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 symmetry is truly fundamental to the universe itself, or merely to the universe as perceived by humans, thus becomes particularly acute.

In it, Porphyry says about Pythagoras: “He himself could hear the harmony of the Universe, and understood the music of the spheres, and the stars which move in concert with them, and which we cannot hear because of the limitations of our weak nature.

Some ancient Indian texts claim that numbers are almost divine, or “Brahma-natured.

Moreover, Galileo argued that by pursuing science using the language of mechanical equilibrium and mathematics, humans could understand the divine mind.

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, scientists have selected what problems to work on based on those problems being amenable to a mathematical treatment.

Indeed, the quality that made Newton’s theories truly stand out-the inherent characteristic that turned them into inevitable laws of nature-was precisely the fact that they were all expressed as crystal-clear, self-consistent mathematical relations.

Note that a rotation by 360 degrees is equivalent to doing nothing at all, or rotating by zero degrees. This is known as the identity transformation. Why bother to define such a transformation at all? As we shall see later in the book, the identity transformation plays a similar role to that of the number zero in the arithmetic operation of addition or the number one in multiplication-when you add zero to a number or multiply a number by one, the number remains unchanged.

Here, however, is where his genius truly took off. Galois managed to associate with each equation a sort of “genetic code” of that equation-the Galois group of the equation-and to demonstrate that the properties of the Galois group determine whether the equation is solvable by a formula or not. Symmetry became the key concept, and the Galois group was a direct measure of the symmetry properties of an equation.

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.

Supersymmetry is a subtle symmetry based on the quantum mechanical property spin.