Tag Archives: Mathematics

The Triangle of Power

September 18, 2016Article962 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!

Category Theory, Isomorphism, Functor (More Hiking in Modern Math World 7/7)

March 06, 2016More Hiking in Modern Math World2284 vuesEdit

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.

The Harmonious Mathematics of Music

February 10, 2015Article2761 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, 2015Article2163 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!

Colours and Dimensions

January 08, 2015Article1716 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 Magic of Analysis

December 05, 2014Article1418 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.

The Magic of Algebra

September 23, 2014Article2498 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, 2014Article5196 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, 2014Article11877 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, 2014Article2366 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, 2014Article2057 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.

Type Theory: A Modern Computable Paradigm for Math

March 20, 2014Article8359 vuesEdit
In 2013, three dozens of today's brightest minds have just laid out new foundation of mathematics after a year of collective effort. This new paradigm better fits both informal and computationally-checkable mathematics. There is little doubt that it will fundamentally change our perspective on rigorous knowledge, and it could be that, in a few decades, the book they published turns out to be the bedrock of all mathematics, and, by extension, all human knowledge! Have a primer of this upcoming revolution, with this article on type theory, the theory that the book builds upon!

The Tortuous Geometry of the Flat Torus

March 09, 2014Article10619 vuesEdit
Take a square sheet of paper. Can you glue opposite sides without ever folding the paper? This is a conundrum that many of the greatest modern mathematicians, like Gauss, Riemann, and Mandelbrot, couldn't figure out. While John Nash did answer yes, he couldn't say how. After 160 years of research, Vincent Borrelli and his collaborators have finally provided a revolutionary and breathtaking example of a bending of a square sheet of paper! And it is spectacularly beautiful!

The Most Beautiful Equation of Math: Euler’s Identity

February 18, 2014Article47946 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 New Big Fish Called Mean-Field Game Theory

February 05, 2014Article8490 vuesEdit
In recent years, at the interface of game theory, control theory and statistical mechanics, a new baby of applied mathematics was given birth. Now named mean-field game theory, this new model represents a new active field of research with a huge range of applications! This is mathematics in the making!

The Revolutionary Galois Theory

January 05, 2014Article12347 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!

Linear Algebra and Higher Dimensions

November 27, 2013Article3398 vuesEdit
Linear algebra is a one of the most useful pieces of mathematics and the gateway to higher dimensions. Using Barney Stinson's crazy-hot scale, we introduce its key concepts.

Numbers and Constructibility

November 05, 2013Article4907 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!

Logarithms and Age Counting

October 09, 2013Article2901 vuesEdit
Amusingly, the age difference between a 45-year-old man and a 25-year-old woman doesn't seem as big as the age difference between them 20 years earlier, when the woman was a little 5-year-old girl. This remark was the insight the late science popularizer Albert Jacquart liked to give to his readers to explain logarithms. This article pays tribute to the great scientist by introducing age difference as he liked to tell it.