Turing and the Art of Classical Computability

1. Mathematics as an Art Mathematics is an art as well as a science. It is an art in the sense of a skill as in Donald Knuth’s series, The Art of Computer Programming, but it is also an art in the sense of an esthetic endeavor with inherent beauty which is recognized by all mathematicians. One of the world’s leading art treasures is Michelangelo’s statue of David as a young man displayed in the Accademia Gallery in Florence. There is a long aisle to approach the statue of David. The aisle is flanked by the statues of Michelangelo’s unfinished slaves struggling as if to emerge from the blocks of marble. These figures reveal Michelangelo’s work process. There are practically no details, and yet they possess a weight and power beyond their physical proportions. Michelangelo thought of himself not as