"THE PROBLEM MAY BE SOLVED IN A NEW AND PERHAPS BETTER, CERTAINLY A REMARKABLE WAY": FOUR MATHEMATICAL PAPERS BY GEORGE BOOLE, 1846-65

BOOLE, George. Four Mathematical Papers: On the Comparison of Transcendents, with Certain Applications to the Theory of Definite Integrals… Read May 7, 1857. BOUND WITH: On the Differential Equations of Dynamics… Read January 22, 1863. BOUND WITH: On the Differential Equations which Determine the Form of the Roots of Algebraic Equations. Read May 26, 1864. BOUND WITH: On the Analysis of Discontinuous Functions. Read July 20, 1846. London: Richard Taylor and William Francis (4th paper Royal Society of Edinburgh), 1858, 1863, 1865, 1846. Octavo, modern marbled paper wrappers. Housed in a custom clamshell box. $2600.

First appearances of four of Boole’s important papers on differential equations, "closely connected with Boole's work on mathematical logic," each extracted from the journal in which it originally appeared: three from Philosophical Transactions, and the fourth from Transactions of the Royal Society of Edinburgh.

"Boole (1815-64) invented the first practical system of logic in algebraic form, which enabled more advances to be made in the decades of the 19th century than in the 22 centuries preceding. Boole's work led to the creation of set theory and probability theory in mathematics, to the philosophical work of Pierce, Russell, Whitehead and Wittgenstein, and to computer technology via the master's thesis of C.E. Shannon (1937), who recognized that the true/false values in Boole's two-valued algebra were analogous to the open and closed states of electric circuits. This invention of the binary digit or 'bit' made possible the development of the digital computer" (Norman 266). Boole's scientific writings consist of some 50 papers, two textbooks, and two volumes dealing with mathematical logic. The 1857 paper collected here, "On the Comparison of Transcendents," is Boole's demonstration of "a fundamental theorem for the summation of integrals whose limits are determined by the roots of an algebraic equation," as well as the "application of that theorem to the problem of the comparison of algebraic transcendents" (p. 745). The earliest paper in this collection, the 1846 "On the Analysis of Discontinuous Functions" (published with "On a Certain Multiple Definite Integral," also present), is designed "to illustrate the mathematical doctrine of discontinuity, and to present a few remarks on some connected subjects… A hope is entertained that the considerations by which the theorem is here deduced will serve to render its real nature less doubtful" (p. 124).

"Other papers dealt with differential equations, and the majority of those published after 1850 studied the theory of probability, closely connected with Boole's work on mathematical logic" (DSB). Indeed, the 1863 and 1864 papers collected here (Boole died in 1864 at the age of 49) tackle various aspects of differential equations. "In all his writings, Boole exhibited considerable technical skill, but his facility in dealing with symbolic operators did not delude him into an undue reliance on analogy… Boole greatly increased the power of the operational calculus, but seldom allowed himself to be carried away by technical success: at a time when the need for precise and unambiguous definitions was often ignored, he was striving, although perhaps not always with complete success, to make his foundations secure… Boole's two-valued algebra has recently been applied to the design of electric circuits containing simple switches, relay, and control elements. In particular, it has a wide field of application in the design of high-speed computers using the binary system of digital numeration" (DSB). The three papers extracted from Philosophical Transactions have been bound with the volume title pages from those journals.

Fine condition.