What is Mathematics not? - Part II

“Mathematics is not a popular subject, even though its importance may be generally conceded. The reason for this is to be found in the common superstition that mathematics is but a continuation, a further development, of the fine art of arithmetic, of juggling with numbers.” (David Hilbert, “Geometry and the Imagination”, 1952)

“Mathematics is not only the model along the lines of which the exact sciences are striving to design their structure; mathematics is the cement which holds the structure together.” (Tobias Dantzig, “Number: The Language of Science”, 1954)

“Mathematics is not, then, merely a bunch of calculations that could be done much faster and better by an electronic machine; nor is it a science developed in ancient times, with nothing added to it since then except a bit of polish here and there .” (C Stanley Ogilvy, “Excursions in Mathematics”, 1956)

“The eternal lesson is that Mathematics is not something static, closed, but living and developing. Try as we may to constrain it into a closed form, it finds an outlet somewhere and escapes alive.” (Péter Rózsa, “Playing with Infinity”, 1961)

“Mathematics is not a question of calculation perforce but rather the presence of royalty: a law of infinite resonance, consonance and order.” (Le Corbusier, "Architecture and the Mathematical Spirit", 1962)

“[…] although mathematical concepts and operations are formulated to represent aspects of the physical world, mathematics is not to be identified with the physical world. However, it tells us a good deal about that world if we are careful to apply it and interpret it properly.” (Morris Kline, “Mathematics for the Nonmathematician”, 1967)

“[…] mathematics is not portraying laws inherent in the design of the universe but is merely providing man-made schemes or models which we can use to deduce conclusions about our world only to the extent that the model is a good idealization.” (Morris Kline, “Mathematics for the Nonmathematician”, 1967)

“The introduction and gradual acceptance of concepts that have no immediate counterparts in the real world certainly forced the recognition that mathematics is a human, somewhat arbitrary creation, rather than an idealization of the realities in nature, derived solely from nature. But accompanying this recognition and indeed propelling its acceptance was a more profound discovery - mathematics is not a body of truths about nature.” (Morris Kline, “Mathematical Thought from Ancient to Modern Times” Vol. III, 1972)

“Mathematics is not a compendium or memorizable formula and magically manipulated figures.” (Scott Buchanan, “Poetry and Mathematics”, 1975)

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple." (Stan Gudder, “A Mathematical Journey”, 1976)

 “Mathematics is not a branch of aesthetics. The mistake, which is common enough, probably stems from the requirement of aesthetic unity but is not identical with that unity.” (J K Feibleman, “Assumptions of Grand Logics”, 1979)