Mathematical Quotations -- S

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Sanford, T. H.

The modern, and to my mind true, theory is that mathematics is the abstract form of the natural sciences; and that it is valuable as a training of the reasoning powers not because it is abstract, but because it is a representation of actual things.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

Santayana, George

It is a pleasant surprise to him (the pure mathematician) and an added problem if he finds that the arts can use his calculations, or that the senses can verify them, much as if a composer found that sailors could heave better when singing his songs.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.

Sarton, G.

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.

Sayers, Dorothy L.

The biologist can push it back to the original protist, and the chemist can push it back to the crystal, but none of them touch the real question of why or how the thing began at all. The astronomer goes back untold million of years and ends in gas and emptiness, and then the mathematician sweeps the whole cosmos into unreality and leaves one with mind as the only thing of which we have any immediate apprehension. Cogito ergo sum, ergo omnia esse videntur. All this bother, and we are no further than Descartes. Have you noticed that the astronomers and mathematicians are much the most cheerful people of the lot? I suppose that perpetually contemplating things on so vast a scale makes them feel either that it doesn't matter a hoot anyway, or that anything so large and elaborate must have some sense in it somewhere.
With R. Eustace, The Documents in the Case, New York: Harper and Row, 1930, p 54.


Of all the intellectual faculties, judgment is the last to mature. A child under the age of fifteen should confine its attention either to subjects like mathematics, in which errors of judgment are impossible, or to subjects in which they are not very dangerous, like languages, natural science, history, etc.


If you would make a man happy, do not add to his possessions but subtract from the sum of his desires.
In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.

Shakespeare, William (1564 - 1616)

I cannot do it without comp[u]ters.
The Winter's Tale.

Though this be madness, yet there is method in't.

O God! I could be bounded in a nutshell, and count myself king of infinite space, were it not that I have bad dreams.

I am ill at these numbers.

Shaw, George Bernard (1856-1950)

Tyndall declared that he saw in Matter the promise and potency of all forms of life, and with his Irish graphic lucidity made a picture of a world of magnetic atoms, each atom with a positive and a negative pole, arranging itself by attraction and repulsion in orderly crystalline structure. Such a picture is dangerously fascinating to thinkers oppressed by the bloody disorders of the living world. Craving for purer subjects of thought, they find in the contemplation of crystals and magnets a happiness more dramatic and less childish than the happiness found by mathematicians in abstract numbers, because they see in the crystals beauty and movement without the corrupting appetites of fleshly vitality.
Preface to Back to Methuselah.

Shaw, J. B.

The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

Simmons, G. F.

Mathematical rigor is like clothing; in its style it ought to suit the occasion, and it diminishes comfort and restrains freedom of movement if it is either too loose or too tight.
In The Mathematical Intelligencer, v. 13, no. 1, Winter 1991.

Slaught, H.E.

...[E.H.] Moore ws presenting a paper on a highly technical topic to a large gathering of faculty and graduate students from all parts of the country. When half way through he discovered what seemed to be an error (though probably no one else in the room observed it). He stopped and re-examined the doubtful step for several minutes and then, convinced of the error, he abruptly dismissed the meeting -- to the astonishment of most of the audience. It was an evidence of intellectual courage as well as honesty and doubtless won for him the supreme admiration of every person in the group -- an admiration which was in no wise diminished, but rather increased, when at a later meeting he announced that after all he had been able to prove the step to be correct.
In The American Mathematical Monthly, 40 (1933), 191-195.

Smith, Adam

I have no faith in political arithmetic.

Smith, David Eugene

One merit of mathematics few will deny: it says more in fewer words than any other science. The formula, e^iπ = -1 expressed a world of thought, of truth, of poetry, and of the religious spirit "God eternally geometrizes."
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.

Smith, Henry John Stephen (1826 - 1883)

[His toast:]
Pure mathematics, may it never be of any use to anyone.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

It is the peculiar beauty of this method, gentlemen, and one which endears it to the really scientific mind, that under no circumstance can it be of the smallest possible utility.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

Soddy, Frederick (1877-1956)

Four circles to the kissing come,
The smaller are the benter.
The bend is just the inverse of
The distance from the centre.
Though their intrigue left Euclid dumb
There's now no need for rule of thumb.
Since zero bend's a dead straight line
And concave bends have minus sign,
The sum of squares of all four bends
Is half the square of their sum.
Nature, v. 137, 1936.

Somerville, Mary (1780-1872)

Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity.
Martha Somerville (ed.) Personal Recollections of Mary Somerville, Boston, 1874.

Spengler, Oswald (1880 -1936)

The mathematic, then, is an art. As such it has its styles and style periods. It is not, as the layman and the philosopher (who is in this matter a layman too) imagine, substantially unalterable, but subject like every art to unnoticed changes form epoch to epoch. The development of the great arts ought never to be treated without an (assuredly not unprofitable) side-glance at contemporary mathematics.
The Decline of the West.

Steiner, G.

For all their wealth of content, for all the sum of history and social institution invested in them, music, mathematics, and chess are resplendently useless (applied mathematics is a higher plumbing, a kind of music for the police band). They are metaphysically trivial, irresponsible. They refuse to relate outward, to take reality for arbiter. This is the source of their witchery.
The American Mathematical Monthly, v. 101, no. 9, November, 1994.

Steinmetz, Charles P.

Mathematics is the most exact science, and its conclusions are capable of absolute proof. But this is so only because mathematics does not attempt to draw absolute conclusions. All mathematical truths are relative, conditional.
In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.

Sternberg, S.

Kepler's principal goal was to explain the relationship between the existence of five planets (and their motions) and the five regular solids. It is customary to sneer at Kepler for this. It is instructive to compare this with the current attempts to "explain" the zoology of elementary particles in terms of irreducible representations of Lie groups.

Stewart, Ian

The successes of the differential equation paradigm were impressive and extensive. Many problems, including basic and important ones, led to equations that could be solved. A process of self-selection set in, whereby equations that could not be solved were automatically of less interest than those that could.
Does God Play Dice? The Mathematics of Chaos. Blackwell, Cambridge, MA, 1989, p. 39.

Sullivan, John William Navin (1886 - 1937)

The mathematician is entirely free, within the limits of his imagination, to construct what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not thereby discovering the fundamental principles of the universe nor becoming acquainted with the ideas of God. If he can find, in experience, sets of entities which obey the same logical scheme as his mathematical entities, then he has applied his mathematics to the external world; he has created a branch of science.
Aspects of Science, 1925.

Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.
Aspects of Science, 1925.

Sun Tze (5th - 6th century)

The control of large numbers is possible, and like unto that of small numbers, if we subdivide them.
Sun Tze Ping Fa.

Swift, Jonathan

If they would, for Example, praise the Beauty of a Woman, or any other Animal, they describe it by Rhombs, Circles, Parallelograms, Ellipses, and other geometrical terms ...
"A Voyage to Laputa" in Gulliver's Travels.

What vexes me most is, that my female friends, who could bear me very well a dozen years ago, have now forsaken me, although I am not so old in proportion to them as I formerly was: which I can prove by arithmetic, for then I was double their age, which now I am not.
Letter to Alexander Pope. 7 Feb. 1736.

Sylvester, J.J. (1814 - 1897)

...there is no study in the world which brings into more harmonious action all the faculties of the mind than [mathematics], ... or, like this, seems to raise them, by successive steps of initiation, to higher and higher states of conscious intellectual being....
Presidential Address to British Association, 1869.

So long as a man remains a gregarious and sociable being, he cannot cut himself off from the gratification of the instinct of imparting what he is learning, of propagating through others the ideas and impressions seething in his own brain, without stunting and atrophying his moral nature and drying up the surest sources of his future intellectual replenishment.

[on graph theory...]
The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation.
In H. Eves Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977.

Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.
Presidential Address to British Association, 1869.

The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connexion of its parts, the infinite hierarchy and absolute evidence of the truths with which it is concerned, these, and such like, are the surest grounds of the title of mathematics to human regard, and would remain unimpeached and unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance.
Presidential Address to British Association, 1869.

I know, indeed, and can conceive of no pursuit so antagonistic to the cultivation of the oratorical faculty ... as the study of Mathematics. An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorical effect the less will he find himself in a fit state to mathematicize.

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