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

By Thibault_Lehouillier |

By Thibault_Lehouillier |

**Updated:**2016-02 |**Views**: 2632Symmetries 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**: 3253Beauty 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.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 6020Topology 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.

What Makes a Published Result Believable? What Makes a Published Result Believable?

By Lê Nguyên Hoang |

This article discusses the validity of scientific results.

By Lê Nguyên Hoang |

**Updated:**2019-06 |**Views**: 159This article discusses the validity of scientific results.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 3415A 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 Tortuous Geometry of the Flat Torus The Tortuous Geometry of the Flat Torus

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Views**: 15294Take 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**Linear Algebra and Higher Dimensions, Optimization by Linear Programming |**Views**: 8107Column 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.

The Revolutionary Galois Theory The Revolutionary Galois Theory

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**Linear Algebra and Higher Dimensions, Imaginary and Complex Numbers, Symmetries and Group Theory |**Views**: 17135In 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 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!

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Views**: 6304Differential calculus is one of the most important concept of mathematics for science and engineering. This article focuses on its fundamental meaning.