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.”

“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.”

“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!”

“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.”

“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.”

“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.”