#### 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.

Spacetime of General Relativity Spacetime of General Relativity

By Lê Nguyên Hoang |

Most popular science explanations of the theory of general relativity are very nice-looking. But they are also deeply misleading. This article presents you a more accurate picture of the spacetime envisioned by Albert Einstein.

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 12541Most popular science explanations of the theory of general relativity are very nice-looking. But they are also deeply misleading. This article presents you a more accurate picture of the spacetime envisioned by Albert Einstein.

The Surprising Flavor of Infinite Series The Surprising Flavor of Infinite Series

By Lê Nguyên Hoang |

1+2+4+8+16+…=-1, as proven by Henry Reich on Minute Physics! Now, as a mathematician, I must say that his proof is far from being rigorous. In fact, anyone familiar with the surprising flavor of infinite series should not find it convincing. Surprisingly though, his proof can be rigorously and naturally justified! Find out how!

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 91401+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!

Duality in Linear Programming Duality in Linear Programming

By Lê Nguyên Hoang |

Duality in linear programming yields plenty of amazing results that help understand and improve algorithms of resolution. This article shows the construction of the dual and its interpretation, as well as major results. In particular, matching of primal and dual bases will be dealt, before presenting the issue of degeneracy and its dual interpretation.

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Prerequisites:**Optimization by Linear Programming, Linear Algebra and Higher Dimensions |**Views**: 19063Duality 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.

Symmetries and Group Theory Symmetries and Group Theory

By Lê Nguyên Hoang |

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.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 3254Beauty 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 Addictive Mathematics of the 2048 Tile Game The Addictive Mathematics of the 2048 Tile Game

By Lê Nguyên Hoang |

2048 is the Internet sensation of the year. This very addictive game has been downloaded hundred of millions of times. Interestingly, this game raises plenty of intriguing mathematical questions. This article unveils some of them!

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 179962048 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!

Primal and Dual Simplex Methods Primal and Dual Simplex Methods

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**Optimization by Linear Programming, Duality in Linear Programming |**Views**: 20632The 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.

Proof by Mathematical Induction Proof by Mathematical Induction

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 5832This 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!

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

By Lê Nguyên Hoang |

While mountaineers aim at tops of mountains, some scientists have sought the bottom of temperature scale with frequent surprising wonders at different scales. This article takes you through these scientists’ journey!

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 2199While 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!

Poincaré Conjecture and Homotopy Poincaré Conjecture and Homotopy

By Lê Nguyên Hoang |

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 |

**Updated:**2016-01 |**Views**: 6934Poincaré 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.

Euclidean Geometry and Navigation Euclidean Geometry and Navigation

By Scott McKinney |

This is the first of a series of three posts. In this post we’ll see how the Greeks developed a system of geometry – literally “Earth measure” – to assist with planetary navigation. We then will see why their assumption that the Earth is flat means that Euclidean geometry is insufficient for studying the Earth. The Earth’s spherical surface looks flat from our perspective, but is actually qualitatively different from a flat surface. In the ensuing posts, we’ll see why this implies that it is impossible to make a perfectly accurate map of the Earth, and build on this idea to get a glimpse into Einstein’s revolutionary theories regarding the geometry of the space-time universe.

By Scott McKinney |

**Updated:**2016-02 |**Views**: 5585This is the first of a series of three posts. In this post we’ll see how the Greeks developed a system of geometry – literally “Earth measure” – to assist with planetary navigation. We then will see why their assumption that the Earth is flat means that Euclidean geometry is insufficient for studying the Earth. The Earth’s spherical surface looks flat from our perspective, but is actually qualitatively different from a flat surface. In the ensuing posts, we’ll see why this implies that it is impossible to make a perfectly accurate map of the Earth, and build on this idea to get a glimpse into Einstein’s revolutionary theories regarding the geometry of the space-time universe.