Benjamin Peirce quotes

Benjamin Peirce was an American mathematician and astronomer, recognized for his contributions to algebra and number theory. His work laid the foundation for mathematical research at Harvard University and advanced the development of American mathematics. He influenced generations of scientists and mathematicians through his teaching and groundbreaking research. Here are 28 of his quotes:

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

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

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

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 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

Ideality is preëminently the foundation of Mathematics.

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 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

Throughout nature the omnipresent beautiful revealed an all-pervading language spoken to the human mind, and to man's highest capacity of comprehension.

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

Ascend with me above the dust, above the cloud, to the realms of the higher geometry, where the heavens are never clouded.

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.

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.

Benjamin Peirce

In all other algebras both relations must be combined, and the algebra must conform to the character of the relations.

Benjamin Peirce

All relations are either qualitative or quantitative.

Benjamin Peirce

The door is wide open and all may enter, but all do not enter with equal thoughtlessness.

Benjamin Peirce

Geometry, to which I have devoted my life, is honoured with the title of the Key of Sciences.

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.

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.

Benjamin Peirce

Some definite interpretation of a linear algebra would, at first sight, appear indispensable to its successful application.

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.

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.

Benjamin Peirce