The contributions of the legendary mathematician Srinivasa Ramanujan are impossible to quantify. Despite his short life, he

compiled nearly 3900 results, many completely novel.

 

The Ramanujan’s sum appeared in his 1918 paper “On certain trigonometrical sums and their applications in the theory of numbers,” where he writes: 

“These sums are obviously of great interest, and a few of their properties have been discussed already. But, so far as I know, they have never been considered from the point of view which I adopt in this paper; and I believe that all the results which it contains are new”.