number of systems would be required for comprehensive results. Stating this thought in terms of Turing machines, he suggested a multiple machine theory of mind — mind because he was still thinking of the computer as a person, and the machine as the algorithm that the person would follow mechanically. The multiple machine idea was that Turing machines would be chained, so that different algorithms would be executed sequentially, thus overcoming some of the limitations of the simple Turing machine. How would the sequence be determined? Initially the idea was that it would be specified by the mathematician, but subsequently other methods were proposed, ranging from stochastic choice to a situation in which each machine would choose the subsequent machine. Eventually Turing proposed that learning could provide the basis of choice. He observed that mathematics advances by means of mathematicians exercising mathematical intuition, which they then use to create new mathematics, a process he thought of as learning. He then imagined a machine that could learn by experience, by means of altering its own algorithms. (Copeland and Shagrir, 2015)

Time had been kept out of mathematics by defining it as consisting only of the achieved corpus of results and ignoring 