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.