Quotes About Mathematics

If you take your thumb and your index finger and look right where they meet - go ahead and do that now - and relax your hand, you'll see a crinkle, and then a wrinkle within the crinkle, and a crinkle within the wrinkle. Right? Your body is covered with fractals.

I have passed English medical examinations in Hong Kong... In my youth, I experienced overseas studies. The languages of the West, its literature, its political science, its customs, its mathematics, its geography, its physics and chemistry - all these I have had the chance to study.

Mathematicians are always playing tricks on each other. They're always pulling jokes on each other.

I do not love to be printed on every occasion, much less to be dunned and teased by foreigners about mathematical things or to be thought by our own people to be trifling away my time about them when I should be about the king's business.

Without troublesome work, no one can have any concrete, full idea of what pure mathematical research is like or of the profusion of insights that can be obtained from it.

If mathematics is to be understood widely, we need to emphasise its elegance and its applications. Sometimes it seems that universities want to emphasise how difficult it is!

For reasons nobody understands, the universe is deeply mathematical. Maybe God made it that way. Or maybe it's the only way a universe with us in it could be, because nonmathematical universes can't harbor life intelligent enough to ask the question. In any case, it's a mysterious and marvelous fact that our universe obeys laws of nature that always turn out to be expressible in the language of calculus as sentences called differential equations.

It relied on measures of geometrical objects: lengths of lines, areas of squares, volumes of cubes. All of these they called magnitudes. They thought of them as distinct from numbers and superior to them. This, I believe, is why Archimedes held pi at arm's length. He didn't know what to make of it. It was a strange, transcendent creature, more exotic than any number.

Yet twenty-two trillion is nothing compared to the infinitude of digits that define the actual pi. Think of how philosophically disturbing this is.

Mathematically, circles embody change without change.

Whenever some aspect of nature doesn't care about direction, circles are bound to appear.

It isn't necessary to learn how to do calculus to appreciate it, just as it isn't necessary to learn how to prepare fine cuisine to enjoy eating it.

the idea of using infinity to solve difficult geometry problems has to rank as one of the best ideas anyone ever had.

Creation is intuitive; reason comes later. In the story of calculus, more than in other parts of mathematics, logic has always lagged behind intuition. This makes the subject feel especially human and approachable, and its geniuses more like the rest of us.

What I've just described is called a system of differential equations. Such equations arise whenever we have rules for speeds depending on current positions.

Though we couldn't see how to explain these results mathematically, an intuitive explanation suggested itself: The shortcuts were providing high-speed communication channels, enabling mutual influence to spread swiftly throughout the population. Of course, the same effect could have been achieved by connecting every oscillator directly to every other, but at a much greater cost in wiring. The small-world architecture apparently fostered global coordination more efficiently.

From a purely mathematical perspective, a power law signifies nothing in particular—it's just one of many possible kinds of algebraic relationship. But when a physicist sees a power law, his eyes light up. For power laws hint that a system may be organizing itself. They arise at phase transitions, when a system is poised at the brink, teetering between order and chaos. They arise in fractals, when an arbitrarily small piece of a complex shape is a microcosm of the whole.

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

Mindless, lifeless things can sync spontaneously. The sympathy of clocks taught us that the capacity for sync does not depend on intelligence, or life, or natural selection. It springs from the deepest source of all: the laws of mathematics and physics.

No matter how erratically something moves, the area accumulated under its speed curve up to time t always equals the total distance it has traveled up to that time.

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I BET I CAN guess your favorite math subject in high school. It was geometry.

Thus, calculus proceeds in two phases: cutting and rebuilding. In mathematical terms, the cutting process always involves infinitely fine subtraction, which is used to quantify the differences between the parts. Accordingly, this half of the subject is called differential calculus. The reassembly process always involves infinite addition, which integrates the parts back into the original whole. This half of the subject is called integral calculus.

Circles are the simplest curves in geometry. Yet, surprisingly, measuring them—quantifying their properties with numbers—transcends geometry.