Quotes from Mario Livio

Pythagoras apparently wrote nothing, and yet his influence was so great that the more attentive of his followers formed a secretive society, or brotherhood, and were known as the Pythagoreans. Aristippus of Cyrene tells us in his Account of Natural Philosphers that Pythagoras derived his name from the fact that he was speaking (agoreuein) truth like the God at Delphi (tou Pythiou).

Mind-boggling, isn't it? Centuries before the question of why mathematics was so effective in explaining nature was even asked, Galileo thought he already knew the answer! To him, mathematics was simply the language of the universe. To understand the universe, he argued, one must speak this language. God is indeed a mathematician.

Noether's theorem fused together symmetries and conservation laws-these two giant pillars of physics are actually nothing but different facets of the same fundamental property.

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.

Creators are hard-driving, focused, dominant, independent risk-takers.

Tolerance of ambiguity is a necessary condition for creativity.

The teleological argument, or argument from design, attempts to furnish evidence for God's existence from the apparent design of the world.

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.

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 themselves, or could be introduced, simplicity crystallized out of comparative chaos.

populations typically have such high reproduction potential that if unchecked they would increase exponentially.

The environment is the agent that does the shaking of the sieve.

In mathematics, if you are of quick mind, you can get to the frontline of cutting-edge research very quickly. In some other domains you may have to read entire thick volumes first. Moreover, if you have been for too long in a certain domain, you get conditioned to think like everybody else. When you are new, you are not compelled to the ideas of the people around you. The younger you are, the more likely you are to be truly original.

Is it odd how asymmetrical Is 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 reading.

One of Lindon's amusing word-unit palindromes reads: Girl, bathing on Bikini, eyeing boy, finds boy eyeing bikini on bathing girl. Other palindromes are symmetric with respect to back-to-front reading letter by letter-Able was I ere I saw Elba (attributed jokingly to Napoleon), or the title of a famous NOVA program: A Man, a Plan, a Canal, Panama.

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.

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.

Having witnessed in his own life much agony and the horrors of war, Kepler concluded that Earth really created two notes, mi for misery (miseria in Latin) and fa for famine (fames in Latin). In Kepler's words: the Earth sings MI FA MI, so that even from the syllable you may guess that in this home of ours Misery and Famine hold sway.

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 responsible for a mingling of mathematics, philosophy of life, and religion unparalleled in history. In this respect it is perhaps interesting to note the historical coincidence that Pythagoras was a contemporary of Buddha and Confucius.

Leonardo had considerable interest in geometry, especially for its practical applications in mathematics. In his words: Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics.

Lagrange was born in Turin (now Italy), but his family was partly French ancestry on his father's side, who was originally wealthy, managed to squander all the family's fortune in speculations, leaving his son with no inheritance. Later in life, Lagrange described this economic catastrophe as the best thing that had ever happened to him: Had I inherited a fortune I would probably not have cast my lot with mathematics.

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.

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 overemphasized, and I will return to it several times. Other symmetries do exist, however, and they are equally relevant.

Accordingly, Pacioli's book also starts with a discussion of proportions in the human body, since in the human body every sort of proportion and proportionality can be found, produced at the beck of the all-Highest through the inner mysteries of nature.

No one, especially not Birkhoff himself, would claim that the intricacies of aesthetic pleasure could be reduced entirely to a mere formula. However, in Birkhoff's words, In the inevitable analytic accompaniment of the creative process, the theory of aesthetic measure is capable of performing a double service: it gives a simple, unified account of the aesthetic experience, and it provides means for the systematic analysis of typical aesthetic fields.