Who was the mathematician who wrote a computer software program that would play chess with a human?

What mathematicians called an “effective” method for solving a problem was simply one that could be carried by a human mathematical clerk working by rote. In Turing’s time, those rote-workers were in fact called “computers,” and human computers carried out some aspects of the work later done by electronic computers. The Entscheidungsproblem sought an effective method for solving the fundamental mathematical problem of determining exactly which mathematical statements are provable within a given formal mathematical system and which are not. A method for determining this is called a decision method. In 1936 Turing and Church independently showed that, in general, the Entscheidungsproblem problem has no resolution, proving that no consistent formal system of arithmetic has an effective decision method. In fact, Turing and Church showed that even some purely logical systems, considerably weaker than arithmetic, have no effective decision method. This result and others—notably mathematician-logician Kurt Gödel’s incompleteness results—dashed the hopes, held by some mathematicians, of discovering a formal system that would reduce the whole of mathematics to methods that (human) computers could carry out. It was in the course of his work on the Entscheidungsproblem that Turing invented the universal Turing machine, an abstract computing machine that encapsulates the fundamental logical principles of the digital computer.

An important step in Turing’s argument about the Entscheidungsproblem was the claim, now called the Church-Turing thesis, that everything humanly computable can also be computed by the universal Turing machine. The claim is important because it marks out the limits of human computation. Church in his work used instead the thesis that all human-computable functions are identical to what he called lambda-definable functions (functions on the positive integers whose values can be calculated by a process of repeated substitution). Turing showed in 1936 that Church’s thesis was equivalent to his own, by proving that every lambda-definable function is computable by the universal Turing machine and vice versa. In a review of Turing’s work, Church acknowledged the superiority of Turing’s formulation of the thesis over his own (which made no reference to computing machinery), saying that the concept of computability by a Turing machine “has the advantage of making the identification with effectiveness…evident immediately.”

The earliest substantial work in the field of artificial intelligence was done in the mid-20th century by the British logician and computer pioneer Alan Mathison Turing. In 1935 Turing described an abstract computing machine consisting of a limitless memory and a scanner that moves back and forth through the memory, symbol by symbol, reading what it finds and writing further symbols. The actions of the scanner are dictated by a program of instructions that also is stored in the memory in the form of symbols. This is Turing’s stored-program concept, and implicit in it is the possibility of the machine operating on, and so modifying or improving, its own program. Turing’s conception is now known simply as the universal Turing machine. All modern computers are in essence universal Turing machines.

Alan Turing© Fine Art Images—Heritage Images/age fotostock

During World War II, Turing was a leading cryptanalyst at the Government Code and Cypher School in Bletchley Park, Buckinghamshire, England. Turing could not turn to the project of building a stored-program electronic computing machine until the cessation of hostilities in Europe in 1945. Nevertheless, during the war he gave considerable thought to the issue of machine intelligence. One of Turing’s colleagues at Bletchley Park, Donald Michie (who later founded the Department of Machine Intelligence and Perception at the University of Edinburgh), later recalled that Turing often discussed how computers could learn from experience as well as solve new problems through the use of guiding principles—a process now known as heuristic problem solving.

chess: Chess and artificial intelligence

Machines capable of playing chess have fascinated people since the latter half of the 18th century, when the Turk, the first of the pseudo-automatons,...

Turing gave quite possibly the earliest public lecture (London, 1947) to mention computer intelligence, saying, “What we want is a machine that can learn from experience,” and that the “possibility of letting the machine alter its own instructions provides the mechanism for this.” In 1948 he introduced many of the central concepts of AI in a report entitled “Intelligent Machinery.” However, Turing did not publish this paper, and many of his ideas were later reinvented by others. For instance, one of Turing’s original ideas was to train a network of artificial neurons to perform specific tasks, an approach described in the section Connectionism.

At Bletchley Park, Turing illustrated his ideas on machine intelligence by reference to chess—a useful source of challenging and clearly defined problems against which proposed methods for problem solving could be tested. In principle, a chess-playing computer could play by searching exhaustively through all the available moves, but in practice this is impossible because it would involve examining an astronomically large number of moves. Heuristics are necessary to guide a narrower, more discriminative search. Although Turing experimented with designing chess programs, he had to content himself with theory in the absence of a computer to run his chess program. The first true AI programs had to await the arrival of stored-program electronic digital computers.

In 1945 Turing predicted that computers would one day play very good chess, and just over 50 years later, in 1997, Deep Blue, a chess computer built by the International Business Machines Corporation (IBM), beat the reigning world champion, Garry Kasparov, in a six-game match. While Turing’s prediction came true, his expectation that chess programming would contribute to the understanding of how human beings think did not. The huge improvement in computer chess since Turing’s day is attributable to advances in computer engineering rather than advances in AI—Deep Blue’s 256 parallel processors enabled it to examine 200 million possible moves per second and to look ahead as many as 14 turns of play. Many agree with Noam Chomsky, a linguist at the Massachusetts Institute of Technology (MIT), who opined that a computer beating a grandmaster at chess is about as interesting as a bulldozer winning an Olympic weightlifting competition.