Tobias Dantzig

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

— Tobias Dantzig

“The symbol is not a mere formality; it is the very essence of algebra. Without the symbol the object is a human…

— Tobias Dantzig

“The letter is susceptible of operations which enables one to transform literal expressions and thus to paraphrase any statement into a number…

— Tobias Dantzig

The harmony of the universe knows only one musical form - the legato; while the symphony of number knows only its opposite…

— Tobias Dantzig

The importance of infinite processes for the practical exigencies of technical life can hardly be overemphasized. Practically all applications of arithmetic to…

— Tobias Dantzig

They [the mathematicians of the Enlightenment] defined their terms vaguely and used their methods loosely, and the logic of their arguments was…

— Tobias Dantzig

The practical man demands an appearance of reality at least. Always dealing in the concrete, he regards mathematical terms not as symbols…

— Tobias Dantzig

And so matching by itself is incapable of creating an art of reckoning. Without our ability to arrange things in ordered succession…

— Tobias Dantzig

Are not most professional mathematicians spared all trouble incident to income?

— Tobias Dantzig

“In the history of culture the discovery of zero will always stand out as one of the greatest single achievements of the…

— Tobias Dantzig