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If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.

It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

Apart from two periods of intense study, of music between the ages of 12 and 14 and of mathematics between the ages of 14 and 16, I coasted, daydreaming, through most of my school years.

"Obvious" is the most dangerous word in mathematics.

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences.

If indeed, as Hilbert asserted, mathematics is a meaningless game played with meaningless marks on paper, the only mathematical experience to which we can refer is the making of marks on paper.

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

The longer mathematics lives the more abstract - and therefore, possibly also the more practical - it becomes.

The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future.

Mathematics is as old as Man.

Mathematics is the most beautiful and most powerful creation of the human spirit.

If mathematics is to be understood widely, we need to emphasise its elegance and its applications. Sometimes it seems that universities want to emphasise how difficult it is!

If a man's wit be wandering, let him study the mathematics.

In mathematics we have long since drawn the rein, and given over a hopeless race.

Charles Babbage

Mathematics was hard, dull work. Geography pleased me more. For dancing I was quite enthusiastic.

John James Audubon