Top 7 Quotes by Tobias Dantzig

Mathematics is the supreme judge; from its decisions there is no appeal.

Mathematics is the supreme judge; from its decisions there is no appeal.

Math, Judging, Decision

Tobias Dantzig (2005). “Number: The Language of Science”, Dutton Juvenile

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

Opposites, Symphony, Numbers

Tobias Dantzig (2005). “Number: The Language of Science”, Dutton Juvenile

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

Reality, Men, Consistency

Tobias Dantzig (1954). “Number, the Language of Science: A Critical Survey Written for the Cultured Non-mathematician”

They [the mathematicians of the Enlightenment] defined their terms vaguely and used their methods loosely, and the logic of their arguments was made to fit the dictates of their intuition. In short, they broke all the laws of rigor and of mathematical decorum. The veritable orgy which followed the introduction of the infinitesimals... was but a natural reaction. Intuition had too long been held imprisoned by the severe rigor of the Greeks. Now it broke loose, and there were no Euclids to keep its romantic flight in check.

Tobias Dantzig

Law, History, Long

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

Statistics, Physics, Infinite

Tobias Dantzig (2005). “Number: The Language of Science”, Dutton Juvenile

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

Art, Numbers, Two

Tobias Dantzig (1954). “Number, the Language of Science: A Critical Survey Written for the Cultured Non-mathematician”