class="rt">39

IV. The Value of Mathematics 49 V. The Teaching of Mathematics 72 VI. Study and Research in Mathematics 86 VII. Modern Mathematics 108 VIII. The Mathematician 121 IX. Persons and Anecdotes (A-M) 135 X. Persons and Anecdotes (N-Z) 166 XI. Mathematics as a Fine Art 181 XII. Mathematics as a Language 194 XIII. Mathematics and Logic 201 XIV. Mathematics and Philosophy 209 XV. Mathematics and Science 224 XVI. Arithmetic 261 XVII. Algebra 275 XVIII. Geometry 292 XIX. The Calculus and Allied Topics 323 XX. The Fundamental Concepts of Time and Space 345 XXI. Paradoxes and Curiosities 364 Index   385

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MEMORABILIA MATHEMATICA

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MEMORABILIA MATHEMATICA

CHAPTER I
DEFINITIONS AND OBJECT OF MATHEMATICS

101. I think it would be desirable that this form of word [mathematics] should be reserved for the applications of the science, and that we should use mathematic in the singular to denote the science itself, in the same way as we speak of logic, rhetoric, or (own sister to algebra) music.—Sylvester, J. J.

Presidential Address to the British Association, Exeter British Association Report (1869); Collected Mathematical Papers, Vol. 2, p. 659.

102. ... all the sciences which have for their end investigations concerning order and measure, are related to mathematics, it being of small importance whether this measure be sought in numbers, forms, stars, sounds, or any other object; that, accordingly, there ought to exist a general science which should explain all that can be known about order and measure, considered independently of any application to a particular subject, and that, indeed, this science has its own proper name, consecrated by long usage, to wit, mathematics. And a proof that it far surpasses in facility and importance the sciences which depend upon it is that it embraces at once all the objects to which these are devoted and a great many others besides; ....—Descartes.

Rules for the Direction of the Mind, Philosophy of D. [Torrey] (New York, 1892), p. 72.

103. [Mathematics] has for its object the indirect measurement of magnitudes, and it purposes to determine magnitudes by each other, according to the precise relations which exist between them.—Comte.

Positive Philosophy [Martineau], Bk. 1, chap. 1.