“A less inflexible picture of mathematics is one that focuses on the fact that it is an open-ended human activity. Inventionism is the belief that mathematics is nothing more than what mathematicians do. …We invent mathematics; we do not discover it. …The independent discovery of the same mathematical theorems by different mathematicians from totally different economic, cultural, and political backgrounds—often at widely separated times in history—argues against such a simple view. The inventionist could respond by pointing to the universality of human languages. …One might expect that those aspects of this universal grammar that share features of logic, and hence counting, would also make counting appear instinctive. In fact, although simple counting… is fairly universal in ancient and primitive cultures, virtually none of them went on to carry out mathematical operations more sophisticated than counting. This suggests that these higher mathematical operations are not genetically programmed into the human brain… They are more likely to be by-products of multi-purpose pattern-recognition capabilities.”

Source: 1970s, Economics As a Science, 1970, p. 97

Source: Achimedes (1920), Ch. I. Archimedes, p.1

Translation as quoted in The Gradual Acceptance of the Copernican Theory of the Universe (1917) by Dorothy Stimson, p. 115
Context: If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash. For it is not unknown that Lactantius, the writer celebrated in other ways but very little in mathematics, spoke somewhat childishly of the shape of the earth when he derided those who declared the earth had the shape of a ball. So it ought not to surprise students if such should laugh at us also. Mathematics is written for mathematicians to whom these our labors, if I am not mistaken, will appear to contribute something even to the ecclesiastical state the headship of which your Holiness now occupies. (Author's preface to de revolutionibus) http://la.wikisource.org/wiki/Pagina:Nicolai_Copernici_torinensis_De_revolutionibus_orbium_coelestium.djvu/8

Source: The Frontiers of Meaning: Three Informal Lectures on Music (1994), Ch. 3 : Explaining the Obvious

100 Years of Mathematics: a Personal Viewpoint (1981)
Context: For the great majority of mathematicians, mathematics is... a whole world of invention and discovery—an art. The construction of a new theorem, the intuition of some new principle, or the creation of a new branch of mathematics is the triumph of the creative imagination of the mathematician, which can be compared to that of a poet, the painter and the sculptor.

Induction and Analogy in Mathematics (1954)

Tout le monde y croit cependant, me disait un jour M. Lippmann, car les expérimentateurs s'imaginent que c'est un théorème de mathématiques, et les mathématiciens que c'est un fait expérimental.
Calcul des probabilités (2nd ed., 1912), p. 171

Preface Letter to Pope Paul III as quoted by Edwin Arthur Burtt in The Metaphysical Foundations of Modern Physical Science (1925)
De revolutionibus orbium coelestium (1543)
Context: Nor do I doubt that skilled and scholarly mathematicians will agree with me if, what philosophy requires from the beginning, they will examine and judge, not casually but deeply, what I have gathered together in this book to prove these things.... Mathematics is written for mathematicians, to whom these my labours, if I am not mistaken, will appear to contribute something.... What... I may have achieved in this, I leave to the decision of your Holiness especially, and to all other learned mathematicians.... If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash.

100 Years of Mathematics: a Personal Viewpoint (1981)