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.

All relations are either qualitative or quantitative.

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, …

Mathematics, under this definition, belongs to every enquiry, moral as well as physical.

Mathematics is the science which draws necessary conclusions.

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 …

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 …

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.

Symbols are essential to comprehensive argument.

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.

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 …

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

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

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 …

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

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

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.

Ideality is preëminently the foundation of Mathematics.

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