Profound study of nature is the most fertile source of mathematical discoveries.
--
Ch. 1, p. 7Joseph Fourier
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I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future.
Benjamin Peirce
He that would speak Divine things in a language which living men of to-day can comprehend, must keep up with the researches and discoveries of men who study nature, and put her words into the speech of the present.
John Heyl Vincent
What these thinkers despise in the man of study is precisely the man who … does not predicate the capture of its environment by the species, or who, if he does predicate it, as the scientist does by his discoveries, retains for himself only the joy of knowledge and abandons the practical exploitation of his discoveries to others.
Julien Benda
My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc. (Perhaps we could say that this is what is involved in harmony between the 'left brain' and the 'right brain'). This kind of overall way of thinking is not only a fertile source of new theoretical ideas: it is needed for the human mind to function in a generally harmonious way, which could in turn help to make possible an orderly and stable society.
David Bohm
I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics. But, once they are conceived, the subject begins to live a peculiar life of its own and is ... governed by almost entirely aesthetical motivations. In other words, at a great distance from its empirical source, or after much "abstract" inbreeding, a mathematical subject is in danger of degeneration. Whenever this stage is reached the only remedy seems to me to be the rejuvenating return to the source: the reinjection of more or less directly empirical ideas.
John von Neumann
Fourier, Joseph
Fowler, Gene
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