updated:2016-04 | Views: 110
Can we measure peace ? The Global Peace Index (GPI)By Estève Giraud | Updated:2016-04 | Views: 110
Non-Euclidean Geometry and Map-Making
Non-Euclidean Geometry and Map-Making
By Scott McKinney | Updated:2016-02 | Views: 3187
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.
Non-Euclidean Geometry and Map-MakingBy Scott McKinney | Updated:2016-02 | Views: 3187
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.
Symmetries and Group Theory Symmetries and Group Theory
By Lê Nguyên Hoang | Updated:2016-02 | Views: 1852
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.
Symmetries and Group TheoryBy Lê Nguyên Hoang | Updated:2016-02 | Views: 1852
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.
The Most Beautiful Equation of Math: Euler’s Identity The Most Beautiful Equation of Math: Euler’s Identity
By Lê Nguyên Hoang | Updated:2016-01 | Views: 38266
In 1988, Euler’s identity was elected most beautiful theorem of mathematics. It has been widely taught worldwide. But have you ever stopped to really sense the meaning of this incredible formula? This article does.
The Most Beautiful Equation of Math: Euler’s IdentityBy Lê Nguyên Hoang | Updated:2016-01 | Views: 38266
In 1988, Euler’s identity was elected most beautiful theorem of mathematics. It has been widely taught worldwide. But have you ever stopped to really sense the meaning of this incredible formula? This article does.
The Revolutionary Galois Theory The Revolutionary Galois Theory
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Linear Algebra and Higher Dimensions, Imaginary and Complex Numbers, Symmetries and Group Theory | Views: 11392
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!
The Revolutionary Galois TheoryBy Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Linear Algebra and Higher Dimensions, Imaginary and Complex Numbers, Symmetries and Group Theory | Views: 11392
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!
The Secretary/Toilet Problem and Online Optimization The Secretary/Toilet Problem and Online Optimization
By Lê Nguyên Hoang | Updated:2015-12 | Views: 2048
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.
The Secretary/Toilet Problem and Online OptimizationBy Lê Nguyên Hoang | Updated:2015-12 | Views: 2048
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.
Geometry and General Relativity Geometry and General Relativity
By Scott McKinney | Updated:2015-12 | Views: 1613
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.
Geometry and General RelativityBy Scott McKinney | Updated:2015-12 | Views: 1613
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.
Fair Division and Cake-Cutting Fair Division and Cake-Cutting
By Lê Nguyên Hoang | Updated:2016-02 | Views: 3501
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.
Fair Division and Cake-CuttingBy Lê Nguyên Hoang | Updated:2016-02 | Views: 3501
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.
Differential Calculus and the Geometry of Derivatives Differential Calculus and the Geometry of Derivatives
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4081
Differential calculus is one of the most important concept of mathematics for science and engineering. This article focuses on its fundamental meaning.
Differential Calculus and the Geometry of DerivativesBy Lê Nguyên Hoang | Updated:2016-02 | Views: 4081
Differential calculus is one of the most important concept of mathematics for science and engineering. This article focuses on its fundamental meaning.
Duality in Linear Programming Duality in Linear Programming
By Lê Nguyên Hoang | Updated:2016-01 | Prerequisites: Optimization by Linear Programming, Linear Algebra and Higher Dimensions | Views: 12341
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.
Duality in Linear ProgrammingBy Lê Nguyên Hoang | Updated:2016-01 | Prerequisites: Optimization by Linear Programming, Linear Algebra and Higher Dimensions | Views: 12341
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.
Dual Variable Stabilization Dual Variable Stabilization
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Optimization by Linear Programming, Duality in Linear Programming, Primal and Dual Simplex Methods | Views: 461
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.
Dual Variable StabilizationBy Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Optimization by Linear Programming, Duality in Linear Programming, Primal and Dual Simplex Methods | Views: 461
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.
The Harmonious Mathematics of Music The Harmonious Mathematics of Music
By Lê Nguyên Hoang | Updated:2015-12 | Views: 2181
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.
The Harmonious Mathematics of MusicBy Lê Nguyên Hoang | Updated:2015-12 | Views: 2181
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.
The Surprising Flavor of Infinite Series The Surprising Flavor of Infinite Series
By Lê Nguyên Hoang | Updated:2016-01 | Views: 6364
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!
The Surprising Flavor of Infinite SeriesBy Lê Nguyên Hoang | Updated:2016-01 | Views: 6364
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!
The Magic of Analysis The Magic of Analysis
By Lê Nguyên Hoang | Updated:2016-02 | Views: 1328
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.
The Magic of AnalysisBy Lê Nguyên Hoang | Updated:2016-02 | Views: 1328
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.
The forces of Nature: from Newton to String Theory
The forces of Nature: from Newton to String Theory
By Thibault_Lehouillier | Updated:2016-02 | Views: 1481
The forces of Nature: from Newton to String TheoryBy Thibault_Lehouillier | Updated:2016-02 | Views: 1481
Marriage Assignment Problem and Variants Marriage Assignment Problem and Variants
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4054
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.
Marriage Assignment Problem and VariantsBy Lê Nguyên Hoang | Updated:2016-02 | Views: 4054
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.
The Massive Puzzles of Gravity The Massive Puzzles of Gravity
By Lê Nguyên Hoang | Updated:2016-02 | Views: 2475
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.
The Massive Puzzles of GravityBy Lê Nguyên Hoang | Updated:2016-02 | Views: 2475
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.
The Essence of Quantum Mechanics The Essence of Quantum Mechanics
By Lê Nguyên Hoang | Updated:2016-02 | Views: 7389
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.
The Essence of Quantum MechanicsBy Lê Nguyên Hoang | Updated:2016-02 | Views: 7389
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.
Temperature Misconception: Heat is Not How it Feels Temperature Misconception: Heat is Not How it Feels
By Lê Nguyên Hoang | Updated:2015-12 | Views: 1676
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.
Temperature Misconception: Heat is Not How it FeelsBy Lê Nguyên Hoang | Updated:2015-12 | Views: 1676
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.
Optimization by Linear Programming Optimization by Linear Programming
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4436
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!
Optimization by Linear ProgrammingBy Lê Nguyên Hoang | Updated:2016-02 | Views: 4436
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!
Advanced Game Theory Overview Advanced Game Theory Overview
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Game Theory and the Nash Equilibrium | Views: 4165
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.
Advanced Game Theory OverviewBy Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Game Theory and the Nash Equilibrium | Views: 4165
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.
Beauty, the Driving Force of our Quest for Truth Beauty, the Driving Force of our Quest for Truth
By Lê Nguyên Hoang | Updated:2015-12 | Views: 1068
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!
Beauty, the Driving Force of our Quest for TruthBy Lê Nguyên Hoang | Updated:2015-12 | Views: 1068
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!
Computing Hunger worldwide: the Global Hunger Index (GHI) Computing Hunger worldwide: the Global Hunger Index (GHI)
By Estève Giraud | Updated:2015-12 | Views: 451
The Global Hunger Index was first published in 2006 by the International Food Policy Research Institute and the NGO Welthungerhilfe. In 2007, Concern worldwide joined them. Since then, the Index reports every year the evolution of the hunger situation worldwide and focus on a given topic. How is it calculated? And what is hunger? How are we connected ? What can be done? To learn more, read the article below.
Computing Hunger worldwide: the Global Hunger Index (GHI)By Estève Giraud | Updated:2015-12 | Views: 451
The Global Hunger Index was first published in 2006 by the International Food Policy Research Institute and the NGO Welthungerhilfe. In 2007, Concern worldwide joined them. Since then, the Index reports every year the evolution of the hunger situation worldwide and focus on a given topic. How is it calculated? And what is hunger? How are we connected ? What can be done? To learn more, read the article below.
Cryptography and Number Theory Cryptography and Number Theory
By Scott McKinney | Updated:2016-01 | Views: 5460
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.
Cryptography and Number TheoryBy Scott McKinney | Updated:2016-01 | Views: 5460
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.
HDI: a measure of human capabilities HDI: a measure of human capabilities
By Estève Giraud | Updated:2016-02 | Views: 4147
HDI: a measure of human capabilitiesBy Estève Giraud | Updated:2016-02 | Views: 4147
The Amazing Physics of Water in Trees The Amazing Physics of Water in Trees
By Lê Nguyên Hoang | Updated:2016-01 | Views: 20865
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!
The Amazing Physics of Water in TreesBy Lê Nguyên Hoang | Updated:2016-01 | Views: 20865
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!
The coach’s dilemma.
The coach’s dilemma.
By Herminio López | Updated:2016-02 | Views: 631
The coach’s dilemma.By Herminio López | Updated:2016-02 | Views: 631
Topology: from the Basics to Connectedness Topology: from the Basics to Connectedness
By Lê Nguyên Hoang | Updated:2016-02 | Views: 3674
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.
Topology: from the Basics to ConnectednessBy Lê Nguyên Hoang | Updated:2016-02 | Views: 3674
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.
The Cubic Ball of the 2014 FIFA World Cup The Cubic Ball of the 2014 FIFA World Cup
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4768
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.
The Cubic Ball of the 2014 FIFA World CupBy Lê Nguyên Hoang | Updated:2016-02 | Views: 4768
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.
Dynamics, Chaos, Fractals (pt 2) Dynamics, Chaos, Fractals (pt 2)
By Scott McKinney | Updated:2015-12 | Views: 1194
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.
Dynamics, Chaos, Fractals (pt 2)By Scott McKinney | Updated:2015-12 | Views: 1194
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.
Numbers and Constructibility Numbers and Constructibility
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4266
Last summer, I got to discover Morellet’s artwork on inclined grids. Amazingly, this artwork is a display of the irrationality of $\sqrt{2}$! It’s also a strong argument for the existence of this number. In this article, after discussing that, I take readers further by discussing what numbers can be constructed geometrically, algebraically, analytically or set theoretically using the power of mathematics!
Numbers and ConstructibilityBy Lê Nguyên Hoang | Updated:2016-02 | Views: 4266
Last summer, I got to discover Morellet’s artwork on inclined grids. Amazingly, this artwork is a display of the irrationality of $\sqrt{2}$! It’s also a strong argument for the existence of this number. In this article, after discussing that, I take readers further by discussing what numbers can be constructed geometrically, algebraically, analytically or set theoretically using the power of mathematics!
Colours and Dimensions Colours and Dimensions
By Lê Nguyên Hoang | Updated:2015-12 | Views: 1560
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!
Colours and DimensionsBy Lê Nguyên Hoang | Updated:2015-12 | Views: 1560
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!
Darwin’s Theory of Evolution Darwin’s Theory of Evolution
By Lê Nguyên Hoang | Updated:2016-01 | Views: 10400
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.
Darwin’s Theory of EvolutionBy Lê Nguyên Hoang | Updated:2016-01 | Views: 10400
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.
Spacetime of Special Relativity Spacetime of Special Relativity
By Lê Nguyên Hoang | Updated:2016-02 | Views: 2290
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.
Spacetime of Special RelativityBy Lê Nguyên Hoang | Updated:2016-02 | Views: 2290
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.
Linear Algebra and Higher Dimensions Linear Algebra and Higher Dimensions
By Lê Nguyên Hoang | Updated:2016-02 | Views: 3154
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.
Linear Algebra and Higher DimensionsBy Lê Nguyên Hoang | Updated:2016-02 | Views: 3154
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.
The Limitless Vertigo of Cantor’s Infinite The Limitless Vertigo of Cantor’s Infinite
By Lê Nguyên Hoang | Updated:2015-12 | Views: 1892
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!
The Limitless Vertigo of Cantor’s InfiniteBy Lê Nguyên Hoang | Updated:2015-12 | Views: 1892
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!
The Tortuous Geometry of the Flat Torus The Tortuous Geometry of the Flat Torus
By Lê Nguyên Hoang | Updated:2015-12 | Views: 9252
Take a square sheet of paper. Can you glue opposite sides without ever folding the paper? This is a conundrum that many of the greatest modern mathematicians, like Gauss, Riemann, and Mandelbrot, couldn’t figure out. While John Nash did answer yes, he couldn’t say how. After 160 years of research, Vincent Borrelli and his collaborators have finally provided a revolutionary and breathtaking example of a bending of a square sheet of paper! And it is spectacularly beautiful!
The Tortuous Geometry of the Flat TorusBy Lê Nguyên Hoang | Updated:2015-12 | Views: 9252
Take a square sheet of paper. Can you glue opposite sides without ever folding the paper? This is a conundrum that many of the greatest modern mathematicians, like Gauss, Riemann, and Mandelbrot, couldn’t figure out. While John Nash did answer yes, he couldn’t say how. After 160 years of research, Vincent Borrelli and his collaborators have finally provided a revolutionary and breathtaking example of a bending of a square sheet of paper! And it is spectacularly beautiful!
