Schriften (Berlin, 1901), Teil 2, p. 222.
[1527]. Any intelligent man may now, by resolutely applying himself for a few years to mathematics, learn more than the great Newton knew after half a century of study and meditation.—Macaulay.
Milton; Critical and Miscellaneous Essays (New York, 1879), Vol. 1, p. 13.
[1528]. In questions of science the authority of a thousand is not worth the humble reasoning of a single individual.—Galileo.
Quoted in Arago’s Eulogy on Laplace; Smithsonian Report, 1874, p. 164.
[1529]. Behind the artisan is the chemist, behind the chemist a physicist, behind the physicist a mathematician.—White, W. F.
Scrap-book of Elementary Mathematics (Chicago, 1908), p. 217.
[1530]. The advance in our knowledge of physics is largely due to the application to it of mathematics, and every year it becomes more difficult for an experimenter to make any mark in the subject unless he is also a mathematician.—Ball, W. W. R.
History of Mathematics (London, 1901), p. 503.
[1531]. In very many cases the most obvious and direct experimental method of investigating a given problem is extremely difficult, or for some reason or other untrustworthy. In such cases the mathematician can often point out some other problem more accessible to experimental treatment, the solution of which involves the solution of the former one. For example, if we try to deduce from direct experiments the law according to which one pole of a magnet attracts or repels a pole of another magnet, the observed action is so much complicated with the effects of the mutual induction of the magnets and of the forces due to the second pole of each magnet, that it is next to impossible to obtain results of any great accuracy. Gauss, however, showed how the law which applied in the case mentioned can be deduced from the deflections undergone by a small suspended magnetic needle when it is acted upon by a small fixed magnet placed successively in two determinate positions relatively to the needle; and being an experimentalist as well as a mathematician, he showed likewise how these deflections can be measured very easily and with great precision.—Foster, G. C.