Mathematics and computer science: The interplay

Mathematics has been an important intellectual preoccupation of man for a long time. Computer science as a formal discipline is about seven decades young. However, one thing in common between all users and producers of mathematical thought is the almost involuntary use of computing. In this article, we bring to fore the many close connections and parallels between the two sciences of mathematics and computing. We show that, unlike in the other branches of human inquiry where mathematics is merely utilized or applied, computer science also returns additional value to mathematics by introducing certain new computational paradigms and methodologies and also by posing new foundational questions. We emphasize the strong interplay and interactions by looking at some exciting contemporary results from number theory and combinatorial mathematics and algorithms of computer science.