Pythagoras is in fact credited with having coined the words philosophy (love of wisdom) and mathematics (that which is learned). To him, a philosopher was someone who gives himself up to discovering t...
One of the string theory pioneers, the Italian physicist Daniele Amati, characterized it as part of the 21st century that fell by chance into the 20th century. Indeed, there is something about the ver...
On the question of whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt-mathematics was real, immutable, omnipresent, and more sublime than anything that could...
Even though it is almost impossible to attribute with certainty any specific mathematical achievements either to Pythagoras himself or to his followers, there is no question that they have been respon...
As we shall see throughout this book, the unifying powers of group theory are so colossal that historian of mathematics Eric Temple Bell (1883-1960) once commented, When ever groups disclosed themselv...
You may begin to realize that groups will pop up wherever symmetries exist. In fact, the collection of all the symmetry transformations of any system always from a group.
Wolfram, one of the most innovative thinkers in scientific computing and in the theory of complex systems, has been best known for the development of Mathematica, a computer program/system that allows...
The result that Noether obtained was stunning. She showed that to every continuous symmetry of the laws of physics there corresponds a conservation law and vice versa. In particular, the familiar symm...
So mathematics is indeed extraordinarily effective for some descriptions, especially those dealing with fundamental science, but it cannot describe our universe in all its dimensions. To some extent,...
In the Middle Ages, the Elements was translated into Arabic three times. The first of these translations was carried out by al-Hajjaj ibn Yusuf ibn Matar, at the request of Caliph Harun ar-Rashid (rul...
The result that Noether obtained was stunning. She showed that to every continuous symmetry of the laws of physics there corresponds a conservation law and vice versa.
The properties that define a group are:1. Closure. The offspring of any two members combined by the operation must itself be a member. In the group of integers, the sum of any two integers is also an...
The Pythagoreans were probably the first to recognize the concept that the basic forces in the universe may be expressed through the language of mathematics.
Is it odd how asymmetricalIs symmetry?Symmetry is asymmetrical.How odd it is.This stanza remains unchanged if read word by word from the end to the beginning-it is symmetrical with respect to backward...
In the late 1960's, physicists Steven Weinberg, Abdus Salam, and Sheldon Glashow conquered the next unification frontier. In a phenomenal piece of scientific work they showed that the electromagnetic...
Either because of mate selection, cognition, predator avoidance, or a combination of all three, our minds are attracted to and are finely tuned to the detection of symmetry. The question of whether sy...
Vấn đề là thông qua sự ham hiểu biết cháy bỏng, sự cố chấp bướng bỉnh, trí tưởng tượng sáng tạo và một quyết tâm mạnh mẽ, loài người đã tìm ra những hình thức luận toán học thích hợp cho việc lập mô h...
The two solutions of the equation for the Golden Ratio are:x1 = (1+ Sqr5) / 2x2 = (1 - Sqr5) / 2
The importance of mirror-reflection symmetry to our perception and aesthetic appreciation, to the mathematical theory of symmetries, to the laws of physics, and to science in general, cannot be overem...
The beauty of the principle idea of string theory is that all the known elementary particles are supposed to represent merely different vibration modes of the same basic string. Just as a violin or a...