“Despite the vociferous claims of the Platonists and Neoplatonists, Plato was not a mathematician. To Plato and his followers mathematics was largely a means to an end... they viewed the technical aspects of mathematics as a mere device for sharpening one's wits, or at most a course of training peparatory to handling the larger issues of philosophy. This is reflected in the very name "mathematics,"... a course of studies or... a curriculum. ...in the Dialogues... such topics as harmony, triangular numbers, figurate numbers... which we view today as more or less irrelevant, if not trivial, were taken up at length. ...the guiding motive behind the... Pythagoreans and Platonists was... metaphysical ...which for the nonprofessional have all the earmarks of the occult. ...We also discover in the Pythagorean speculations more than a mere germ of... the scientific attitude.”
“The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. ...The conic sections, invented in an attempt to solve the problem of ...”
Tobias Dantzig
“But how can we avoid the use of human language? The... symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition an...”
Tobias Dantzig
“The progress of mathematics has been most erratic, and... intuition has played a predominant rôle in it. ...It was the function of intuition to create new forms; it was the acknowledged right of logic...”
Tobias Dantzig
“There exists among the most primitive tribes of Australia and Africa a system of numeration which has neither 5, 10, nor 20 for base. It is a binary system, i.e., of base two. These savages have not y...”
Tobias Dantzig
“The preface to the French edition of that work contains the following passage: "To me the French edition of my work is not a mere translation, but a transcription of ideas into a language in which it ...”
Tobias Dantzig