Abstract

Computer science and mathematics are closely related subjects, and over the last fifty years, each has fed off the other. Mathematicians have used computers to prove (or disprove) traditional results of mathematics, computer scientists have used more and more advanced mathematics in their work, and new areas of mathematics have been inspired by questions thrown up by computing.

Introduction

The academic subjects of mathematics and computer science, the oldest science and one of the newest, are closely related. This article considers the various ways in which they interact, and each influences the development of the other.

It is worth noting that we do not consider here the influence of computer technology (and the associated communications revolution) on the infrastructure and sociology of mathematics. Developments such as

• CD-ROM publication (particularly of Mathematical Reviews),

• electronic databases (again one thinks of Mathematical Reviews, but also of the Science Citation Index, which, even in its paper form, could not be compiled without computers),

• electronic manuscripts and camera-ready copy,

• ftp preprint systems and

• electronic mail

have changed, and will continue to change, the way in which mathematicians consider, and add to, their literature, but this is not specific to mathematics, even though mathematicians have often been in the vanguard of such movements, presumably because of their general use of computers.

The Influence of Computers on Mathematics

Mathematicians have always numbered prodigious calculators among their kind, be they numerical calculators or symbolic ones (Delaunay's lunar theory (1860) contained a 120-page formula). Hence it is not surprising that the digital computer soon interested some pure mathematicians. With its help, they could perform far larger calculations than before, and investigate phenomena that were inaccessible to human computation.