Computers & Information Science
(Benioff, Hugo) [Lehmer, Derrick]  "Machine Performs Difficult Mathematical Calculations" in Carnegie Institution of Washington News Service Bulletin Staff Edition Volume III, Nos. 131.
£100.00

First edition, staff issue. The present volume collects three years of Carnegie Institution News Service Bulletins (19331935), including articles and scientific papers on a variety of subjects researched by Carnegie staff members around the world (this is the staff edition, as opposed to the press and school editions, which do not include the "Notes on Institution Affairs").
The key article in this volume is "Machine Performs Difficult Mathematical Calculations", an account of the "Congruence Machine" (now known as a Lehmer sieve) developed to determine prime numbers by University of California mathematician Derrick Norman Lehmer (18671938). Determining which numbers are prime is a key problem in mathematics, and Lehmer made his name in 1914 by completing the series of primes up to 10 million. The first Lehmer sieve was constructed by Lehmer and his son Derrick Henry in 1926, using bicycle chains and metal rods that closed an electrical circuit when a solution to a factorization problem was found. In 1932 they completed a more advanced device utilizing gears and light beams, which is detailed in the present article. Lehmer sieves were an important early type of mechanical calculator, and the basic concept is still used for mathematical sieves in modern software.
With the ownership inscription of renowned seismologist Hugo Benioff, known for the innovative seismographs he developed, as well as his work charting the locations of deep earthquakes in the Pacific seabed.
 Washington D. C.: Carnegie Institution, 193335. Tall quarto. Original green cloth, titles to upper board gilt. Illustrations throughout. Upper corner bumped, a little dampstain to tail of spine slightly affecting contents, minor rubbing at extremities, margins of contents toned. A very good copy.
(Fox, Phyllis) MilneThompson, L. M.  The Calculus of Finite Differences
£750.00

Second edition of this classic in applied mathematics, originally published in 1933. With the ownership signature of computer scientist Phyllis Fox and the date January 31, 1956, indicating that Fox purchased this volume while working on the numerical solution of partial differential equations for UNIVAC.
During the late 1940s Phyllis Fox (1923  ) earned undergraduate degrees in mathematics and electrical engineering and worked as an operator for GE’s differential analyser. In 1949 she obtained her master’s in electrical engineering at MIT, writing a program for the school’s unfinished vacuum tube computer the Whirlwind I. Fox then earned her doctorate in mathematics at MIT, supervised by the prominent applied mathematician ChiaChiao Lin (19162013).
As Fox explained to an interviewer from the Society for Industrial and Applied Mathematics in 2005, between 1954 and 1958 she worked at the Courant Institute, an Atomic Energy Commissionfunded department of the City University of New York. “[Richard] Courant ran it, but Courant, Kurt O. Friedrichs, Levy, all these famous, really, applied mathematicians were there, and I got a job. As what, I don’t know. But I wasn’t really a fluid dynamicist. They had bought a computer, a Univac. Now, none of these applied mathematicians really wanted to bother with the machine, but a physicist named Bob Richtmyer who came out of AEC and Los Alamos was there. He was interested in doing computations on the Univac... At that time, the main problem thing they were looking for was controlled thermonuclear. Now this isn’t the bomb. The controlled fusion, of course, is the source of all power, if you can make it work. Fine. Theoretically it was clean, and an infinite source of power, once you got it going. And the Russians were probably working on it, so it was very secret. But of course, the technique would apply also to Teller and his bomb. I wasn’t in the abstract analysis part of the research, but I helped with the computer probably, and some of the analysis of the equations involved, because I had that experience from MIT.”
After leaving CUNY, Fox worked on the DYNAMO programming language and the first LISP interpreter and manual, taught at the Newark College of Engineering, and consulted for Bell Labs until her retirement in 1984.
The author of the present volume, Louis Melville MilneThomson (18911974), was a professor at the Royal Naval College at Greenwich who made significant contributions to applied mathematics, including the MilneThomson circle theorem and the MilneThomson method for finding a holomorphic function. He was particularly concerned with “making mathematics accessible to the beginner or nonspecialist” and in 1933 “published the first of several textbooks. The Calculus of Finite Differences was based on his own experience of making tables and, in its preface, he states that one motivation for writing it was the lack of other texts suitable for his students” (ODNB).

London: Macmillan and Co., Limited, 1951.
Octavo. Original blue cloth, titles to spine gilt. With the dust jacket. Lower corner of upper board bumped, tips lightly rubbed, contents faintly toned. A very good copy in the priceclipped jacket with tanned spine panel and a few small chips and splits.
Hartree, Douglas R.  Calculating Machines: Recent & Prospective Developments
£575.00
 First edition, first impression of "the first booklet on electronic computers separately published by a conventional publisher, and also one of the earliest discussions of how these machines could be used in scientific calculations" (Origins of Cyberspace 649). In addition to his significant contributions to ballistics and quantum theory, British mathematician Douglas Hartree (18971958) was a leader in efforts to automate scientific calculations. He was "involved in the development of the digital electronic computer, which emerged from wartime attempts to automate calculation further... In 1946 Hartree's advice was sought in the application of the United States army's ENIAC (electronic numerical integrator and computer) to the production of ballistic tables" (ODNB). This booklet was based on his experience with ENIAC, and describes in detail the machine's operation, its memory capacity, how problems are encoded for it to process, and what types of mathematical questions it can address. It also offers hints of future applications, such as research in fluid dynamics, statistics, number theory, and economics, where the burden of manual calculation was previously too great to allow for indepth analysis.
 Cambridge: Cambridge University Press, 1947. Octavo. Original cream wrappers printed in brown. 2 plates from photographs, equations and charts within the text. Ownership signature to upper cover, title and author's name written in ink on the spine. Wrappers tanned, crease to lower cover also slightly affecting final ten leaves. A very good copy.
Robinson, J. A.  "A MachineOriented Logic Based on the Resolution Principle"
£450.00

First publication of the resolution principle, the standard of logical deduction in AI applications.
The basic computational method in logic programming, the unification algorithm, was proposed by mathematician Jacques Herbrand in 1930, but its first practical use was not discovered until Robinson introduced it in this paper as the basic operation of his resolution principle. “Robinson described his resolution principle as ‘machineoriented’ in that it was particularly suitable for proofs to be performed by computer, having only one rule of inference that could be applied many times. Robinson’s resolution has since been used as the standard of logical deduction in AI applications” (Hook & Norman, Origins of Cyberspace 865).
“Born in Halifax, England, and having served in the RAF, [Robinson] attended Cambridge University, where he read classics. He received his master's degree in philosophy from the University of Oregon and his doctorate in philosophy from Princeton University in 1956. His interests thereafter focused on computers and logic. In 1963, as a visitor from Rice University in Texas to the Argonne National Laboratories, he became interested in automated reasoning, and in 1963 invented Resolution and Unification. In 1967 he became the Distinguished University Professor at Syracuse University and later Visiting Professor at Edinburgh University in Scotland.” (New York Times obituary).
Bibliography: Hook & Norman, Origins of Cyberspace 865.

[in] Journal of the Association for Computing Machinery, volume 12, number 1, pages 2341. Baltimore, MD: The Association for Computing Machinery, 1965. Quarto. Original cream wrappers printed in black. Remnants of a mailing label to the upper wrapper. Just a little rubbed and creased. Excellent condition.
Von Neumann, John  Theory of SelfReproducing Automata
£1,200.00

First edition of this important work on selfreproduction in machines and life forms, scare in the dust jacket.
Von Neumann became interested in the abilities of computers to selfreproduce during his work on the Institute for Advanced Studies computer project  noting that, since a Turing machine can make exact copies of any readable sequence, it can copy itself. He hoped to formulate a theory of selfreproduction that would be general enough to explain and predict selfreproduction in both machines and living things. “Viewing the logic of selfreplication and selfreproduction through the lens of formal logic and and selfreferential systems, von Neumann applied the results of Gödel and Turing to the foundations of biology” with his conjectures hitting “the heart of the probability or improbability of the origin of life” (Dyson, Turing’s Cathedral, pp. 283285).
Together with Stanislaw Ulam, von Neumann attempted to develop these ideas for publication, but they remained remained unfinished at his death. “The incomplete manuscript, including a lengthy introduction based on a series of five lectures given by von Neumann at the University of Illinois in 1949, was eventually assembled, with careful editing by Arthur Burks, and published as Theory of SelfReproducing Automata almost ten years after von Neumann’s death... Our understanding of selfreproduction in biology, and our development of selfreproducing technology, proceeded almost exactly as the proposed theory described” (Dyson, p. 286).

Edited and Compiled by Arthur W. Banks. Urbana & London: University of Illinois Press, 1966.
Octavo. Original green cloth, titles to spine and upper board in black. With the dust jacket. Contemporary ownership signature in blue ink to the front free endpaper. An excellent, fresh copy in the lightly rubbed jacket that is tanned, particularly along the spine panel, and has some nicks and short splits at the edges.