James Joseph Sylvester Quotes

At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate.

The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system.

Like works of literature, mathematical ideas help expand our circle of empathy, liberating us from the tyranny of a single, parochial point of view. Numbers, properly considered, make us better people.

Number, the most excellent of all inventions.

A mathematician ... has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.

Only Numbers. Pure math. You have to accustom yourself to thinking that way.

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.

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.

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.

For a long time the objects that mathematicians dealt with were mostly ill-defined; one believed one knew them, but one represented them with the senses and imagination; but one had but a rough picture and not a precise idea on which reasoning could take hold.

I truly believe that age - if you're healthy - age is just a number.

We find in the history of ideas mutations which do not seem to correspond to any obvious need, and at first sight appear as mere playful whimsies such as Apollonius' work on conic sections, or the non-Euclidean geometries, whose practical value became apparent only later.

Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be supposed to have on a Browning or a Tennyson. Indeed it seems to me that an exact homology exists between painting and poetry on the one hand and modem chemistry and modem algebra on the other. In poetry and algebra we have the pure idea elaborated and expressed through the vehicle of language, in painting and chemistry the idea enveloped in matter, depending in part on manual processes and the resources of art for its due manifestation.

Number theorists are like lotus-eaters -- having once tasted of this food they can never give it up.

Law Number IX: Acronyms and abbreviations should be used to the maximum extent possible to make trivial ideas profound ... Q.E.D.

It would be a very bad idea... to exhibit even a small number of this new series, as the whole effect can only be achieved from an exhibition of the entire group.

"Nought usually comes at the beginning," Ralph said. "Not necessarily," said Sibyl. "It might come anywhere. Nought isn't a number at all. It's the opposite of number." Nancy looked up from the cards. "Got you, aunt," she said. "What about ten? Nought's a number there - it's part of ten." "Well, if you say that any mathematical arrangement of one and nought really makes ten - " Sibyl smiled. "Can it possibly be more than a way of representing ten?"

People, alas, are more impressed by statistics than they are by ideas.

I rummage around in artistic things from the past. If you don't understand the context, they wouldn't make any sense. I rummage around in conceptual ideas of the future, but if you don't know the source of the thinking, [it] wouldn't make any sense.

Our ideas must agree with realities, be such realities concrete or abstract, be they facts or be they principles, under penalty of endless inconsistency and frustration.

Many psychiatrists and psychologists refuse to entertain the idea that society as a whole may be lacking in sanity. They hold that the problem of mental health in a society is only that of the number of 'unadjusted' individuals, and not of a possible unadjustment of the culture itself.

Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.

If equations are trains threading the landscape of numbers, then no train stops at pi.

When I start on a film I always have a number of ideas about my project. Then one of them begins to germinate, to sprout, and it is this, which I take and work with. My films come from my need to say a particular thing at a particular time. The beginning of any film for me is this need to express something. It is to make it nurture and grow that I write my script- it is directing it that makes my tree blossom and bear fruit.

The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps.