37 Quotes by Mario Livio

The Greek excellence in mathematics was largely a direct consequence of their passion for knowledge for its own sake, rather than merely for practical purposes. A story has it that when a student who learned one geometrical proposition with Euclid asked, “But what do I gain from this?” Euclid told his slave to give the boy a coin, so that the student would see an actual profit.

Because of the “divine” properties attributed to the Golden Ratio, mathematician Clifford A. Pickover suggested that we should refer to that point as “the Eye of God.

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.

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

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.

Group theory has been called by the noted mathematics scholar James R. Newman “the supreme art of mathematical abstraction.” It derives its incredible power from the intellectual flexibility afforded by its definition.

The key point to keep in mind, however, is that symmetry is one of the most important tools in deciphering nature’s design.

The Golden Rectangle is the only rectangle with the property that cutting a square from it produces a similar rectangle.

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.