Source: Science and Sanity (1933), p. 64.
Context: Any organism must be treated as-a-whole; in other words, that an organism is not an algebraic sum, a linear function of its elements, but always more than that. It is seemingly little realized, at present, that this simple and innocent-looking statement involves a full structural revision of our language...
“Some definite interpretation of a linear algebra would, at first sight, appear indispensable to its successful application.”
On the Uses and Transformations of Linear Algebra (1875)
Context: Some definite interpretation of a linear algebra would, at first sight, appear indispensable to its successful application. But on the contrary, it is a singular fact, and one quite consonant with the principles of sound logic, that its first and general use is mostly to be expected from its want of significance. The interpretation is a trammel to the use. Symbols are essential to comprehensive argument.
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Benjamin Peirce 24
American mathematician 1809–1880Related quotes
“The first epoch-making algebra to appear in print was the Ars Magna of Cardan”
Source: History of Mathematics (1925) Vol.2, p.384
Context: The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). This was devoted primarily to the solution of algebraic equations. It contained the solution of the cubic and biquadratic equations, made use of complex numbers, and in general may be said to have been the first step toward modern algebra.
Source: History of Mathematics (1925) Vol.2, Ch. 6: Algebra
The octonions, Bull. Amer. Math. Soc., 39, 145–205, 2002 http://doi.org/10.1090/S0273-0979-01-00934-X, (p. 147)
"On the Harmony of Theory and Practice in Mechanics" (Jan. 3, 1856)
Context: In treating of the practical application of scientific principles, an algebraical formula should only be employed when its shortness and simplicity are such as to render it a clearer expression of a proposition or rule than common language would be, and when there is no difficulty in keeping the thing represented by each symbol constantly before the mind.<!--p. 177
"Über die verschiedenen Ansichten in Bezug auf die actualunendlichen Zahlen" ["Over the different views with regard to the actual infinite numbers"] - Bihand Till Koniglen Svenska Vetenskaps Akademiens Handigar (1886)
The Differential and Integral Calculus (1836)