Chaos is lawless behavior governed entirely by law.

One of the biggest problems of mathematics is to explain to everyone else what it is all about. The technical trappings of the subject, its symbolism and formality, its baffling terminology, its apparent delight in lengthy calculations: these tend to obscure its real nature. A musician would be horrified if his art were to be summed up as "a lot of tadpoles drawn on a row of lines"; but that"s all that the untrained eye can see in a page of sheet music... In the same way, the symbolism of mathematics is merely its coded form, not its substance.

Mathematics is the science of patterns, and nature exploits just about every pattern that there is.

Religion hinges upon faith, politics hinges upon who can tell the most convincing lies or maybe just shout the loudest, but science hinges upon whether its conclusions resembe what actually happens.

...a major triumph of mathematical imagination: the use of visual imagery to condense a large quantity of information into a single comprehensible picture... Mathematicians are just beginning to understand these basic building blocks of change and to analyze how they combine. The methodology involved has a very different spirit from traditional modeling with differential equations: it is more like chemistry than calculus, requiring careful counterpoint between analysis and synthesis.

During the past fifty years, more mathematics has been created than in all previous ages put together.

If our brains were simple enough for us to understand them, we'd be so simple that we couldn't.