Quotes About Mathematics

Do you know why I love mathematics? Because it blew your mind for free when you couldn't get drugs? Eccles snorted in surprise. Well, yes, but there's another reason.

But Einstein refused to be mathematics' pawn. He bucked the equations in favor of his intuition about how the cosmos should be, his deep-seated belief that the universe was eternal and, on the largest of scales, fixed and unchanging. The universe, Einstein admonished Lemaître, is not now expanding and never was.

Extraordinary emblems of math's ability to illuminate the dark corners of the cosmos, black holes have become the cynosures of modern physics.

Stephen Hawking showed mathematically that the entropy of a black hole equals the number of Planck-sized cells that it takes to cover its event horizon. It's as if each cell carries one bit, one basic unit of information.

Physicists traced the failure to the jitters of quantum uncertainty. Mathematical techniques had been developed for analyzing the jitters of the strong, weak, and electromagnetic fields, but when the same methods were applied to the gravitational field-a field that governs the curvature of spacetime itself-they proved ineffective. This left the mathematics saturated with inconsistencies such as infinite probabilities.

We need a means for measuring the sizes of different infinite collections of universes. It is this information that we need in order to work out how likely it is that we reside in one type of universe rather than another. Until we find a fundamental dictum for how we should compare infinite collections of universes, we won't be able to foretell mathematically what typical multiverse dwellers-us-should see in experiments and observations. Solving the measure problem is imperative.

By shaping our intuition and developing our cognitive skills, evolution initiated our education in physics but our more comprehensive understanding has emerged from the force of human curiosity expressed through the language of mathematics.

The entropy of a system is related to the number of indistinguishable rearrangements of its constituents, but properly speaking is not equal to the number itself. The relationship is expressed by a mathematical operation called a logarithm; don't be put off if this brings back bad memories of high school math class. In our coin example, it simply means that you pick out the exponent in the number of rearrangements-that is, the entropy is defined as 1,000 rather than 2^1000.

Notice that the value of the entropy and the amount of hidden information are equal. That's no accident. The number of possible heads-tails rearrangements is the number of possible answers to the 1,000 questions-(yes,yes,no,no,yes,...) or (yes,no,yes,yes,no,...) or (no,yes,no,no,no,...), and so on-namely, 2^1000. With entropy defined as the logarithm of the number of such rearrangements-1,000 in this case-entropy is the number of yes-no questions any one such sequence answers.

can envision a future when scientists will be able to provide a mathematically complete articulation of the fundamental microphysical processes underlying anything that happens, anywhere and anywhen.

I can envision calculations all the way to infinity," she said, as if in a trance. "I don't have to write them down.

The astonishing fact is that similar mathematics applies so well to planets and to clocks. It needn't have been this way. We didn't impose it on the Universe. That's the way the Universe is. If this is reductionism, so be it.

Nevertheless his prodigious intellectual powers persisted unabated. In 1696, the Swiss mathematician Johann Bernoulli challenged his colleagues to solve an unresolved issue called the brachistochrone problem, specifying the curve connecting two points displaced from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time.

Kepler and Newton represent a critical transition in human history, the discovery that fairly simple mathematical laws pervade all of Nature; that the same rules apply on Earth as in the skies; and that there is a resonance between the way we think and the way the world works.

The progress and perfection of mathematics are linked closely with the prosperity of the state.

The fifth regular solid must then, they thought, correspond to some fifth element that could only be the substance of the heavenly bodies.

No even number is prime, for example.

As ages passed, people learned from their ancestors. The more accurately you knew the position and movements of the Sun and Moon and stars, the more reliably you could predict when to hunt, when to sow and reap, when to gather the tribes. As precision of measurement improved, records had to be kept, so astronomy encouraged observation and mathematics and the development of writing.

Presumably no one would argue that the conservative view on the sum of 14 and 27 differs from the liberal view

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.

Sooner or later all things are numbers, yes?

You could trust numbers, except perhaps for pi, but he was working on that in his spare time and it was bound to give in sooner or later.

Newton and Descartes started to try and prove that God existed in the same way as they would try and prove something in the laboratory or with their mathematics And when you try and mix science and religion you get bad science and bad religion. The two are doing two different things. ... Science can give you a diagnosis of cancer. It can even cure your disease, but it cannot touch your grief and disappointment, nor can it help you to die well.

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