Tobias Dantzig: Most

Tobias Dantzig was American mathematician. Explore interesting quotes on most.
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“One part of the dreams of the eighteenth century intellectuals was realized: the resources of nature did yield a magnificent harvest. But the thinkers who helped to tap these resources… failed to attend, detained in their studies and laboratories, lost in their dreams and calculations, seeking new fields, co-ordinating old and new, spinning abstract theories… the thinkers were unequal to the task of developing these vast resources, most of which they had themselves uncovered. The shrewd declassés, who had… the world to gain, pioneered this development and took possession of the earth.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 2. The Age of Innocence

World , Dreams , Nature , Study

“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.”

Tobias Dantzig

...We also discover in the Pythagorean speculations more than a mere germ of... the scientific attitude.
The Bequest of the Greeks (1955)

Mathematics , Motivation , Study , Training

“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.”

Tobias Dantzig

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

Mathematics , Idea

“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 should have been written in the first place… I proudly acknowledge… my master. His words are among the most brilliant recollections of my youth; his piercing wisdom and potent prose have inspired my efforts of a riper age. To the memory of Henri Poincaré, the intellectual giant who was the first to recognize the role which the idiosyncrasies of the race play in the evolution of scientific ideas, I dedicate this book.”

Tobias Dantzig

Preface
Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954)

Wisdom , Books , Youth , Age

“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.”

Tobias Dantzig

The Bequest of the Greeks (1955)

Art , Mathematics , Time

“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 yet reached finger counting. They have independent numbers for one and two, and composite numbers up to six. Beyond six everything is denoted by “heap.””

Tobias Dantzig

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.”

Tobias Dantzig

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

Children , Mathematics , Birth , Waiting

“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.”

Tobias Dantzig

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

Birth , Mathematics , Parting