Tobias Dantzig: Quotes about mathematics

Tobias Dantzig was American mathematician. Explore interesting quotes on mathematics.

Tobias Dantzig: 50 quotes0 likes

“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 doubling the alter of an oracle, ended by becoming the orbits followed by the planets… The imaginary magnitudes invented by Cardan and Bombelli describe… the characteristic features of alternating currents. The absolute differential calculus, which originated as a fantasy of Reimann, became the mathematical model for the theory of Relativity. And the matrices which were a complete abstraction in the days of Cayley and Sylvester appear admirably adapted to the… quantum of the atom.”

Number: The Language of Science (1930)

“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 Bequest of the Greeks (1955)

“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 and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.”

p, 125
Number: The Language of Science (1930)

“The arithmetization of mathematics… which began with Weierstrass… had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics.
These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought.”

p, 125
Number: The Language of Science (1930)

“Mathematics fluourished as long as freedom of thought prevailed; it decayed when creative joy gave way to blind faith and fanatical frenzy.”

The Bequest of the Greeks (1955)

“The mathematical activity of Ancient Greece reached its peak during the glorious era of Euclid, Eratosthenes, Archimedes and Apollonius, a time when Greek letters, art and philosophy were already on the decline. …it was not Greece proper but its outposts in Asia Minor, in Lower Italy, in Africa that had contributed most to the development of mathematics.”

The Bequest of the Greeks (1955)

“In the history of mathematics, the "how" always preceded the "why," the technique of the subject preceded its philosophy.”

Number: The Language of Science (1930)

“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 to accept or reject these new forms, in whose birth in had no part…. the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied.”

p, 125
Number: The Language of Science (1930)

“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 to accept or reject these new forms, in whose birth in had no part.”

...the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied.
Number: The Language of Science (1930)