Alan M. Turing published "On Computable Numbers," in which he developed the Turing machine, the abstact precursor of the computer.  A Turing machine consists of a finite set of logical and mathematical rules and a tape of infinite length. Alonzo Church proved the thesis that any mental process, such as the brain or a computer, which divides numbers into two sorts can be described by some general recursive function.  It is sometimes called the Church- Turing thesis.