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.
Proof by Mathematical Induction
Proof by Mathematical Induction
By Lê Nguyên Hoang | Updated:2015-12 | Views: 5455
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!
Proof by Mathematical InductionBy Lê Nguyên Hoang | Updated:2015-12 | Views: 5455
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!
Poincaré Conjecture and Homotopy Poincaré Conjecture and Homotopy
By Lê Nguyên Hoang | Updated:2016-01 | Views: 6489
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: 6489
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.
The Limitless Vertigo of Cantor’s Infinite The Limitless Vertigo of Cantor’s Infinite
By Lê Nguyên Hoang | Updated:2015-12 | Views: 2527
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: 2527
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 Magic of Analysis The Magic of Analysis
By Lê Nguyên Hoang | Updated:2016-02 | Views: 1563
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: 1563
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.
Mechanism Design and the Revelation Principle Mechanism Design and the Revelation Principle
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4139
Whenever you need to make a group of people interact, you are designing a mechanism. If you want to achieve a good interaction, you need to make sure your mechanism is well designed. In this article, I’ll show you main features of mechanisms through various examples. I’ll also talk about a great mathematical tool for mechanism design: the revelation principle.
Mechanism Design and the Revelation PrincipleBy Lê Nguyên Hoang | Updated:2016-02 | Views: 4139
Whenever you need to make a group of people interact, you are designing a mechanism. If you want to achieve a good interaction, you need to make sure your mechanism is well designed. In this article, I’ll show you main features of mechanisms through various examples. I’ll also talk about a great mathematical tool for mechanism design: the revelation principle.
Advanced Game Theory Overview Advanced Game Theory Overview
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Game Theory and the Nash Equilibrium | Views: 4934
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: 4934
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.
Numbers and Constructibility Numbers and Constructibility
By Lê Nguyên Hoang | Updated:2016-02 | Views: 5789
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: 5789
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!
Does God play dice?
Does God play dice?
By Arthur Marronnier | Updated:2016-02 | Views: 1096
For Albert Einstein, the answer is no. But what did he mean? Has the greatest theoretical physicist of all time really missed the bandwagon of quantum physics? What are the real issues of the controversy that has opposed him to the Copenhagen School (Bohr, Heisenberg …)? Back to the physics of the early twentieth century, its history, philosophy and ideas.
Does God play dice?By Arthur Marronnier | Updated:2016-02 | Views: 1096
For Albert Einstein, the answer is no. But what did he mean? Has the greatest theoretical physicist of all time really missed the bandwagon of quantum physics? What are the real issues of the controversy that has opposed him to the Copenhagen School (Bohr, Heisenberg …)? Back to the physics of the early twentieth century, its history, philosophy and ideas.
Homotopy Type Theory and Higher Inductive Types Homotopy Type Theory and Higher Inductive Types
By Lê Nguyên Hoang | Updated:2015-12 | Views: 6572
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: 6572
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.
Web Programming: From HTML to AJAX Web Programming: From HTML to AJAX
By Lê Nguyên Hoang | Updated:2016-02 | Views: 3474
The Internet is an unavoidable component of today’s life, and will only become more and more important in the future. In this article, we”ll have an overview of its development in terms of coding languages. This article explains how webpages actually work. In particular, we’ll discuss HTML, CSS, PHP, WordPress, MySQL, Javascript, XML and JSON, as well as their competitors.
Web Programming: From HTML to AJAXBy Lê Nguyên Hoang | Updated:2016-02 | Views: 3474
The Internet is an unavoidable component of today’s life, and will only become more and more important in the future. In this article, we”ll have an overview of its development in terms of coding languages. This article explains how webpages actually work. In particular, we’ll discuss HTML, CSS, PHP, WordPress, MySQL, Javascript, XML and JSON, as well as their competitors.
