"We construct concepts when we represent them in intuition a priori, without experience, or when we represent in intuition the object which corresponds to our concept of it. - The mathematician can never apply his reason to mere concepts, nor the philosopher to the construction of concepts. - In mathematics the reason is employed in concreto, however, the intuition is not empirical, but the object of contemplation is something a priori." (Immanuel Kant, "Logic", 1800)
"A mathematician is only perfect insofar as he is a perfect man, sensitive to the beauty of truth." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)
"Each mathematician for himself, and not anyone for any other, not even all for one, must tread that more than royal road which leads to the palace and sanctuary of mathematical truth.” (Sir William R Hamilton, “Report of the Fifth Meeting of the British Association for the Advancement of Science”, [Address] 1835)
"Every one knows there are mathematical axioms. Mathematicians have, from the days of Euclid, very wisely laid down the axioms or first principles on which they reason. And the effect which this appears to have had upon the stability and happy progress of this science, gives no small encouragement to attempt to lay the foundation of other sciences in a similar manner, as far as we are able." (William K Clifford et al, "Scottish Philosophy of Common Sense", 1915)
"Men have fallen in love with statues and pictures. I find it easier to imagine a man falling in love with a differential equation, and I am inclined to think that some mathematicians have done so. Even in a nonmathematician like myself, some differential equations evoke fairly violent physical sensations to those described by Sappho and Catallus when viewing their mistresses. Personally, I obtain an even greater 'kick' from finite difference equations, which are perhaps more like those which an up-to-date materialist would use to describe human behavior." (John B S Haldane, "The Inequality of Man and Other Essays", 1932)
"Any applied mathematicians - any engineer using mathematics - works sometimes more and sometimes less mathematically. When he is most mathematical he makes least appeal to experience." (Chandler Davis, "Materialist Mathematics", 1974)
"Mathematicians seem to have no difficulty in creating new concepts faster than the old ones become well understood." (Edward N Lorenz, "A scientist by choice", [acceptance speech of the Kyoto Prize 1991)
"Mathematicians are used to game-playing according to a set of rules they lay down in advance, despite the fact that nature always writes her own. One acquires a great deal of humility by experiencing the real wiliness of nature." (Philip W Anderson, "More and Different: Notes from a Thoughtful Curmudgeon", 2011)
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