Quotes About Arithmetic

in 1900, David Hilbert listed what he considered to be the twenty-three most important unsolved problems of mathematics. The second item on his list was a request for a proof of the consistency of arithmetic. Such a proof would ensure the consistency of a great deal of higher mathematics. What this proof had to guarantee was, in essence, that one could never prove one equals two. Few mathematicians regarded this as a matter of much import.

That's right. Arithmetic as a formal system is inconsistent.

By the end of the nineteenth century, the best that was achieved was a proof that Euclidean geometry was consistent as long as arithmetic was consistent.

Golf is just a lot of walking, broken up by disappointment and bad arithmetic.

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.

Crystals grew inside rock like arithmetic flowers. They lengthened and spread, added plane to plane in an awed and perfect obedience to an absolute geometry that even stones - maybe only the stones - understood.

Convert any common fraction to a decimal fraction by dividing the lower number (denominator) into the upper number (numerator). For example, ¾ = 3 + 4 = 0.75. The result is also known as a proportion. Multiply it by 100 to convert it into a percentage. Recognition

There's a very simple point about arithmetic—if you happen to be in a swing state, a state where the outcome is indefinite, and you don't vote for, say, Clinton, that's equivalent to voting for Trump. That's arithmetic.

music is the arithmetic of sounds as optics is the geometry of light

The whole of arithmetic now appeared within the grasp of mechanism.

The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic, because in arithmetic there is knowledge, but in theology there is only opinion.

The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.

The bottle, with its impotent message, was gone out to sea, and the problem that it had provoked was reduced to a simple sum in addition—one and one make two, by the rule of arithmetic; one by the rule of romance.

We don't carry in subtraction, however; we borrow, and that involves an intrinsically different mechanism—a messy back-and-forth kind of thing.

Music is a hidden arithmetic exercise of the soul, which does not know that it is counting.

This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem - and in particular to perform integration - you have to be smart about which integration technique should be used: integration by partial fractions, integration by parts, and so on.

Fundamental to understanding the arithmetic of Rd is the following question: which ordinary prime numbers p are irreducible elements of Rd and which ones factorize as products of irreducible elements in Rd? We will see shortly that if a prime number does factorize in Rd, it must be expressible as the product of precisely two irreducible factors.

He's teaching her arithmetic, He said it was his mission, He kissed her once and said, Now that's addition. And as he added smack by smack In silent satisfaction, She sweetly gave the kisses back and said, Now that's subtraction. Then he kissed her, she kissed him, Without an explanation, And both together smiled and said, That's multiplication. Then Dad appeared upon the scene and Made a quick decision. He kicked that kid three blocks away And said, That's long division!

But this feeling had come, that day, and swallowed everything up inside it, so big you couldn't really prove it was there except by an arithmetic of absence and the memory of better days.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.

It's a simple matter of mathematics.

I can multiply. Long divisions start to be a stretch.

In C there are no data structures: there are pointers and pointer arithmetic. So you have a pointer into a data structure.

Opinions of language are as interesting as opinions of arithmetic.