“In short, mathematics is what we make it; not by each of us acting without due regard for what constitutes mathematics in our culture, but by seeking to build up new theories in the light of the old, and to solve outstanding problems generally recognized as valuable for the progress of mathematics as we know it. Until we make it, it fails to ‘exist’. And, having been made, it may at some future time even fail to be ‘mathematics’ any longer.” (Raymond L Wilder, “Introduction to the Foundations of Mathematics”, 1952)
“Mathematics does not grow because a Newton, a Riemann, or a Gauss happened to be born at a certain time; great mathematicians appeared because the cultural conditions - and this includes the mathematical materials - were conducive to developing them.” (Raymond L Wilder, “Introduction to the Foundations of Mathematics”, 1952)
“The principal mathematical element in the culture, embodying the living and growing mass of modern mathematics, will be chiefly possessed by the professional mathematicians. True, certain professions, such as engineering, physics, and chemistry, which employ a great deal of mathematics, carry a sizable amount of the mathematical tradition, and in some of these, as in the case of physics and engineering research, some individuals contribute to the growth of the mathematical element in the culture. But, in the main, the mathematical element of our culture is dependent for its existence and growth on the class of those individuals known as ‘mathematicians’.” (Raymond L Wilder, “Introduction to the Foundations of Mathematics”, 1952)
“The trouble seems to lie chiefly in the assumption that mathematics is by nature something absolute, unchanging with time and place, and therefore capable of being identified once the genius with the eye sharp enough to perceive and characterize it appears on the human scene. And, since mathematics is nothing of the sort (although the layman will probably go on for centuries hence believing that it is), only failure can ensue from the attempt so to characterize it.” (Raymond L Wilder, “Introduction to the Foundations of Mathematics”, 1952)
“There is nothing mysterious, as some have tried to maintain, about the applicability of mathematics. What we get by abstraction from something can be returned.” (Raymond L Wilder, “Introduction to the Foundations of Mathematics”, 1952)
“The only reality mathematical concepts have is as cultural elements or artifacts.” (Raymond L Wilder, “Evolution of Mathematical Concepts. An Elementary Study”, 1968)
“Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible.” (Raymond L Wilder, American Mathematical Monthly, 1994)
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