#### 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**: 11042Most 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.

Model-Dependent Realism Model-Dependent Realism

By Lê Nguyên Hoang |

Introduced by the two renowned theoretical physicists Stephen Hawking and Leonard Mlodinov in their book The Grand Design in 2010, model-dependent realism is a new controversial understanding of the universe. Based on solid logical reasonings and recent developments in physics, this concept may well be an incredible breakthrough for philosophy and science, as well as metaphysics.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 3134Introduced by the two renowned theoretical physicists Stephen Hawking and Leonard Mlodinov in their book The Grand Design in 2010, model-dependent realism is a new controversial understanding of the universe. Based on solid logical reasonings and recent developments in physics, this concept may well be an incredible breakthrough for philosophy and science, as well as metaphysics.

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

By Lê Nguyên Hoang |

Colours… 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 colourful!

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 3087Colours… 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 colourful!

Santa Routing and Heuristics in Operations Research Santa Routing and Heuristics in Operations Research

By Lê Nguyên Hoang |

Designing routes to visit customers has become one of applied mathematicians’ favorite optimization problems, as companies offer millions to solve them! This article discusses the clever technics they have come up with, and use them to help Santa deliver toys to kids all over the world!

By Lê Nguyên Hoang |

**Updated:**2016-01 |**Views**: 6078Designing routes to visit customers has become one of applied mathematicians’ favorite optimization problems, as companies offer millions to solve them! This article discusses the clever technics they have come up with, and use them to help Santa deliver toys to kids all over the world!

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

By Herminio López |

By Herminio López |

**Updated:**2016-02 |**Views**: 703Temperature Misconception: Heat is Not How it Feels Temperature Misconception: Heat is Not How it Feels

By Lê Nguyên Hoang |

In the last FIFA football world cup, many players complain about Manaus’ unbearable heat condition. Yet, the thermometer only went up to 30°C (86°F). Why is that? Well, as it turns out, how you feel is not really the outside temperature. This article unveils many of our deep misconceptions about heat.

By Lê Nguyên Hoang |

**Updated:**2015-12 |**Views**: 2044In the last FIFA football world cup, many players complain about Manaus’ unbearable heat condition. Yet, the thermometer only went up to 30°C (86°F). Why is that? Well, as it turns out, how you feel is not really the outside temperature. This article unveils many of our deep misconceptions about heat.

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

By Lê Nguyên Hoang |

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 |

**Updated:**2016-02 |**Prerequisites:**The Essence of Quantum Mechanics, Imaginary and Complex Numbers, Linear Algebra and Higher Dimensions |**Views**: 6122On 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!

Univalent Foundations of Mathematics Univalent Foundations of Mathematics

By Lê Nguyên Hoang |

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 |

**Updated:**2015-12 |**Prerequisites:**Type Theory: A Modern Computable Paradigm for Math, Homotopy Type Theory and Higher Inductive Types |**Views**: 2887In 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.

Mechanism Design and the Revelation Principle Mechanism Design and the Revelation Principle

By Lê Nguyên Hoang |

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.

By Lê Nguyên Hoang |

**Updated:**2016-02 |**Views**: 3758Whenever 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.

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

By Scott McKinney |

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 |

**Updated:**2015-12 |**Views**: 1402Dynamical 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.