Pure Mathematics Quotes

“It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty.”
― Bertrand Russell, A History of Western Philosophy

“This is not mathematics, it is theology.
(On being exposed to Hilbert's work in invariant theory.)”
― Paul Gordan

“One rather curious conclusion emerges, that pure mathematics is on the whole distinctly more useful than applied. ... For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.”
― G.H. Hardy, A Mathematician's Apology

“It is the dull and elementary parts of applied mathematics, as it is the dull and elementary parts of pure mathematics, that work for good or ill. Time may change all this. No one foresaw the applications of matrices and groups and other purely mathematical theories to modern physics, and it may be that some of the 'highbrow' applied mathematics will become 'useful' in as unexpected a way; but the evidence so far points to the conclusion that, in one subject as in the other, it is what is commonplace and dull that counts for practical life.”
― G.H. Hardy, A Mathematician's Apology

“Even a pure mathematician may find his appreciation of this geometry [applied geometry] quickened, since there is no mathematician so pure that he feels no interest at all in the physical world; but, in so far as he succumbs to this temptation, he will be abandoning his purely mathematical position.”
― G.H. Hardy, A Mathematician's Apology

“I spoke of the 'real' mathematics of Fermat and other great mathematicians, the mathematics which has permanent aesthetic value, as for example the best Greek mathematics has, the mathematics which is eternal because the best of it may, like the best literature, continue to cause intense emotional satisfaction to thousands of people after thousands of years. These men were all primarily pure mathematicians; but I was not thinking only of pure mathematics. I count Maxwell and Einstein, Eddington and Dirac, among 'real' mathematicians. The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are, at present at any rate, almost as 'useless' as the theory of numbers. It is the dull and elementary parts of applied mathematics, as it is the dull and elementary parts of pure mathematics, that work for good or ill.”
― G.H. Hardy, A Mathematician's Apology

“Pure mathematics shall be convinced by definite equations for the given indefinite number system”
― P.S. Jagadeesh Kumar

“Classical music and pure mathematics get trapped in their own history, their own self-awareness, their own high standards.”
― Lloyd N. Trefethen, TREFETHEN'S INDEX CARDS: FORTY YEARS OF NOTES ABOUT PEOPLE, WORDS AND MATHEMATICS