“If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good; and both Gauss and lesser mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean.” ScienceEvilMathematicsGoodHonorablePracticalApplicationsNumber TheoryGauss Book:A Mathematician's Apology Source: A Mathematician's Apology
“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.” TechniqueUsefulnessApplied ScienceApplicationsApplied KnowledgePure Mathematics Book:A Mathematician's Apology Source: A Mathematician's Apology
“We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not.” MathematicsUsefulnessApplicationsMathematicians Book:A Mathematician's Apology Source: 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.” AppreciationMathematicianApplied ScienceApplicationsPhysical WorldPure MathematicsApplied Problem Solving Book:A Mathematician's Apology Source: A Mathematician's Apology