Written by the mathematician Alan Turing and published in 1936, this paper demonstrates that there are problems to which no mechanically computable solution exists by detailing the design of a theoretical digital computer. German mathematician David Hilbert theorized in 1928 that all math problems could be solved and that a machine could do it. Turing set out to prove Hilbert wrong, describing what is now known as the Turing machine. It manually scanned a tape that was punched with 1s and 0s (which was later used in the first calculating computers), and used instructions programmed by a person to solve the problems. The values were recorded on tape, delivering the outcomes in binary and handling the process without human intervention. In this theoretical scenario, the machine can only calculate problems if it is capable of it. This demonstrates that there are some math and logic problems that cannot be solved with algorithms. This paper immortalizes Turing in the annals of computing history, introducing the basic concepts of digital computing upon which modern computer science is based.
On Computable Numbers
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