All posts by Lê Nguyên Hoang

The Greatest Challenge of Mathematics | White Group Maths

February 03, 2016Web0 vuesEdit
This is a guest post I wrote on White Group Mathematics on December 30, 2012.

Shannon’s Information Theory (Trek through Math 5/8)

February 03, 2016A Trek through 20th Century Mathematics0 vuesEdit

Fractals, Mandelbrot, Pixar (Trek through Math 4/8)

February 01, 2016A Trek through 20th Century Mathematics0 vuesEdit

Topology, Homotopy and Poincaré’s Conjecture (Trek through Math 3/8)

January 30, 2016A Trek through 20th Century Mathematics0 vuesEdit

Graphs and the 4 Color Theorem (Trek through Math 2/8)

January 29, 2016A Trek through 20th Century Mathematics0 vuesEdit

Linear Programming (Trek through Math 1/8)

January 28, 2016A Trek through 20th Century Mathematics0 vuesEdit

The Secretary/Toilet Problem and Online Optimization

April 02, 2015Article5514 vuesEdit
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.

The Harmonious Mathematics of Music

February 10, 2015Article16755 vuesEdit
It was when hearing the sounds of hammers that Pythagoras realized the ubiquity of numbers in mathematical harmony. He would go on laying down the mathematical foundations of music, based on octaves, perfect fifths and major thirds. This mathematics of music would then become the favourite playground of all musicians, from Beethoven to Gangnam Style.

The Limitless Vertigo of Cantor’s Infinite

January 29, 2015Article4075 vuesEdit
No one believed him. Not even fellow mathematicians. They thought he was wrong. They thought he was crazy. Even he ended up doubting himself and went crazy. And yet, he had mathematically proved it all. Georg Cantor had figured out how to manipulate the infinite. Even more remarkable, he showed that there were actually several infinities; and some are bigger than others!

A Mathematical Guide to Selling

January 19, 2015Article5168 vuesEdit
How to best sell a good? Should we auction it like in movies? Since the 1960s, economists have addressed this question mathematically and found surprising results. Most notably, in 1981, Nobel prize winner Roger Myerson proved that most auctions you could think of would win you just as much as any basic auction, but that, as well, you could do better using his approach. Since, today, billions of dollars are at play in online auctions, you can imagine how hot a topic it has now become!

Colours and Dimensions

January 08, 2015Article4737 vuesEdit
You've probably learned early on that there are three primary colours. But why three? And why these three? Surprisingly, the answer lies in the beautiful mathematics of linear algebra and (high) dimension spaces!

The Massive Puzzles of Gravity

December 11, 2014Article4271 vuesEdit
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 Magic of Analysis

December 05, 2014Article1935 vuesEdit
This article retraces the endless pursuit of the infinite that is at the basis of mathematical analysis. From the first approximations of pi to the shape of our limitless universe, from the essential usefulness of differential equations to the troubles with infinite sums, we present the great ideas of mathematical geniuses all along History.

Temperature Misconception: Heat is Not How it Feels

October 03, 2014Article3047 vuesEdit
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.

The Magic of Algebra

September 23, 2014Article3854 vuesEdit
The power of algebra lies in abstraction, and abstraction is basically forgetting. By retracing the History of algebra from its roots to more recent advancements, this article unveils the numerous breakthrough in our understanding of the world, by abusing of the power of forgetting.

The Cubic Ball of the 2014 FIFA World Cup

June 24, 2014Article9705 vuesEdit
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.

The Addictive Mathematics of the 2048 Tile Game

June 04, 2014Article29451 vuesEdit
2048 is the Internet sensation of the year. This very addictive game has been downloaded hundred of millions of times. Interestingly, this game raises plenty of intriguing mathematical questions. This article unveils some of them!

Column Generation and Dantzig-Wolfe Decomposition

May 24, 2014Article13805 vuesEdit
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.

The Unlikely Correctness of Newton’s Laws

April 30, 2014Article9566 vuesEdit
Do moving objects exhaust? Does the Moon accelerate? How strong is the gravity pull of the Moon on the Earth compared to that of the Earth on the Moon? While we've all learned Newton's laws of motion, many of us would get several answers of these questions wrong. That's not so surprising, as Newton's laws are deeply counter-intuitive. By stressing their weirdness with Veritasium videos, this article dives into a deep understanding of classical mechanics.

Univalent Foundations of Mathematics

April 21, 2014Article4263 vuesEdit
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.