Benjamin Peirce quotes

Mathematics is the science which draws necessary conclusions. (Benjamin Peirce)
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. View quote
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. View quote
Benjamin Peirce
What is man? ... What a strange union of matter and mind! A machine for converting material into spiritual force. View quote
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. View quote
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. View quote
Benjamin Peirce
Ideality is preëminently the foundation of Mathematics. View quote
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. View quote
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. View quote
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. View quote
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)
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. View quote
Benjamin Peirce
Ascend with me above the dust, above the cloud, to the realms of the higher geometry, where the heavens are never clouded. View quote
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. View quote
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. View quote
Benjamin Peirce
In all other algebras both relations must be combined, and the algebra must conform to the character of the relations. View quote
Benjamin Peirce
All relations are either qualitative or quantitative. View quote
Benjamin Peirce
The door is wide open and all may enter, but all do not enter with equal thoughtlessness. View quote
Benjamin Peirce
Geometry, to which I have devoted my life, is honoured with the title of the Key of Sciences. View quote
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. View quote
Benjamin Peirce
Mathematics, under this definition, belongs to every enquiry, moral as well as physical. (Benjamin Peirce)
The sphere of mathematics is here extended, in accordance with the derivation of its name, to all demonstrative research, so as to include all knowledge strictly capable of dogmatic teaching. View quote
Benjamin Peirce
Some definite interpretation of a linear algebra would, at first sight, appear indispensable to its successful application. View quote
Benjamin Peirce
When the formulas admit of intelligible interpretation, they are accessions to knowledge; but independently of their interpretation they are invaluable as symbolical expressions of thought. View quote
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. View quote
Benjamin Peirce