Nature and Mathematics III

“The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena." (David Hilbert)

“What we can observe is not nature itself, but nature exposed to our method of questioning.”  (Werner Heisenberg)

"All the pictures which science draws of Nature, and which alone seem capable of according with observational facts, are mathematical pictures." (Sir James Jeans)

"Nature is probably quite indifferent to the aesthetic preferences of mathematicians.” (Alfred N Whitehead, “Science and the Modern World”, 1925)

"Among all of the mathematical disciplines the theory of differential  equations is the most important […]. It furnishes the explanation of all those elementary manifestations of nature which involve time."  (Sophus Lie)

“This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.” (William Whewell, “The Philosophy of the Inductive Sciences”, 1858)

“Mathematics in its pure form, as arithmetic, algebra, geometry, and the applications of the analytic method, as well as mathematics applied to matter and force, or statics and dynamics, furnishes the peculiar study that gives to us, whether as children or as men, the command of nature in this its quantitative aspect; mathematics furnishes the instrument, the tool of thought, which we wield in this realm.” (William T  Harris, “Psychologic Foundations of Education”, 1898)

"It will probably be the new mathematical discoveries which are suggested through physics that will always be the most important, for, from the beginning Nature has led the way and established the pattern which mathematics, the Language of Nature, must follow." (George D Birkhoff)

"Nature imitates mathematics." (Gian-Carlo Rota)

"For me mathematics cultivates a perpetual state of wonder about the nature of mind, the limits of thoughts, and our place in this vast cosmos." (Clifford A Pickover)