37 Quotes by Mario Livio

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.

While composite faces tend, by construction, to also be more symmetric, Langlois found that even after the effects of symmetry have been controlled, averageness was still judged to be attractive. These findings argue for a certain level of prototyping in the mind, since averageness might well be coupled with a prototypical template.

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.

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

While Euclid himself may not have been the greatest mathematician who ever lived, he was certainly the greatest teacher of mathematics.

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.

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.

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.

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