Tag Archives: Numbers

The Triangle of Power

September 18, 2016Article943 vuesEdit
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!

MIT Glimpse (Episode 4)

April 02, 2016Web0 vuesEdit
I was interviewed in November 2015 by Alex Albanese on MIT Glimpse. We discussed Benford’s law, cake cutting, and online optimization. We also discussed how to pick the right toilet, why pi sucks, and why you should watch plenty of Youtube videos!

Can you “add” colours? Relativity 5

March 24, 2016Relativity1349 vuesEdit

Why is π so interesting? Relativity 1

March 16, 2016Relativity1242 vuesEdit

Big Numbers, Googol, Googolplex, Graham (Trek through Math 7/8)

February 06, 2016A Trek through 20th Century Mathematics1556 vuesEdit

The Harmonious Mathematics of Music

February 10, 2015Article2759 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 Magic of Algebra

September 23, 2014Article2495 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 Addictive Mathematics of the 2048 Tile Game

June 04, 2014Article11852 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!

Univalent Foundations of Mathematics

April 21, 2014Article2364 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.

Homotopy Type Theory and Higher Inductive Types

April 06, 2014Article2051 vuesEdit
In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) circle and sphere.

The Most Beautiful Equation of Math: Euler’s Identity

February 18, 2014Article47842 vuesEdit
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.

The Revolutionary Galois Theory

January 05, 2014Article12328 vuesEdit
In 1832, Évariste Galois died. He was 20. The night before his death, he wrote a legendary letter to his friend, in which he claims to have found a mathematical treasure! Sadly, this treasure had long been buried in total indifference! It took nearly a century to rediscover it! Since then, Galois' legacy has become some of the finest pure mathematics, which represents a hugely active field of research today with crucial applications to cryptography. Galois' work is now known as Galois theory. In essence, it unveils the hidden symmetries of numbers!

Numbers and Constructibility

November 05, 2013Article4904 vuesEdit
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!

Imaginary and Complex Numbers

August 29, 2013Article4743 vuesEdit
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).

The Surprising Flavor of Infinite Series

July 01, 2013Article7012 vuesEdit
1+2+4+8+16+...=-1, as proven by Henry Reich on Minute Physics! Now, as a mathematician, I must say that his proof is far from being rigorous. In fact, anyone familiar with the surprising flavor of infinite series should not find it convincing. Surprisingly though, his proof can be rigorously and naturally justified! Find out how!

Proof by Mathematical Induction

June 09, 2013Article5097 vuesEdit
This article explores the potency of proofs by induction with 4 different stunning puzzles, from a lock puzzle and a lion issue, to the monk problem and the pencil conundrum!

Construction and Definition of Numbers

December 07, 2012Article4651 vuesEdit
Although they have been used for thousands of years, an actual definition of numbers was given less than a century ago! From the most fundamental level of set theory, this article takes you to the journey of the construction of natural, integer, rational, real and complex numbers.