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

The Biology Civil War Opposing Kin to Group Selection

The Biology Civil War Opposing Kin to Group Selection
By Lê Nguyên Hoang | Updated:2015-12 | Views: 4468
In 2010, a controversial article published in Nature violently criticized the last 40 years of developments in evolutionary biology, triggering an ongoing war within the scientific community. This article explains the essence of the controversy!

Self-Reference, Math Foundations and Gödel's Incompleteness

Self-Reference, Math Foundations and Gödel's Incompleteness
By Lê Nguyên Hoang | Updated:2016-02 | Views: 6625
Although highly appreciated by artists, self-reference has been a nightmare for mathematicians. It took one of the greatest, Kurt Gödel, to provide a better understanding of it. This article deals with paradoxes, recursion, fractals and Gödel's incompleteness theorems.

Imaginary and Complex Numbers

Imaginary and Complex Numbers
By Lê Nguyên Hoang | Updated:2016-02 | Views: 6845
My first reaction to imaginary numbers was... What the hell is that? Even now, I have trouble getting my head around these mathematical objects. Fortunately, I have a secret weapon: Geometry! This article proposes constructing complex numbers with a very geometrical and intuitive approach, which is probably very different from what you've learned (or will learn).

Colors: It's not just about Wavelengths!

Colors: It's not just about Wavelengths!
By Lê Nguyên Hoang | Updated:2016-02 | Views: 7474
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!

The Cubic Ball of the 2014 FIFA World Cup

The Cubic Ball of the 2014 FIFA World Cup
By Lê Nguyên Hoang | Updated:2016-02 | Views: 9747
I know this sounds crazy. Even stupid. But Adidas did design a cubic ball, called brazuca, for the 2014 World Cup. And, yet, this cubic ball is rounder than any previous ball in football History. How is it possible? This article explains it.

Probabilistic Algorithms, Probably Better

Probabilistic Algorithms, Probably Better
By Lê Nguyên Hoang | Updated:2016-02 | Views: 1992
Probabilities have been proven to be a great tool to understand some features of the world, such as what can happen in a dice game. Applied to programming, it has enabled plenty of amazing algorithms. In this article, we discuss its application to the primality test as well as to face detection. We'll also deal with quantum computers, as well as fundamental computer science open problems P=BPP and NP=BQP.

Space Deformation and Group Representation

Space Deformation and Group Representation
By Lê Nguyên Hoang | Updated:2015-12 | Views: 2752
All along the 20th century, pure algebraists have dug deep into the fundamental structures of mathematics. In this extremely abstract effort, they were greatly help by the possibility of representing these structures by space deformations, which could then be understood much better. This has led to breakthroughs, including the proof of Fermat's las theorem. This article introduces the ideas of group representations.

Santa Routing and Heuristics in Operations Research

Santa Routing and Heuristics in Operations Research
By Lê Nguyên Hoang | Updated:2016-01 | Views: 8285
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!

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: 4269
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.

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: 13895
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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