# Quote — Tobias Dantzig, Number

> 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.

- Author: [Tobias Dantzig](https://www.leafyquotes.com/tobias-dantzig.md)
- Book: [Number](https://www.leafyquotes.com/tobias-dantzig/number.md)
- Source: [Wikiquote](https://en.wikiquote.org/wiki/Tobias_Dantzig#Number:_The_Language_of_Science_(1930)) ([CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/))
- Quote page: https://www.leafyquotes.com/tobias-dantzig/number/the-progress-of-mathematics

## More from this book

> 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 Riemann, 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.

[Quote page](https://www.leafyquotes.com/tobias-dantzig/number/the-mathematician-may.md)

> 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.”

[Quote page](https://www.leafyquotes.com/tobias-dantzig/number/there-exists-among.md)

> 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.

[Quote page](https://www.leafyquotes.com/tobias-dantzig/number/the-arithmetization-of-mathematics.md)