# Make it simple. Make it cool.

Science4All is a website of *Quality Popular Science*.

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

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

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

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 1041

A large chunk of applied mathematics has focused on optimizing something with respect to all relevant data. However, in practice, especially in the online world, the data is not available to us, and, yet, we’re still expected to make nearly optimal decisions. This problem is exemplified by the famous secretary problem, where a manager needs to decide to hire candidates right after interviews, even though he has not yet met all the candidates. In this article, we review this classic as well as many very recent developments., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Harmonious Mathematics of Music The Harmonious Mathematics of Music

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1367

It was when hearing the sounds of hammers that Pythagoras realized the ubiquity of numbers in mathematical harmony. He would go on laying down the mathematical foundations of music, based on octaves, perfect fifths and major thirds. This mathematics of music would then become the favourite playground of all musicians, from Beethoven to Gangnam Style., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1225

No one believed him. Not even fellow mathematicians. They thought he was wrong. They thought he was crazy. Even he ended up doubting himself and went crazy. And yet, he had mathematically proved it all. Georg Cantor had figured out how to manipulate the infinite. Even more remarkable, he showed that there were actually several infinities; and some are bigger than others!, by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Advanced Game Theory Overview Advanced Game Theory Overview

By Lê Nguyên Hoang | **Updated:**2015-01 | **Prerequisites: **Game Theory and the Nash Equilibrium | **Views**: 3428

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1000

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Thomas C | **Updated:**2013-05 | **Views**: 1909

, by Thomas C Thomas C

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

Pluto is NOT (not?) a Planet Pluto is NOT (not?) a Planet

By Lê Nguyên Hoang | **Updated:**2014-01 | **Views**: 1135

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Space Deformation and Group Representation Space Deformation and Group Representation

By Lê Nguyên Hoang | **Updated:**2014-03 | **Views**: 1474

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2054

Colors… 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 colorful!, by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Geometry and General Relativity Geometry and General Relativity

By Scott McKinney | **Updated:**2013-01 | **Views**: 1213

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 Scott McKinney

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

Dual Variable Stabilization Dual Variable Stabilization

By Lê Nguyên Hoang | **Updated:**2012-07 | **Prerequisites: **Optimization by Linear Programming, Duality in Linear Programming, Primal and Dual Simplex Methods | **Views**: 366

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Cryptography and Quantum Physics Cryptography and Quantum Physics

By Scott McKinney | **Updated:**2012-12 | **Views**: 1480

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

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

The Frontier of Cold: The Quest for Absolute Zero The Frontier of Cold: The Quest for Absolute Zero

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 1399

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Scott McKinney | **Updated:**2013-04 | **Views**: 2352

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 Scott McKinney

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

Spacetime of General Relativity Spacetime of General Relativity

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 8245

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

A Model of Football Games A Model of Football Games

By Lê Nguyên Hoang | **Updated:**2014-10 | **Views**: 3848

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2013-11 | **Views**: 3190

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Herminio López | **Updated:**2012-06 | **Views**: 564

, by Herminio López Herminio López

Degree in Economics and Business. Bank worker. Maths fan.

Webmaster of www.matifutbol.com

The Magic of Analysis The Magic of Analysis

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 919

This article retraces the endless pursuit of the infinite that is at the basis of mathematical analysis. From the first approximations of pi to the shape of our limitless universe, from the essential usefulness of differential equations to the troubles with infinite sums, we present the great ideas of mathematical geniuses all along History., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Cryptography and Number Theory Cryptography and Number Theory

By Scott McKinney | **Updated:**2012-12 | **Views**: 4079

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

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

The Beauty of Ellipses, Parabolas and Hyperbolas The Beauty of Ellipses, Parabolas and Hyperbolas

By Lê Nguyên Hoang | **Updated:**2013-10 | **Views**: 14280

The conic sections, that is, ellipses, parabolas and hyperbolas, are too often presented analytically. Yet, their amazing beauty is actually their spectacular geometry, as well as their omnipresence! This article presents plenty of illustrative descriptions of their uncountable applications!, by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Probabilistic Algorithms, Probably Better Probabilistic Algorithms, Probably Better

By Lê Nguyên Hoang | **Updated:**2013-08 | **Views**: 1017

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 4620

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2485

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Scott McKinney | **Updated:**2013-01 | **Views**: 2039

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

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

A Mathematical Guide to Selling A Mathematical Guide to Selling

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1209

How to best sell a good? Should we auction it like in movies? Since the 1960s, economists have addressed this question mathematically and found surprising results. Most notably, in 1981, Nobel prize winner Roger Myerson proved that most auctions you could think of would win you just as much as any basic auction, but that, as well, you could do better using his approach. Since, today, billions of dollars are at play in online auctions, you can imagine how hot a topic it has now become!, by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Massive Puzzles of Gravity The Massive Puzzles of Gravity

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 1763

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-02 | **Views**: 2522

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Scott McKinney | **Updated:**2013-04 | **Views**: 939

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

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

Numbers and Constructibility Numbers and Constructibility

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 3345

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Thibault_Lehouillier | **Updated:**2012-10 | **Views**: 1180

, by Thibault_Lehouillier Thibault_Lehouillier

PhD candidate at Ecole Polytechnique of Montréal (Canada)

Engineer of the ENSIMAG (France)

Evolutionary Game Theory Evolutionary Game Theory

By Lê Nguyên Hoang | **Updated:**2014-02 | **Views**: 2215

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Multicriteria with MACBETH Multicriteria with MACBETH

By Lê Nguyên Hoang | **Updated:**2013-07 | **Views**: 1513

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 1041

A large chunk of applied mathematics has focused on optimizing something with respect to all relevant data. However, in practice, especially in the online world, the data is not available to us, and, yet, we’re still expected to make nearly optimal decisions. This problem is exemplified by the famous secretary problem, where a manager needs to decide to hire candidates right after interviews, even though he has not yet met all the candidates. In this article, we review this classic as well as many very recent developments., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Imaginary and Complex Numbers Imaginary and Complex Numbers

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 3509

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 1222

In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) circle and sphere., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 3351

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2587

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Harmonious Mathematics of Music The Harmonious Mathematics of Music

By Lê Nguyên Hoang | **Updated:**2015-02 | **Views**: 1367

It was when hearing the sounds of hammers that Pythagoras realized the ubiquity of numbers in mathematical harmony. He would go on laying down the mathematical foundations of music, based on octaves, perfect fifths and major thirds. This mathematics of music would then become the favourite playground of all musicians, from Beethoven to Gangnam Style., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Univalent Foundations of Mathematics Univalent Foundations of Mathematics

By Lê Nguyên Hoang | **Updated:**2015-01 | **Prerequisites: **Type Theory: A Modern Computable Paradigm for Math, Homotopy Type Theory and Higher Inductive Types | **Views**: 1659

In an effort to make mathematics more computable, a consortium of today’s greatest mathematicians have laid out new foundations. Amazingly, they all lie upon one single axiom, called univalence. The goal of this axiom is to make formal mathematics more similar to informal mathematics. With univalence, our Arabic numbers aren’t just like natural numbers; They are natural numbers. Univalence also has unforeseen and mesmerizing consequences., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-05 | **Views**: 1898

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Spacetime of Special Relativity Spacetime of Special Relativity

By Lê Nguyên Hoang | **Updated:**2014-03 | **Views**: 1890

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Geological Wonders of Iceland Geological Wonders of Iceland

By Lê Nguyên Hoang | **Updated:**2013-06 | **Views**: 1047

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Shannon’s Information Theory Shannon’s Information Theory

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 12035

Claude Shannon may be considered one of the most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Yet, unfortunately, he is virtually unknown to the public. This article is a tribute to him. And the best way I’ve found is to explain some of the brilliant ideas he had., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2013-12 | **Views**: 7187

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 3219

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 7445

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Revolutionary Galois Theory The Revolutionary Galois Theory

By Lê Nguyên Hoang | **Updated:**2014-12 | **Prerequisites: **Linear Algebra and Higher Dimensions, Imaginary and Complex Numbers, Symmetries and Group Theory | **Views**: 9844

In 1832, Évariste Galois died. He was 20. The night before his death, he wrote a legendary letter to his friend, in which he claims to have found a mathematical treasure! Sadly, this treasure had long been buried in total indifference! It took nearly a century to rediscover it! Since then, Galois’ legacy has become some of the finest pure mathematics, which represents a hugely active field of research today with crucial applications to cryptography. Galois’ work is now known as Galois theory. In essence, it unveils the hidden symmetries of numbers!, by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Proof by Mathematical Induction Proof by Mathematical Induction

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 4314

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Tortuous Geometry of the Flat Torus The Tortuous Geometry of the Flat Torus

By Lê Nguyên Hoang | **Updated:**2015-05 | **Views**: 7104

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!, by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

## Here’s what they say about Science4All…

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

— SciAfterSchool (@SciAfterSchool) January 28, 2013

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

— Emma Alexander (@emmaaaaa8) November 27, 2012

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

— IMUVA (@IMUVA_) March 7, 2013

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

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

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

— Berlanda Mauro (@mauroberlanda) April 12, 2013

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

— Fawn Nguyen (@fawnpnguyen) April 18, 2013

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

— Derek Muller (@veritasium) April 18, 2013

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

— James Grime (@jamesgrime) May 17, 2013

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

— Jennifer Crouch (@JenniferCrouch) May 30, 2013

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

— Avivah Yamani (@ivie97) June 5, 2013

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

— Fawn Nguyen (@fawnpnguyen) June 20, 2013

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

— Joshua Bowman (@Thalesdisciple) June 21, 2013

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

— Alexander Bogomolny (@CutTheKnotMath) June 21, 2013

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

— James Grime (@jamesgrime) June 21, 2013

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

— Fawn Nguyen (@fawnpnguyen) July 22, 2013

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

— David Valin (@gbdavid1) July 22, 2013

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

— Margarita Parra (@BMPM1) September 9, 2013

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

— Arthur Doohan (@artied) September 29, 2013

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

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

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

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

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

— James Grime (@jamesgrime) November 7, 2013

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

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

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

— MathDaily (@MathDaily) November 28, 2013

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

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

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

— AmericanMathSociety (@amermathsoc) December 23, 2013

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

— InTheNext10Years (@inthenext10year) December 25, 2013

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

— Nick Gotch (@pszNicx) December 30, 2013

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

— Xavi (@nymiro) December 30, 2013

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

— James Grime (@jamesgrime) January 10, 2014

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

— Danica McKellar (@danicamckellar) February 21, 2014

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

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

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

— Adam Mandelman (@amandelman) February 25, 2014

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

— LucasVB (@LucasVB) March 16, 2014

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

— Rimwe (@RimweLLC) April 27, 2014

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

— Dave Radcliffe (@daveinstpaul) June 20, 2014

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

— Kirk Borne (@KirkDBorne) July 8, 2014

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

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

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

— Anita Hall (@ani2tall) September 24, 2014

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

— Prasad Gokhale (@Prasad_Gokhale) September 28, 2014

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

— Kim Langen (@KimLangen) October 2, 2014

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

— Numan Sheikh (@numansheikh) October 13, 2014

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

— Pankaj Saraf (@saraf_pankaj) December 21, 2014

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

— Vandana Narasimhan (@vandy_ie) December 25, 2014

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

— Prasad Gokhale (@Prasad_Gokhale) January 10, 2015

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

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

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

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

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

— 상일 (@sioum) April 2, 2015