
The only royal road to elementary geometry is ingenuity.
Eric Temple Bell 
Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.
Eric Temple Bell

A number of aspects of mathematics are not much talked about in contemporary histories of mathematics. We have in mind business and commerce, war, number mysticism, astrology, and religion. In some instances, writers, hoping to assert for mathematics a noble parentage and a pure scientific experience, have turned away their eyes. Histories have been eager to put the case for science, but the Handmaiden of the Sciences has lived a far more raffish and interesting life than her historians allow.
Eric Temple Bell 
Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.
Eric Temple Bell 
The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry as did Clifford, for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.
Eric Temple Bell 
The very basis of creative work is irreverence! The very basis of creative work is bold experimentation. There has never been a creator of lasting importance who has not also been an innovator.
Eric Temple Bell 
In his wretched life of less than twentyseven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century could say without exaggeration, "Abel has left mathematicians enough to keep them busy for five hundred years." Asked how he had done all this in the six or seven years of his working life, Abel replied, "By studying the masters, not the pupils."
Eric Temple Bell 
If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.
Eric Temple Bell

Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.
Eric Temple Bell 
Pick the assumptions to pieces till the stuff they are made of is exposed to plain view  this is the cardinal rule for understanding the basis of our beliefs.
Eric Temple Bell 
Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.
Eric Temple Bell 
Archimedes, Newton, and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit.
Eric Temple Bell 
Galois read the geometry from cover to cover as easily as other boys read a pirate yarn.
Eric Temple Bell 
Poincaré [was the last man to take practically all mathematics, pure and applied, as his province. ... Few mathematicians have had the breadth of philosophic vision that Poincaré had, and none in his superior in the gift of clear exposition.
Eric Temple Bell

Even stranger things have happened; and perhaps the strangest of all is the marvel that mathematics should be possible to a race akin to the apes.
Eric Temple Bell 
Had Poincaré been as strong in practical science as he was in theoretical he might have made a fourth with the incomparable three, Archimedes, Newton, and Gauss.
Eric Temple Bell