Eric Temple Bell
Obvious is the most dangerous word in mathematics.Collection: Knowledge
The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future...Collection: Mistake
Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the prevailing famine of substance.Collection: Imagination
In his wretched life of less than twenty-seven 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."Collection: Seven Years
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.Collection: Creative
If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics.Collection: Writing
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.Collection: Math
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.Collection: Views
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.Collection: Engineering
Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos.Collection: Simplicity
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.Collection: Beauty
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.Collection: Men
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.Collection: Math
Galois read the geometry from cover to cover as easily as other boys read a pirate yarn.Collection: Teenager
The only royal road to elementary geometry is ingenuity.Collection: Science
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.Collection: Opponents
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.Collection: Science
If "Number rules the universe" as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number.Collection: Math