Quotes about mathematics

Galileo wrote that 'the book of nature is written in the language of mathematics; without its help it is impossible to comprehend a single word of it.'

Yes. God makes the world using mathematics, and he has given us minds that can see it. We can discover the laws He used! It is a most beautiful thing to witness and understand! It's prayer. It's more than prayer, it's a sacrament, a kind of communion. An apprehension—an epiphany—it's seeing God, while still in this body and in this world! How blessed we are, to be able to experience God like that! Who would not devote their time to understanding more, to seeing deeper in God's manner of thinking about these things?

The world operates by number, by physical laws, expressed mathematically. If you know these, you will have a better grasp of things. And some possible job skills.

And so he struggled on. As he did he saw it anew, as fresh as in his undergraduate days: the structure of science was so beautiful. It was surely one of the greatest achievements of the human spirit, a kind of stupendous parthenon of the mind, constantly a work in progress, like a symphonic epic poem of thousands of stanzas, being composed by them all in a giant ongoing collaboration. The language of the poem was mathematics, because this appeared to be the language of nature itself; there was no other way to explain the startling adherence of natural phenomena to mathematical expressions of great difficulty and subtlety. And so in this marvelous family of languages their songs explored the various manifestations of reality, in different fields of science, and each science worked up its standard model to explain things, all constellating at some distance around the basics of particle physics, depending on what level or scale was being investigated, so that all the standard models hopefully interlocked in a coherent larger structure.

Waves striking the sea cliffs bounced back outward, creating interference patterns with the incoming waves that could have come right out of a physics wave tank: so beautiful. And so strange, that the world should conform so well to mathematical formulation. The unreasonable effectiveness of math; it was at the heart of the great unexplainable.

Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.

Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.

Mathematical knowledge may, just like our scientific knowledge, be deep and broad, it may be subtle and wonderfully explanatory, it may be uncontroversially accepted; but it cannot be certain.

Gödel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not sufficient to reduce the statement to marks on paper and to study the behavior of the marks. Except in trivial cases, you can decide the truth of a statement only by studying its meaning and its context in the larger world of mathematical ideas.

I doubt not, but from self-evident Propositions, by necessary Consequences, as incontestable as those in Mathematics, the measures of right and wrong might be made out.

...I don't believe in the idea that there are a few peculiar people capable of understanding math and the rest of the world is normal. Math is a human discovery, and it's no more complicated than humans can understand. I had a calculus book once that said, "What one fool can do, another fool can." What we've been able to work out about nature may look abstract and threatening to someone who hasn't studied it, but it was fools who did it, and in the next generation, all the fools will understand it. There's a tendency to pomposity in all this, to make it all deep and profound...

Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another.