“ Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes K… Mario Livio
“ The strength of the familiar electromagnetic force between two electrons, for example, is expressed in physics in terms of a constant known as the fine structure constant. The value of this constant,… Mario Livio
“ 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… Mario Livio
“ Tegmark argues that our universe is not just described by mathematics-it is mathematics [emphasis added]. His argument starts with the rather uncontroversial assumption that an external physical reali… Mario Livio
“ Nature loves logarithmic spirals. From sunflowers, seashells, and whirlpools, to hurricanes and giant spiral galaxies, it seems that nature chose this marvelous shape as its favorite ornament. The con… Mario Livio
“ 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 o… Mario Livio
“ The legendary inscription above the Academy's door speaks loudly about Plato's attitude toward mathematics. In fact, most of the significant mathematical research of the fourth century BC was carried… Mario Livio
“ The realization that symmetry is the key to the understanding of the properties of subatomic particles led to an inevitable question: Is there an efficient way to characterize all of these symmetries… Mario Livio
“ The number 6 was the first perfect number, and the number of creation. The adjective perfect was attached that are precisely equal to the sum of all the smaller numbers that divide into them, as 6=1+2… Mario Livio
“ Unlike classically spinning bodies, such as tops, however, where the spin rate can assume any value fast or slow, electrons always have only one fixed spin. In the units in which this spin is measured… Mario Livio
“ 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 t… Mario Livio
“ The teleological argument, or argument from design, attempts to furnish evidence for God's existence from the apparent design of the world. Mario Livio
“ Populations typically have such high reproduction potential that if unchecked they would increase exponentially. Mario Livio
“ The biggest stumbling block that has traditionally plagued all the unification endeavors has been the simple fact that on the face of it, general relativity and quantum mechanics really appear to be i… Mario Livio
“ 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
“ 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
“ Moreover, Galileo argued that by pursuing science using the language of mechanical equilibrium and mathematics, humans could understand the divine mind. Mario Livio
“ What can we conclude from all of these insights in terms of the role of symmetry in the cosmic tapestry? My humble personal summary is that we don't know yet whether symmetry will turn out to be the m… Mario Livio
