Tag Archives: Topology

The Poincaré conjecture | Relativité 21

June 08, 2016Relativity6608 vuesEdit

Can you glue opposite edges of a square? Relativity 7

April 05, 2016Relativity2642 vuesEdit

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

January 30, 2016A Trek through 20th Century Mathematics2127 vuesEdit

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

January 29, 2016A Trek through 20th Century Mathematics1152 vuesEdit

The Harmonious Mathematics of Music

February 10, 2015Article2719 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 Analysis

December 05, 2014Article1401 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 Addictive Mathematics of the 2048 Tile Game

June 04, 2014Article11680 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, 2014Article2343 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, 2014Article2009 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 Tortuous Geometry of the Flat Torus

March 09, 2014Article10432 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!

Imaginary and Complex Numbers

August 29, 2013Article4707 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).

Euler’s Formula and the Utilities Problem

June 20, 2013Article8379 vuesEdit
I was a kid when I was first introduced to the deceptively simple utilities problem. It's only lately that I've discovered its solution! And it's an amazing one! Indeed, it provides a wonderful insight into some fundamental mathematics, including Euler's formula! This is nothing less than the gateway to the wonderful world of algebraic topology!

Poincaré Conjecture and Homotopy

March 25, 2013Article5754 vuesEdit
Poincaré conjecture is the most recent major proven theorem. Posited a century ago by Henri Poincaré, this major conjecture of topology was solved by Gregori Perelman. It has revolutionized our understanding of space and raised intriguing questions regarding the global structure of our Universe.

Topology: from the Basics to Connectedness

December 20, 2012Article4126 vuesEdit
Topology was my favorite course in pure maths. I love it because it's a powerful abstract theory to describe intuitive and visual ideas about space. This article gives you an introduction to this amazing field. We'll introduce graph topology, metric spaces, continuity and connectedness.