8 Quotes by Tobias Dantzig

The letter is susceptible of operations which enables one to transform literal expressions and thus to paraphrase any statement into a number of equivalent forms. It is this power of transformation that lifts algebra above the level of a convenient shorthand.

The symbol is not a mere formality; it is the very essence of algebra. Without the symbol the object is a human perception and reflects all the phases under which the human senses grasp it; replaced by a symbol the object becomes a complete abstraction, a mere operand subject to certain indicated operations.

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

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.

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.

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

In the history of culture the discovery of zero will always stand out as one of the greatest single achievements of the human race.

It is not a story of brilliant achievement, heroic deeds, or noble sacrifice. It is a story of blind stumbling and chance discovery, of groping in the dark and refusing to admit the light. It is a story replete with obscurantism and prejudice, of sound judgement often eclipsed by loyalty to tradition, and of reason long held subservient to custom. In short, it is a human story.