"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."

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

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

"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."

"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."

"Looking back over the space of fifty years since I entered Harvard College, Benjamin Peirce still impresses me as having the most massive intellect with which I have ever come in contact, and as being the most profoundly inspiring teacher I ever had. … As soon as he had finished the problem or filled the blackboard he would rub everything out and begin again. He was impatient of detail, and sometimes the result would not come out right; but instead of going over his work to find the error, he would rub it out, saying that he had made a mistake in a sign somewhere, and that we should find it when we went over our notes. Described in this way it may seem strange that such a method of teaching should be inspiring; yet to us it was so to the highest degree. We were carried along by the rush of his thought, by the ease and grasp of his intellectual movement. The inspiration came, I think, partly from his treating us as highly competent pupils, capable of following his line of thought even through errors in transformations; partly from his rapid and graceful methods of proof, which reached a result with the least number of steps in the process, attaining thereby an artistic or literary character; and partly from the quality of his mind which tended to regard any mathematical theorem as a particular case of some more comprehensive one, so that we were led onward to constantly enlarging truths."

"He gave us his "Curves and Functions", in the form of lectures; and sometimes, even while stating his propositions, he would be seized with some mathematical inspiration, would forget pupils, notes, everything, and would rapidly dash off equation after equation, following them out with smaller and smaller chalk-marks into the remote corners of the blackboard, forsaking his delightful task only when there was literally no more space to be covered, and coming back with a sigh to his actual students. There was a great fascination about these interruptions; we were present, as it seemed, at mathematics in the making; it was like peeping into a necromancer's cell, and seeing him at work; or as if our teacher were one of the old Arabian algebraists recalled to life."

"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."

"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."

"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."

"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..."

"Ideality is preëminently the foundation of Mathematics."

"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."

"Geometry, to which I have devoted my life, is honoured with the title of the Key of Sciences; but it is the Key of an ever open door which refuses to be shut, and through which the whole world is crowding, to make free, in unrestrained license, with the precious treasures within, thoughtless both of lock and key, of the door itself, and even of Science, to which it owes such boundless possessions, the New World included. The door is wide open and all may enter, but all do not enter with equal thoughtlessness. There are a few who wonder, as they approach, at the exhaustless wealth, as the sacred shepherd wondered at the burning bush of Horeb, which was ever burning and never consumed. Casting their shoes from off their feet and the world's iron-shod doubts from their understanding, these children of the faithful take their first step upon the holy ground with reverential awe, and advance almost with timidity, fearful, as the signs of Deity break upon them, lest they be brought face to face with the Almighty."

"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."

"Ascend with me above the dust, above the cloud, to the realms of the higher geometry, where the heavens are never clouded; where there is no impure vapour, and no delusive or imperfect observation, where the new truths are already arisen, while they are yet dimly dawning on the world below; where the earth is a little planet; where the sun has dwindled to a star; where all the stars are lost in the Milky Way to which they belong; where the Milky Way is seen floating through space like any other nebula; where the whole great girdle of nebulae has diminished to an atom and has become as readily and completely submissive to the pen of the geometer, and the slave of his formula, as the single drop, which falls from the clouds, instinct with all the forces of the material world."

"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."

"Throughout nature the omnipresent beautiful revealed an all-pervading language spoken to the human mind, and to man's highest capacity of comprehension. By whom was it spoken? Whether by the gods of the ocean, or the land, by the ruling divinities of the sun, moon, and stars, or by the dryads of the forest and the nymphs of the fountain, it was one speech and its written cipher was cabalistic. The cabala were those of number, and even if they transcended the gemetricl skill of the Rabbi and the hieroglyphical learning of the priest of Osiris, they were, distinctly and unmistakably, expressions of thought uttered to mind by mind; they were the solutions of mathematical problems of extraordinary complexity."