Benjamin Peirce

“Linear Associative Algebra (1882)”

“Profile at Stanford University”

“Profile at University of St. Andrews”

“Profile at NNDB”

“When this wizard stepped down from his post, crossed his moat, and opened his garden gate, nothing could be more attractive than the vistas and plantations he opened to our view. … Few men could suggest more while saying so little, or stimulate so much while communicating next to nothing that was tangible and comprehensible. The young man that would learn the true meaning of apprehension as distinct from comprehension, should have heard the professor lecture.”

“It is not given to us — it is given to but few men of any generation — to roam those Alpine solitudes of science to which his genius reached.”

“Benjamin Peirce deserves recognition, not only as a founding father of American mathematics, but also as a founding father of modern abstract algebra.”

“His talk was informal, often far above their heads. "Do you follow me?" asked the Professor one day. No one could say Yes. "I'm not surprised," said he; "I know of only three persons who could." At Paris, the year after, at the great Exposition, Flagg stood before a mural tablet whereon were inscribed the names of the great mathematicians of the earth for more than two thousand years. Archimedes headed, Peirce closed the list; the only American.”

“Authority was nothing to Peirce. He took his own path up the mountain. … Like Pythagoras, Peirce taught that everything owes its existence and consistency to the harmony which he considered the basis of all beauty, and found music in the revolving spheres.”

“Of the great mathematician as an instructor several of his pupils who ventured on the higher planes of the science have written. These were youths who, though they could follow him but a few steps in that rarefied atmosphere, had the privilege of a glimpse now and then into shining infinities wherein this giant sped rejoicing on.”

“He was such a great, big ray of Light and Goodness, always so simple, cheerful and showing more than amiability, that his great power did not seem to assert itself.”

“Benjamin Peirce's lectures dealt, to be sure, with the higher mathematics, but also with theories of the universe and the infinities of nature, and with man's power to deal with infinities and infinitesimals alike. His University Lectures were many a time way over the heads of his audience, but his aspect, his manner, and his whole personality held and delighted them.”

“Peirce stood alone — a mountain peak whose absolute height might be hard to measure, but which towered above the surrounding country.”

“He was one of the most stimulating men I have ever known.”

“I always had the feeling that his attitude toward his loved science was that of a devoted worshipper, rather than a clear expounder. Although we could rarely follow him, we certainly sat up and took notice. … To him mathematics was not a humanly devised instrument of investigation, it was Philosophy itself, the divine revealer of TRUTH.”

“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. 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. {{pb}} 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. {{pb}} In all other algebras both relations must be combined, and the algebra must conform to the character of the relations.”

“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.”

“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 satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future.”