[1594]. The effort of the economist is to see, to picture the inter-play of economic elements. The more clearly cut these elements appear in his vision, the better; the more elements he can grasp and hold in his mind at once, the better. The economic world is a misty region. The first explorers used unaided vision. Mathematics is the lantern by which what before was dimly visible now looms up in firm, bold outlines. The old phantasmagoria disappear. We see better. We also see further.—Fisher, Irving.
Transactions of Connecticut Academy, Vol. 9 (1892), p. 119.
[1595]. In the great inquiries of the moral and social sciences ... mathematics (I always mean Applied Mathematics) affords the only sufficient type of deductive art. Up to this time, I may venture to say that no one ever knew what deduction is, as a means of investigating the laws of nature, who had not learned it from mathematics, nor can any one hope to understand it thoroughly, who has not, at some time in his life, known enough of mathematics to be familiar with the instrument at work.—Mill, J. S.
An Examination of Sir William Hamilton’s Philosophy (London, 1878), p. 622.
[1596]. Let me pass on to say a word or two about the teaching of mathematics as an academic training for general professional life. It has immense capabilities in that respect. If you consider how much of the effectiveness of an administrator depends upon the capacity for co-ordinating appropriately a number of different ideas, precise accuracy of definition, rigidity of proof, and sustained reasoning, strict in every step, and when you consider what substitutes for these things nine men out of every ten without special training have to put up with, it is clear that a man with a mathematical training has incalculable advantages.—Shaw, W. H.
Perry’s Teaching of Mathematics (London, 1902), p. 73.
[1597]. Before you enter on the study of law a sufficient ground work must be laid.... Mathematics and natural philosophy are so useful in the most familiar occurrences of life and are so peculiarly engaging and delightful as would induce everyone to wish an acquaintance with them. Besides this, the faculties of the mind, like the members of a body, are strengthened and improved by exercise. Mathematical reasoning and deductions are, therefore, a fine preparation for investigating the abstruse speculations of the law.—Jefferson, Thomas.
Quoted in Cajori’s Teaching and History of Mathematics in the U. S. (Washington, 1890), p. 35.
[1598]. It has been observed in England of the study of law,—though the acquisition of the most difficult parts of its learning, the interpretation of laws, the comparison of authorities, and the construction of instruments, would seem to require philological and critical training; though the weighing of evidence and the investigation of probable truth belong to the province of the moral sciences, and the peculiar duties of the advocate require rhetorical skill,—yet that a large proportion of the most distinguished members of the profession has proceeded from the university (that of Cambridge) most celebrated for the cultivation of mathematical studies.—Everett, Edward.
Orations and Speeches (Boston, 1870), Vol. 2, p. 511.