Ian Stewart Quotes & Sayings

Mathematicians are beginning to view order and chaos as two distinct manifestations of an underlying determinism. And neither state exists in isolation. The typical system can exist in a variety of states, some ordered, some chaotic. Instead of two opposed polarities, there is a continuous spectrum. As harmony and discord combine in musical beauty, so order and chaos combine in mathematical [and physical] beauty. — Ian Stewart

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 — Ian Stewart

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

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. — Ian Stewart

The power of equations lies in the philosophically difficult correspondence between mathematics, a collective creation of human minds, and an external physical reality. Equations model deep patterns in the outside world. By learning to value equations, and to read the stories they tell, we can uncover vital features of the world around us ... — Ian Stewart

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. — Ian Stewart

Most information doesn't constitute a story. Think of a telephone directory: lots of information, strong cast, but a bit weak on narrative. What counts in a story is its meaning. And that's a very different concept from information. — Ian Stewart

Chaos is lawless behavior governed entirely by law. — Ian Stewart

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

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. — Ian Stewart

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

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

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. — Ian Stewart

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

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. — Ian Stewart

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. — Ian Stewart

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. — Ian Stewart

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. — Ian Stewart

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. — Ian Stewart

IQ is a statistical method for quantifying specific kinds of problem-solving ability, mathematically convenient but not necessarily corresponding to a real attribute of the human brain, and not necessarily representing whatever it is that we mean by 'intelligence'. — Ian Stewart

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. — Ian Stewart

Let us weigh the gain and the loss in wagering that God is [exists]. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is ... There is here an infinity of an infinitely happy life to gain, a chance of gain against a finite number of chances of loss, and what you stake is finite. And so our proposition is of infinite force, when there is the finite to stake in a game where there are equal risks of gain and of loss, and the infinite to gain. — Ian Stewart

Unless you are genuinely interested in working with someone, don't. It doesn't matter how big an expert they are, or how much grant money the project would bring in. Stay away from things that do not interest you. — Ian Stewart

First is first, and second is nowhere. — Ian Stewart

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