You treat world history as a mathematician does mathematics, in which nothing but laws and formulae exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.

You treat world history as a mathematician does mathematics, in which nothing but laws and formulae exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.

The Glass Bead Game, 1943.

One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.

E. T. Bell, *Men
of Mathematics,*
New York, 1937.

We are servants rather than masters in mathematics.

In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

Abel has left mathematicians enough to keep them busy for 500 years.

In G. F. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.

There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation.

In The Mathematical Intelligencer, v. 5, no. 4.

One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics.

L.A. Steen and D.J.
Albers (eds.),
*Teaching
Teachers, Teaching
Students,*
Boston: Birkhauser,
1981, p. 89.

[T]o characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.

"Geometry and
Empirical Science"
in J. R. Newman
(ed.), The World of
Mathematics, New
York: Simon and
Schuster, 1956.

The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results.

"Geometry and Empirical Science" in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.

The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as "All bachelors are unmarried," but they also share the complete lack of empirical content which is associated with that certainty: The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter.

"On the Nature of Mathematical Truth" in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.

An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them.

Physics and Beyond. 1971.