Tag Archives: Algebra

The Triangle of Power

September 18, 2016Article1345 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!

The Poincaré conjecture | Relativité 21

June 08, 2016Relativity7983 vuesEdit

Can you “add” colours? Relativity 5

March 24, 2016Relativity1429 vuesEdit

The Magic of Algebra

September 23, 2014Article2549 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 Most Beautiful Equation of Math: Euler’s Identity

February 18, 2014Article50437 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, 2014Article12702 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, 2013Article3495 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.

Imaginary and Complex Numbers

August 29, 2013Article4841 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).

Space Deformation and Group Representation

February 22, 2013Article1962 vuesEdit
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.

Symmetries and Group Theory

October 21, 2012Article2183 vuesEdit
Beauty is extremely hard to define. Yet, physicists and artists seem to agree on an important feature of beauty, created by mathematicians: Symmetries. This article aims at introducing the beauty and the concepts on symmetries, from the basic geometrical symmetries to the more abstract fundamental automorphisms.