The art of doing mathematics consists in finding that special case which contains all the germs of generality.
David Hilbert

The completion of my undergraduate training at the University of California (Berkeley) provided just the needed touches of rigor at advanced levels in both economics and mathematics.
Lawrence R. Klein

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
Andrew Wiles

The essence of mathematics lies in its freedom.
Georg Cantor

The infinite in mathematics is alway unruly unless it is properly treated.
James Newman

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

The mathematics is not there till we put it there.
Arthur Eddington

The mathematics of rhythm are universal. They don't belong to any particular culture.
John McLaughlin

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

The most painful thing about mathematics is how far away you are from being able to use it after you have learned it.
James Newman

The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence.
James Joseph Sylvester

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern.
Daniel Dennett

The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.
Charles Caleb Colton

The Theory of Groups is a branch of mathematics in which one does something to something and then compares the result with the result obtained from doing the same thing to something else, or something else to the same thing.
James Newman

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.
Edsger Dijkstra

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
Bertrand Russell

There should be no such thing as boring mathematics.
Edsger Dijkstra

This book is about physics and its about physics and its relationship with mathematics and how they seem to be intimately related and to what extent can you explore this relationship and trust it.
Roger Penrose

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.
Felix Klein

To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be.
Leonhard Euler