The Interplay Between Mathematics And Computer Science

ABSTRACT

The assertion that the taproots of mathematics lie in its applications is a familiar one, and for a clear statement of this thought we have only to quote von Neumann: “The most vitally characteristic fact about mathematics is, in my opinion, its quite peculiar relationship to the natural sciences, or, more generally, to any science which interprets experience on a higher than purely descriptive level." “Most people, mathematicians and others, will agree that mathematics is not an empirical science, or at least that it is practiced in a manner which differs in several decisive respects from the techniques of the empirical sciences. And yet its development is very closely linked with the natural sciences .... Some of the best inspirations of modern mathematics (I believe, the best ones), clearly originate in the natural sciences." Although it is not a natural science (and indeed, has been characterized as the 'science of the artificial') computer science is imbedded in an ongoing mass of computer practice which plays the role for computer science that technology and experiment play for such natural sciences as physics. And, as this talk and the other presentations at this session will illustrate, computer science and mathematics are joined by a network of fructifying mutual connections which very much exemplify von Neumann's point of view.

REFERENCES

• 1: John von Neumann, The Mathematician, from 'The Works of the Mind,' pp. 180- 196, edited by R. B. Heywood (University of Chicago Press, 1947).

INDEX TERMS

Primary Classification:
  K. Computing Milieux
  K.3 COMPUTERS AND EDUCATION
      K.3.2 Computer and Information Science Education
          Subjects: Computer science education

Additional Classification:
  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Mathematics and statistics

General Terms:
Theory