Articles

Towards a Mathematical Science of Computation

Towards a Mathematical Science of Computation was given at the congress IFIP-62 and published in the proceedings of that conference. It extends the results of A Basis for a Mathematical Theory of Computation which was first given in 1961.

In this paper I shall discuss the prospects for a mathematical science of computation. In a mathematical science, it is possible to deduce from the basic assumptions, the important properties of the entities treated by the science. Thus, from Newton's law of gravitation and his laws of motion, one can deduce that the planetary orbits obey Kepler's laws.

What are the entities with which the science of computation deals?

What kinds of facts about these entities would we like to derive?

What are the basic assumptions from which we should start?

What important results have already been obtained?

How can the mathematical science help in the solution of practical problems?

I would like to propose some partial answers to these questions. These partial answers suggest some problems for future work.

Download the article in PDF.