Top 35 Mario Livio Quotes (2025 Update)

1. “Tolerance of ambiguity is a necessary condition for creativity.”

— Mario Livio

2. “Put simply, the cosmological argument claims that since the physical world had to come into existence somehow, there must be a First Cause, namely, a creator God.”

— Mario Livio

3. “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.”

— Mario Livio

4. “For Newton, the world’s very existence and the mathematical regularity of the observed cosmos were evidence for God’s presence.”

— Mario Livio

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

— Mario Livio

6. “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.”

— Mario Livio

7. “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.”

— Mario Livio

8. “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.”

— Mario Livio

9. “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.”

— Mario Livio

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

— Mario Livio

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

— Mario Livio

12. “The Golden Ratio has the unique properties that we produce its square by simply adding the number 1 and its reciprocal by subtracting the number 1.”

— Mario Livio

13. “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.”

— Mario Livio

14. “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.”

— Mario Livio

15. “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.”

— Mario Livio

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

— Mario Livio

17. “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.”

— Mario Livio

18. “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.”

— Mario Livio

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

— Mario Livio

20. “Our mathematics is the symbolic counterpart of the universe we perceive, and its power has been continuously enhanced by human exploration.”

— Mario Livio

21. “Indeed, the genius of Abel and Galois could be compared only to a supernova-an exploding star that for a short while outshines all the billions of stars in its host galaxy.”

— Mario Livio

22. “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.”

— Mario Livio

23. “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.”

— Mario Livio

24. “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.”

— Mario Livio

25. “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.”

— Mario Livio

26. “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.”

— Mario Livio

27. “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.”

— Mario Livio

28. “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.”

— Mario Livio

29. “The environment is the agent that does the shaking of the sieve.”

— Mario Livio

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

— Mario Livio

31. “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.”

— Mario Livio

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

— Mario Livio

33. “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.”

— Mario Livio

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

— Mario Livio

35. “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.”

— Mario Livio

36. “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.”

— Mario Livio

37. “Galileo was hailed as a Columbus of the heavens. The Scottish librarian Thomas Segeth raved: “Columbus gave man lands to conquer by bloodshed, Galileo new worlds harmful to none. Which is better?”

— Mario Livio

38. “Galileo established what has since become the modern approach to the study of all natural phenomena.”

— Mario Livio