one of the most famous art treasures is Michelangelo's statue of David displayed in the Accademia Gallery in Florence. the long aisle to approach the statue is flanked with the statues of Michelangelo's unfinished slaves struggling as if to emerge from the block of marble. there are practically no details, and yet they possess a weight and power beyond their physical proportions. Michelangelo thought of himself, not as carving a statue, but as seeing the figure within the marble and then chipping away the marble to release it. the unfinished slaves are perhaps a more revealing example of this talent than the finished statue of David.
similarly, it was Alan Turing in 1936 and 1939 who saw the figure of computability in the marble more clearly than anyone else. finding a formal definition for effectively calculable functions was the first step, but demonstrating that it captured computability was as much an artistic achievement as a purely mathematical one. Gödel himself had expressed doubt that it would be possible to do so. the other researchers thought in terms of mathematical formalisms like def-mu-recursive-functions, -definable functions, and arithmetization of syntax. it was Turing who saw the computer itself in the marble, a simple intuitive device equipped with only a finite program and using only a finite sequence of strokes at each stage in a finite computation, the vision closest to our modern computer. even more remarkable, Turing saw how to explicitly demonstrate that this mechanical device captured all effectively calculable processes. Gödel immediately recognized this achievement in Turing and in no one else.