§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.
“Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.”
Symmetry (1952)
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Hermann Weyl 28
German mathematician 1885–1955Related quotes
“The essence of mathematics lies entirely in its freedom.”
Variant translation: The essence of mathematics is in its freedom.
From Kant to Hilbert (1996)
Vorlesungen über analytische Mechanik [Lectures on Analytical Mechanics] (1847/48; edited by Helmut Pulte in 1996).
“Only by a study of the development of mathematics can its contemporary significance be understood.”
100 Years of Mathematics: a Personal Viewpoint (1981)
Context: The professional mathematician can scarcely avoid specialization and needs to transcend his private interests and take a wide synoptic view of the whole landscape of contemporary mathematics. His scientific colleagues are continually seeking enlightenment on the relevance of mathematical abstractions. The undergraduate needs a guidebook to the topography of the immense and expanding world of mathematics. There seems to be only one way to satisfy these varied interests... a concise historical account of the main currents... Only by a study of the development of mathematics can its contemporary significance be understood.
Footnote: In the future by 'mathematics' will always be meant 'pure mathematics'.
The Foundations of Mathematics (1925)
“All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty.”
As quoted in Lichtenberg : A Doctrine of Scattered Occasions (1959) by Joseph Peter Stern, p. 84
Context: All mathematical laws which we find in Nature are always suspect to me, in spite of their beauty. They give me no pleasure. They are merely auxiliaries. At close range it is all not true.