Ivars Peterson

“As the mathematician Clifford Taubes noted, “Physics is the study of the world, while mathematics is the study of all possible worlds.” Thus, mathematics unveils the infinite possibilities; physics pinpoints the few that structure our universe and our existence.”

“To an increasing number of practitioners, computer simulations rooted in mathematics represent a third way of doing science, alongside theory and experiment.”

“More often than not, a piece of mathematics worked out years before—and believed to be totally without practical value—finds a role in the “real” world.”

“Randomness, chaos, uncertainty, and chance are all a part of our lives. They reside at the ill-defined boundaries between what we know, what we can know, and what is beyond our knowing. They make life interesting.”

“The aim of science is to reduce the scope of chance.”

“Indeed, mathematics is full of conjectures—questions waiting for answers—with no assurance that the answers even exist.”

“Tversky was fond of describing his work as “debugging human intuition.”...Tversky could establish again and again the existence of mismatches between intuition and probability—between cognitive illusion and reality.”

“Most coincidences are simply chance events that turn out to be far more probable than many people imagine.”

“In mathematics, in science, and in life, we constantly face the delicate, tricky task of separating design from happenstance.”

“Ramsey theory implies that complete disorder is impossible. Somehow, no matter how complicated, chaotic, or random something appears, deep within that morass lurks a smaller entity that has a definite structure. Striking regularities are bound to arise even in a universe that has no rules.”

“The theory of probability combines commonsense reasoning with calculation. It domesticates luck, making it subservient to reason.”

“Intriguingly, the mathematics of randomness, chaos, and order also furnishes what may be a vital escape from absolute certainty—an opportunity to exercise free will in a deterministic universe. Indeed, in the interplay of order and disorder that makes life interesting, we appear perpetually poised in a state of enticingly precarious perplexity. The universe is neither so crazy that we can’t understand it at all nor so predictable that there’s nothing left for us to discover.”