Ramanujan in Computing Technology

TL;DR

This paper explores Ramanujan's mathematical discoveries and their influence on computing technology, including applications in pi calculation, Ramanujan graphs, and the development of a Ramanujan machine simulating his thought process.

Contribution

It highlights the novel applications of Ramanujan's mathematical results in modern computing, including new algorithms, graph theory, and machine design.

Findings

Ramanujan's series improve pi computation methods

Ramanujan graphs have unique spectral properties

The Ramanujan machine models Ramanujan's thought process

Abstract

This paper is a tribute to the genius of the legendary Indian mathematician Srinivasa Ramanujan (22 December 1887 - 26 April 1920) in the centenary year of his death. The life story of Ramanujan is so well known that it needs no elaboration not even a summarisation. In his short life period he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan independently compiled nearly 3,900 results in the form of identities and equations. Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research. Nearly all his claims have now been proven correct. The focus of the paper is the increasing influence of the ideas propounded by Ramanujan in the development of computing technology. We shall discuss the application of certain infinite series discovered by Ramanujan in computing the value of the mathematical constant $\pi$. We shall also consider certain special graphs known as Ramanujan graphs and the reason for designating them as such. We shall examine how certain researchers are attempting to create an abstract machine which they call Ramanujan machine which is thought of as simulating the hypothesised thought process of Ramnujan. We shall also have a brief look at the applications of Ramanujan's discoveries in signal processing.