James Newman Quotes

I can show you that the art of calculation has to do with odd and even numbers in their numerical relations to themselves and to each other.

Two times two is twenty-two, four times four is forty-four. When numbers get serious, they leave a mark on your door.

The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.

Look somewhere else for someone who can follow you in your researches about numbers. For my part, I confess that they are far beyond me, and I am competent only to admire them.

The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties.

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.

The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.

Those numbers with Tony are so often and so interesting.

The more one thinks, the more one feels the hopeless immensity of man's ignorance.

Nature does not count nor do integers occur in nature. Man made them all, integers and all the rest, Kronecker to the contrary notwithstanding.

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

While we can prove that almost all numbers in the continuum are random, we cannot prove that any specific number is indeed random.

I tell you, with complex numbers you can do anything.

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite.

Topology and number theory are my faves.

All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.

If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.

One thing in any case is certain: man is neither the oldest nor the most constant problem that has been posed for human knowledge.

One may say that mathematics talks about the things which are of no concern to men. Mathematics has the inhuman quality of starlight - brilliant, sharp but cold ... thus we are clearest where knowledge matters least: in mathematics, especially number theory.

It will be another million years, at least, before we understand the primes.

Number, place, and combination . . . the three intersecting but distinct spheres of thought to which all mathematical ideas admit of being referred.

The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he has to speak of numbers, vectors, tensors, state-functions, or whatever to make the abstraction.

Number is the Word but is not utterance it is wave and light, though no one sees it it is rhythm and music, though no one hears it. Its variations are limitless and yet it is immutable. Each form of life is a particular reverberation of Number.

The young specialist in English Lit, ...lectured me severely on the fact that in every century people have thought they understood the Universe at last, and in every century they were proved to be wrong. It follows that the one thing we can say about our modern "knowledge" is that it is wrong.