Benjamin Peirce Quotes

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There are many cases of these algebras which may obviously be combined into natural classes, but the consideration of this portion of the subject will be reserved to subsequent researches.

Benjamin Peirce
Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics.

Benjamin Peirce
If American genius is not fettered by the chains of necessity, and helplessly exposed to the assaults of envious mediocrity, but is generously nourished in the bosom of liberty, it will joyfully expand its free wings, and soar with the eagle to the conquest of the skies.

Benjamin Peirce
To translate a great poem demands months and years of earnest devotion, coupled with poetic inspiration. But to read the book of Nature is the province and privilege of consummate genius, submissive to unremitting discipline.

Benjamin Peirce
The brilliant and majestic firmament is studded with stars, distributed under no order which can be deciphered, and with an irregularity greater than that of the spots of water on a floor, dashed from a dripping brush.

Benjamin Peirce
Science and religion are born of the same house, and that house is not divided against itself. There will at all times be an apparent conflict between them, arising from defects of human nature; but all this conflict is of human origin, and it originates in the deficiency of our knowledge, not in the greatness of it.

Benjamin Peirce
You cannot think that any man, with a man's soul in his body, could devote his life to the drudgery of addition, subtraction, multiplication, and division, for the mere pleasure of the thing.

Benjamin Peirce
What is this which we call fact? It is not a sound; it is not a star. It is sound heard by the ear; it is a star seen by the eye.

Benjamin Peirce
So long as a scientific doubt remains, the story of cosmogony is partially untold.

Benjamin Peirce
Gentlemen, we have not the slightest idea of what this equation means, but we may be sure that it means something very important.

Benjamin Peirce
The arithmetical formula, considered as an end, is the embodiment of fact, and isolated fact is as worthless as the idle gossip of the parlor or the club; whereas facts combined into formulae and formulae organized into theory penetrate the whole domain of physical science, and ascend to the very throne of ideality.

Benjamin Peirce
Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth.

Benjamin Peirce
Throughout nature the omnipresent beautiful revealed an all-pervading language spoken to the human mind, and to man's highest capacity of comprehension. By whom was it spoken? Whether by the gods of the ocean, or the land, by the ruling divinities of the sun, moon, and stars, or by the dryads of the forest and the nymphs of the fountain, it was one speech and its written cipher was cabalistic. The cabala were those of number, and even if they transcended the gemetricl skill of the Rabbi and the hieroglyphical learning of the priest of Osiris, they were, distinctly and unmistakably, expressions of thought uttered to mind by mind; they were the solutions of mathematical problems of extraordinary complexity.

Benjamin Peirce
Descend from the infinite to the infinitesimal. Long before... observation had begun to penetrate the veil under which Nature has hidden her mysteries, the restless mind sought some principle of power strong enough and of sufficient variety to collect and bind together all parts of a world. This seemed to be found, where one might least expect it, in abstract numbers. Everywhere the exactest numerical proportion was seen to constitute the spiritual element of the highest beauty.

Benjamin Peirce
The strongest use of the symbol is to be found in its magical power of doubling the actual universe, and placing by its side an ideal universe, its exact counterpart, with which it can be compared and contrasted, and, by means of curiously connecting fibres, form with it an organic whole, from which modern analysis has developed her surpassing geometry.

Benjamin Peirce
There is proof enough furnished by every science, but by none more than geometry, that the world to which we have been allotted is peculiarly adapted to our minds, and admirably fitted to promote our intellectual progress. There can be no reasonable doubt that it was part of the Creator's plan. How easily might the whole order have been transposed! How readily might we have been assigned to some complicated system which our feeble and finite powers could not have unravelled!

Benjamin Peirce
The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.

Benjamin Peirce
Ideality is preëminently the foundation of Mathematics.

Benjamin Peirce
What is man? … What a strange union of matter and mind! A machine for converting material into spiritual force.

Benjamin Peirce
All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole.
Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra.
In all other algebras both relations must be combined, and the algebra must conform to the character of the relations.

Benjamin Peirce
The very spirits of the winds, when they were sent to carry the grateful harvest to the thirsting fields of Calabria, did not forget the geometry which they had studied in the caverns of Æolus and of which the geologist is daily discovering the diagrams.

Benjamin Peirce
The Key! it is of wonderful construction, with its infinity of combination, and its unlimited capacity to fit every lock. … it is the great master-key which unlocks every door of knowledge and without which no discovery which deserves the name — which is law, and not isolated fact — has been or ever can be made. Fascinated by its symmetry the geometer may at times have been too exclusively engrossed with his science, forgetful of its applications; he may have exalted it into his idol and worshipped it; he may have degraded it into his toy... when he should have been hard at work with it, using it for the benefit of mankind and the glory of his Creator.

Benjamin Peirce
I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future.

Benjamin Peirce
Mathematics is the science which draws necessary conclusions.

Benjamin Peirce
Some definite interpretation of a linear algebra would, at first sight, appear indispensable to its successful application. But on the contrary, it is a singular fact, and one quite consonant with the principles of sound logic, that its first and general use is mostly to be expected from its want of significance. The interpretation is a trammel to the use. Symbols are essential to comprehensive argument.

Benjamin Peirce