Presidential Address British Association for the Advancement of Science, Section A (1873); Nature, Vol. 8, p. 449.
[1522]. Another way of convincing ourselves how largely this process [of assimilation of mathematics by physics] has gone on would be to try to conceive the effect of some intellectual catastrophe, supposing such a thing possible, whereby all knowledge of mathematics should be swept away from men’s minds. Would it not be that the departure of mathematics would be the destruction of physics? Objective physical phenomena would, indeed, remain as they are now, but physical science would cease to exist. We should no doubt see the same colours on looking into a spectroscope or polariscope, vibrating strings would produce the same sounds, electrical machines would give sparks, and galvanometer needles would be deflected; but all these things would have lost their meaning; they would be but as the dry bones—the disjecta membra—of what is now a living and growing science. To follow this conception further, and to try to image to ourselves in some detail what would be the kind of knowledge of physics which would remain possible, supposing all mathematical ideas to be blotted out, would be extremely interesting, but it would lead us directly into a dim and entangled region where the subjective seems to be always passing itself off for the objective, and where I at least could not attempt to lead the way, gladly as I would follow any one who could show where a firm footing is to be found. But without venturing to do more than to look from a safe distance over this puzzling ground, we may see clearly enough that mathematics is the connective tissue of physics, binding what would else be merely a list of detached observations into an organized body of science.—Foster, G. C.
Presidential Address British Association for the Advancement of Science, Section A (1877); Nature, Vol. 16, p. 313.
[1523]. In Plato’s time mathematics was purely a play of the free intellect; the mathematic-mystical reveries of a Pythagoras foreshadowed a far-reaching significance, but such a significance (except in the case of music) was as yet entirely a matter of fancy; yet even in that time mathematics was the prerequisite to all other studies! But today, when mathematics furnishes the only language by means of which we may formulate the most comprehensive laws of nature, laws which the ancients scarcely dreamed of, when moreover mathematics is the only means by which these laws may be understood,—how few learn today anything of the real essence of our mathematics!... In the schools of today mathematics serves only as a disciplinary study, a mental gymnastic; that it includes the highest ideal value for the comprehension of the universe, one dares scarcely to think of in view of our present day instruction.—Lindeman, F.
Lehren und Lernen in der Mathematik (München, 1904), p. 14.
[1524]. All applications of mathematics consist in extending the empirical knowledge which we possess of a limited number or region of accessible phenomena into the region of the unknown and inaccessible; and much of the progress of pure analysis consists in inventing definite conceptions, marked by symbols, of complicated operations; in ascertaining their properties as independent objects of research; and in extending their meaning beyond the limits they were originally invented for,—thus opening out new and larger regions of thought.—Merz, J. T.
History of European Thought in the 19th Century (Edinburgh and London, 1903), Vol. 1, p. 698.
[1525]. All the effects of nature are only mathematical results of a small number of immutable laws.—Laplace.
A Philosophical Essay on Probabilities [Truscott and Emory] (New York, 1902), p. 177; Oeuvres, t. 7, p. 139.
[1526]. What logarithms are to mathematics that mathematics are to the other sciences.—Novalis.