Ivars Peterson

"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."

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

"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."

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

"The aim of science is to reduce the scope of chance."

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

"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."

"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."