"[…] mathematics is not, never was, and never will be, anything more than a particular kind of language, a sort of shorthand of thought and reasoning. The purpose of it is to cut across the complicated meanderings of long trains of reasoning with a bold rapidity that is unknown to the mediaeval slowness of the syllogisms expressed in our words." (Charles Nordmann, "Einstein and the Universe", 1922)
"Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means." (Hermann Weyl, "The Open World: Three Lectures In the Metaphysical Implications of Science", 1932)
"Just as mathematics aims to study such entities as numbers, functions, spaces, etc., the subject matter of metamathematics is mathematics itself." (Frank C DeSua, "Mathematics: A Non-Technical Exposition", American Scientist, 1954)
"There are at least four fundamental purposes that the study of mathematics should attain. First, it should serve as a functional tool in solving our individual everyday problems. [...] In the second place, mathematics serves as a handmaiden for the explanation of the quantitative situations in other subjects, such as economics, physics, navigation, finance, biology, and even the arts. [...] In the third place, mathematics, when properly conceived, becomes a model for thinking, for developing scientific structure, for drawing conclusions, and for solving problems. [...] In the fourth place, mathematics is the best describer of the universe about us." (Howard F Fehr, "Reorientation in Mathematics Education", Teachers Record 54, 1953)
"To find the simple in the complex, the finite in the infinite - that is not a bad description of the aim and essence of mathematics." (Jacob T Schwartz, "Discrete Thoughts: Essays on Mathematics, Science, and Philosophy", 1992)
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