Ian Stewart Quotes

Chaos is lawless behavior governed entirely by law.

Math is a product of human minds but not bendable to human will

Maxwell's equations didn't just change the world. They opened up a new one.

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

The urban myth that carrots are good for your eyesight originated in wartime disinformation, intended to stop the Nazis wondering why the British were getting so good at spotting raiding bombers.

Our teaching of mathematics revolves around a fundamental conflict. Rightly or wrongly, students are required to master a series of mathematical concepts and techniques, and anything that might divert them from doing so is deemed unnecessary. Putting mathematics into its cultural context, explaining what is has done for humanity, telling the story of its historical development, or pointing out the wealth of unsolved problems or even the existence of topics that do not make it into school textbooks leaves less time to prepare for the exam. So most of these things aren't discussed.

Only three constants are significant for star formation: the gravitational constant, the fine structure constant, and a constant that governs nuclear reaction rates.

I don't want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that - by some mysterious agency - capture patterns of the universe around us? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.

In mathematics, it's unwise to abandon an interesting idea just because it's wrong.

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.

Music can be appreciated from several points of view: the listener, the performer, the composer. In mathematics there is nothing analogous to the listener; and even if there were, it would be the composer, rather than the performer, that would interest him. It is the creation of new mathematics, rather than its mundane practice, that is interesting. Mathematics is not about symbols and calculations. These are just tools of the tradequavers and crotchets and five-finger exercises. Mathematics is about ideas. In particular it is about the way that different ideas relate to each other. If certain information is known, what else must necessarily follow? The aim of mathematics is to understand such questions by stripping away the inessentials and penetrating to the core of the problem. It is not just a question of getting the right answer; more a matter of understanding why an answer is possible at all, and why it takes the form that it does. Good mathematics has an air of economy and an element of surprise. But, above all, it has significance.

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

if a theorem is geometrically obvious why prove it? This was exactly the attitude taken in the eighteenth century. The result, in the nineteenth century, was chaos and confusion: for intuition, unsupported by logic, habitually assumes that everything is much nicer behaved than it really is. Good

The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does.

First is first, and second is nowhere.

There are 10 kinds of people in the world: those who understand binary numerals, and those who don't.

Mathematicians need proofs to keep them honest. All technical areas of human activity need reality checks. It is not enough to believe that something works, that it is a good way to proceed, or even that it is true. We need to know why it's true. Otherwise, we won't know anything at all.

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.

To criticize mathematics for its abstraction is to miss the point entirely. Abstraction is what makes mathematics work. If you concentrate too closely on too limited an application of a mathematical idea, you rob the mathematician of his most important tools: analogy, generality, and simplicity. Mathematics is the ultimate in technology transfer.

Two centuries ago Carl Friedrich Gauss, one of the greatest mathematicians and a founder of number theory, described his brainchild as "the queen of mathematics." Queens are regal, but they are also largely decorative, and this nuance was not lost on Gauss.