Authors
Topics
Lists
Pictures
Resources
More about Tobias Dantzig
Tobias Dantzig Quotes
33 Sourced Quotes
Source
Report...
Mathematical achievement shall be measured by standards which are peculiar to mathematics. These standards are independent of a crude reality of our senses. They are: freedom from logical contradictions, the generality of the laws governing the created form, the kinship which exists between this new form and those that have preceded it.
Tobias Dantzig
Source
Report...
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.
Tobias Dantzig
Source
Report...
In the history of mathematics, the "how" always preceded the "why," the technique of the subject preceded its philosophy.
Tobias Dantzig
Source
Report...
The harmony of the universe knows only one musical form - the legato; while the symphony of number knows only its opposite - the staccato. All attempts to reconcile this discrepancy are based on the hope that an accelerated staccato may appear to our senses as a legato.
Tobias Dantzig
Source
Report...
Between the philosopher's attitude towards the issue of reality and that of the mathematician there is this essential difference: for the philosopher the issue is paramount; the mathematician's love for reality is purely platonic.
Tobias Dantzig
Source
Report...
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
Source
Report...
With regard to the Pythagorean theorem my conjecture is that... it was known to Thales. ...the hypotenuse theorem is a direct consequence of the principle of similitude, and... Thales was fully conversant with the theory of similar triangles.
Tobias Dantzig
Source
Report...
Thales the teacher produced the first geometers, even as Thales the thinker founded the first geometry worthy of the name.
Tobias Dantzig
Source
Report...
Banish the infinite process, and mathematics pure and applied is reduced to the state in which it was known to the pre-Pythagoreans.
Tobias Dantzig
Source
Report...
The evolution of scientific thought is inseparable from the history of man's efforts to resolve the perplexities of his own existence.
Tobias Dantzig
Source
Report...
Today we know that possibility and impossibility have each only a relative meaning; that neither is an intrinsic property of the operation but merely a restriction which human tradition has imposed on the field of the operand. Remove the barrier, extend the field, and the impossible becomes possible.
Tobias Dantzig
Source
Report...
Are not most professional mathematicians spared all trouble incident to income?
Tobias Dantzig
Source
Report...
Mathematics is not only the model along the lines of which the exact sciences are striving to design their structure; mathematics is the cement which holds the structure together.
Tobias Dantzig
Source
Report...
And so matching by itself is incapable of creating an art of reckoning. Without our ability to arrange things in ordered succession little progress could have been made. Correspondence and succession, the two principles that permeate all mathematics - nay, all realms of exact thought - are woven into the very fabric of our number system.
Tobias Dantzig
Source
Report...
The practical man demands an appearance of reality at least. Always dealing in the concrete, he regards mathematical terms not as symbols or thought but as images of reality. A system acceptable to the mathematician because of its inner consistency may appear to the practical man to be full of contradictions because of the incomplete manner in which it represents reality.
Tobias Dantzig
Source
Report...
It is a remarkable fact that the mathematical inventions which have proved to be most accessible to the masses are also those which exercised the greatest influence on the development of pure mathematics.
Tobias Dantzig
Source
Report...
The importance of infinite processes for the practical exigencies of technical life can hardly be overemphasized. Practically all applications of arithmetic to geometry, mechanics, physics and even statistics involve these processes directly and indirectly.
Tobias Dantzig
Source
Report...
Poincaré was an artist par excellence. Estheticism with him was not a mere creed: it was a way of life.
Tobias Dantzig
Source
Report...
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
Source
Report...
Poincaré's mind was not subject to hysteresis or hibernation. He had the unique faculty of dismissing an idea from his mind, the instant the stimulus was gone, and to supplant it immediately with another creative idea.
Tobias Dantzig
Source
Report...
Mathematics fluourished as long as freedom of thought prevailed; it decayed when creative joy gave way to blind faith and fanatical frenzy.
Tobias Dantzig
Source
Report...
To describe means to classify, and the man Poincaré defies classification, as does indeed his philosophy.
Tobias Dantzig
Source
Report...
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
Source
Report...
Mathematics is the supreme judge; from its decisions there is no appeal.
Tobias Dantzig
Source
Report...
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
1
2
Quote of the day
To die is poignantly bitter, but the idea of having to die without having lived is unbearable.
Erich Fromm
Tobias Dantzig
Born:
February 19, 1884
Died:
August 9, 1956
(aged 72)
Bio:
Tobias Dantzig was a mathematician of Baltic German and Russian American heritage, the father of George Dantzig, and the author of Number: The Language of Science and Aspects of Science.
Most used words:
mathematics
thought
human
ideas
nature
poincaré
mere
symbol
mathematical
object
language
intuition
logic
subject
industrial
Tobias Dantzig on Wikipedia
Suggest an edit or a new quote
Tobias Dantzig Quotes
Tobias Dantzig Short Quotes
American Mathematician Quotes
Mathematician Quotes
19th-century Mathematician Quotes
Featured Authors
Lists
Predictions that didn't happen
If it's on the Internet it must be true
Remarkable Last Words (or Near-Last Words)
Picture Quotes
Confucius
Philip James Bailey
Eleanor Roosevelt
Letitia Elizabeth Landon
Popular Topics
life
love
nature
time
god
power
human
mind
work
art
heart
thought
men
day
×
Lib Quotes