Stencils Solving by Raphael Robinson (2 results)

Condition: Very Good. Booklet and stenciled Hollerith cards are in original cloth case. Case is missing one end panel. Booklet (14 pages) has the following sections: The Method of Exclusion; Use of the Stencils; Large or Negative Values of a; Construction of the Stencils. No marks in very lightly read booklet. Front softcover sunning. The stencils are made on 275 Hollerith cards (7 3/8 inches x 3 3/4 inches). All, save one, is labelled âExclusion Modulus, Quadratic Character of m, Value of a/m, Stencils for Solving [formula], by R.M Robinson. One card has no label. First card is gift-inscribed âTo Derrick H. and Emma Lehmer with the compliments of the ââauthorââ [and signed] Raphael M. Robinsonâ. The Lehmerâs, both famous mathematicians, were in the center of research into early electronic computing (including ENIAC). No DJ.

First edition. Narrow octavo. 14 pp. Publisher's printed wrappers. Together with 274 IBM punch cards (each with the same printed title across the top - "Quadratic Character of m" and with Robinson's name and copyright data). Both housed together in the publisher's cloth case with metallic snap and spine lettering in black. Bit of wear to bottom case joint but overall an excellent copy.From the introduction - "Since quadratic congruences play a fundamental role in the theory of numbers, it seems very desirable to have a simple way to solve them, even when moderately large numbers are involved. The method of exclusion, when combined with a suitable mechanical device (such as these stencils), provides an easy method for solution" Raphael M. Robinson was a leading figure in mathematics and taught at Berkeley from 1937 to 1973."Even among world-renowned mathematicians, Robinson was exceptional. In an age of specialization he contributed significantly to six fields: logic, set theory, geometry, complex analysis, number theory, and combinatorics; and in a subject often considered a young person's game, he continued to produce significant mathematics into his eighties. He also anticipated most of the mathematical community by a good 20 years in making use of computers to obtain results in pure mathematics. In 1951, never having seen one of the new computing machines and working only from a manual, he coded the first successful program to test very large numbers for primality. ?That the code was without error was (and still is) a remarkable feat,? according to the recently published history of the Institute for Numerical Analysis on the UCLA campus. ?In an age where most of our journals are filled with papers which (even if good) exploit theories for their own sake. it is refreshing and stimulating to encounter one of Robinson's papers,? one of the foremost number theorists of the century has written. ?In each of them he takes a problem, old or new, which can be stated in simple and intelligible terms, and either solves it, or at least adds much that is new. His scholarship is impeccable; it is plain that he never writes until he has thought deeply, and until he has sought out every relevant piece of existing knowledge.?Approximately a quarter of Robinson's publications are distributed among seven different topics in logic and the foundations of mathematics. The one to which he gave most attention was that of undecidable theories, an interest that he shared with his wife, Julia. By way of illustration, the mathematical structure consisting of the integers with their operation of addition is said to have a decidable theory. This means it is possible to program a computer so that, given any sentence about the structure in a logically defined language, the computer will make a finite computation that determines whether the sentence is true or false. Another mathematical structure with a decidable theory is that of all real numbers with their operations of addition and multiplication. (This was shown by Alfred Tarski, also of Berkeley) But a major mathematical discovery of this century was the fact that that the structure of integers with both operations of addition and multiplication has an undecidable structure, because there is no computer program that can decide the truth or falsity of every sentence of its language. In several papers Robinson was able to show that a number of other mathematical theories are also undecidable. His most valuable contribution, however, was devising a theory with a finite number of axioms that is ?essentially undecidable?--a concept introduced by Tarski. The book Undecidable Theories (Mostowski, Robinson and Tarski) has provided a tool for researchers to identify undecidable theories in all parts of mathematics. " (Calisphere).