Science4All

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.

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P versus NP: A Crucial Open Problem

P versus NP: A Crucial Open Problem
By Lê Nguyên Hoang | Updated:2016-01 | Views: 6188
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.

The Most Beautiful Equation of Math: Euler’s Identity

The Most Beautiful Equation of Math: Euler’s Identity
By Lê Nguyên Hoang | Updated:2016-01 | Views: 70537
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.

Topology: from the Basics to Connectedness

Topology: from the Basics to Connectedness
By Lê Nguyên Hoang | Updated:2016-02 | Views: 5653
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.

Shannon’s Information Theory

Shannon’s Information Theory
By Lê Nguyên Hoang | Updated:2016-01 | Views: 39410
Claude Shannon may be considered one of the most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Yet, unfortunately, he is virtually unknown to the public. This article is a tribute to him. And the best way I’ve found is to explain some of the brilliant ideas he had.

The Triangle of Power

The Triangle of Power
By Lê Nguyên Hoang | Updated:2016-10 | Views: 5131
Notations do not matter to the essence of mathematics. But poor notations can be misleading. Notations based on exponents, radicals and logarithms definitely are. They are very distinct, even though they are supposed to describe very similar relations between numbers. The triangle of power is a recently proposed alternative. In short, I am convinced!

Multicriteria with MACBETH

Multicriteria with MACBETH
By Lê Nguyên Hoang | Updated:2016-02 | Views: 2546
As more and more complex problems are dealt with in our societies, developing models such as multi-criteria analysis is crucial to better understand these problems. MACBETH is a state-of-the-art method to do just that. Its functioning is described in this article.

Column Generation and Dantzig-Wolfe Decomposition

Column Generation and Dantzig-Wolfe Decomposition
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Linear Algebra and Higher Dimensions, Optimization by Linear Programming | Views: 7476
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.

Symmetries and Group Theory

Symmetries and Group Theory
By Lê Nguyên Hoang | Updated:2016-02 | Views: 2987
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.

The Beauty of Ellipses, Parabolas and Hyperbolas

The Beauty of Ellipses, Parabolas and Hyperbolas
By Lê Nguyên Hoang | Updated:2016-01 | Views: 46847
The conic sections, that is, ellipses, parabolas and hyperbolas, are too often presented analytically. Yet, their amazing beauty is actually their spectacular geometry, as well as their omnipresence! This article presents plenty of illustrative descriptions of their uncountable applications!

Univalent Foundations of Mathematics

Univalent Foundations of Mathematics
By Lê Nguyên Hoang | Updated:2015-12 | Prerequisites: Type Theory: A Modern Computable Paradigm for Math, Homotopy Type Theory and Higher Inductive Types | Views: 3381
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.

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