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.
I now run a Robustly Beneficial wiki, mostly on AI ethics, which has come to fascinate me!

Check my articles

Symmetries and Group Theory

Symmetries and Group Theory
By Lê Nguyên Hoang | Updated:2016-02 | Views: 4175
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 forces of Nature: from Newton to String Theory

The forces of Nature: from Newton to String Theory
By Thibault_Lehouillier | Updated:2016-02 | Views: 2792

Spacetime of Special Relativity

Spacetime of Special Relativity
By Lê Nguyên Hoang | Updated:2016-02 | Views: 3192
Einstein's theory of relativity is the best-known breakthrough of the History of science. The reason for that isn't only the accuracy of the theory, but also and mainly its beauty. As Einstein once said: "Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone." This is what the article aims at showing Einstein's simple ideas of special relativity and their beauty.

Mechanism Design and the Revelation Principle

Mechanism Design and the Revelation Principle
By Lê Nguyên Hoang | Updated:2016-02 | Views: 5544
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.

The Amazing Physics of Water in Trees

The Amazing Physics of Water in Trees
By Lê Nguyên Hoang | Updated:2016-01 | Views: 50835
As explained by Derek Muller on Veritasium, the flow of water in trees involves complex physical phenomena including pressure, osmosis, negative pressure, capillarity and evapotranspiration. What seems simple will blow your mind!

Numbers and Constructibility

Numbers and Constructibility
By Lê Nguyên Hoang | Updated:2016-02 | Views: 7417
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!

The Massive Puzzles of Gravity

The Massive Puzzles of Gravity
By Lê Nguyên Hoang | Updated:2016-02 | Views: 3815
This article follows the footsteps of the giants of physics that have moulded our current understanding of gravity. It is a series of brilliant inspirations, usually accompanied by deceiving misconceptions. After all, even today, gravity is still a slippery concept.

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: 80975
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.

Primal and Dual Simplex Methods

Primal and Dual Simplex Methods
By Lê Nguyên Hoang | Updated:2016-02 | Prerequisites: Optimization by Linear Programming, Duality in Linear Programming | Views: 22763
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.

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: 9680
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.

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