# 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**: 1464

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**: 1694

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**: 1446

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.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2845

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.

Linear Algebra and Higher Dimensions Linear Algebra and Higher Dimensions

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 2715

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

The Magic of Algebra The Magic of Algebra

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 2070

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-02 | **Prerequisites: **The Essence of Quantum Mechanics, Imaginary and Complex Numbers, Linear Algebra and Higher Dimensions | **Views**: 3844

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Computing Hunger worldwide: the Global Hunger Index (GHI) Computing Hunger worldwide: the Global Hunger Index (GHI)

By Estève Giraud | **Updated:**2014-04 | **Views**: 405

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. , by Estève Giraud Estève Giraud

I hold a MSc in Management from Toulouse Business School (France). I currently work as a MRes/PhD student in University Pompeu Fabra (Barcelona, Spain) and research on ethical mindsets in business.

Colours and Dimensions Colours and Dimensions

By Lê Nguyên Hoang | **Updated:**2015-09 | **Views**: 1335

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 785

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Column Generation and Dantzig-Wolfe Decomposition Column Generation and Dantzig-Wolfe Decomposition

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Linear Algebra and Higher Dimensions, Optimization by Linear Programming | **Views**: 3153

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., 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.

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

By Lê Nguyên Hoang | **Updated:**2014-11 | **Views**: 18325

The second law of thermodynamics is my favorite law in physics, mainly because of the troubling puzzles it raises! Indeed, what your professors may have forgotten to tell you is that this law connects today’s world to its first instant, the Big Bang! Find out why!, by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-09 | **Views**: 3814

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-06 | **Views**: 6668

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 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**: 7774

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.

A Mathematical Guide to Selling A Mathematical Guide to Selling

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1635

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.

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

By Lê Nguyên Hoang | **Updated:**2013-04 | **Views**: 1289

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 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**: 4785

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.

Regulation of Electricity Markets Regulation of Electricity Markets

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 1245

Electricity markets are not like any markets. In particular, they cannot be liberalized without regulation. In the article, I list the reasons why this market is specific and I conclude by giving you important features of a good regulation., by Lê Nguyên Hoang 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**: 1223

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.

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

By Scott McKinney | **Updated:**2013-01 | **Views**: 2308

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.

Duality in Linear Programming Duality in Linear Programming

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Optimization by Linear Programming, Linear Algebra and Higher Dimensions | **Views**: 9479

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-03 | **Views**: 1833

In 2010, a controversial article published in Nature violently criticized the last 40 years of developments in evolutionary biology, triggering an ongoing war within the scientific community. This article explains the essence of the controversy!, by Lê Nguyên Hoang 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**: 3316

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 Surprising Flavor of Infinite Series The Surprising Flavor of Infinite Series

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 5502

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 Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

Primal and Dual Simplex Methods Primal and Dual Simplex Methods

By Lê Nguyên Hoang | **Updated:**2014-05 | **Prerequisites: **Optimization by Linear Programming, Duality in Linear Programming | **Views**: 5544

The simplex method is one of the major algorithm of the 20th century, as it enables the resolution of linear problems with millions of variables. An intuitive approach is given. But that’s not all. We present an important variant called the dual simplex. Finally, we’ll explain its main default, that is, when facing degeneracy., by Lê Nguyên Hoang 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**: 2154

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.

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

By Scott McKinney | **Updated:**2013-04 | **Views**: 994

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.

Geological Wonders of Iceland Geological Wonders of Iceland

By Lê Nguyên Hoang | **Updated:**2013-06 | **Views**: 1103

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.

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

By Lê Nguyên Hoang | **Updated:**2015-04 | **Views**: 1464

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.

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

By Lê Nguyên Hoang | **Updated:**2014-04 | **Views**: 1376

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.

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

By Lê Nguyên Hoang | **Updated:**2014-02 | **Views**: 2661

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.

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**: 1828

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.

Construction and Definition of Numbers Construction and Definition of Numbers

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 3775

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 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**: 8043

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.

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

By Scott McKinney | **Updated:**2013-04 | **Views**: 2492

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.

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

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 3047

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 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**: 4432

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.

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

By Lê Nguyên Hoang | **Updated:**2013-12 | **Views**: 960

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

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2015-01 | **Views**: 6794

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 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**: 2681

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.

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

By Lê Nguyên Hoang | **Updated:**2014-06 | **Views**: 7606

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 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**: 1446

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.

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

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 25049

In 1988, Euler’s identity was elected most beautiful theorem of mathematics. It has been widely taught worldwide. But have you ever stopped to really sense the meaning of this incredible formula? This article does., by Lê Nguyên Hoang Lê Nguyên Hoang

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

PhD from Polytechnique Montreal. MS from Polytechnique ParisTech.

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

By Lê Nguyên Hoang | **Updated:**2014-01 | **Views**: 1382

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.

The Magic of Analysis The Magic of Analysis

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 1150

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.

A Model of Football Games A Model of Football Games

By Lê Nguyên Hoang | **Updated:**2014-10 | **Views**: 4034

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.

Cryptography and Number Theory Cryptography and Number Theory

By Scott McKinney | **Updated:**2012-12 | **Views**: 4357

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.

Poincaré Conjecture and Homotopy Poincaré Conjecture and Homotopy

By Lê Nguyên Hoang | **Updated:**2014-12 | **Views**: 4820

Poincaré conjecture is the most recent major proven theorem. Posited a century ago by Henri Poincaré, this major conjecture of topology was solved by Gregori Perelman. It has revolutionized our understanding of space and raised intriguing questions regarding the global structure of our Universe., by Lê Nguyên Hoang 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**: 2001

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.

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