Ramanujan's Thoughts from God

TL;DR

This paper reviews Ramanujan's significant contributions to mathematics, including series for 1/π, modular forms, and partitions, highlighting his collaboration with Hardy and the profound influence of his work on number theory.

Contribution

It provides a concise overview of Ramanujan's key mathematical achievements and their interconnectedness, emphasizing their importance for future mathematicians.

Findings

Ramanujan's series for 1/π revolutionized computational methods.

His work on modular forms established foundational concepts in number theory.

The deep link between partitions and modular forms is crucial for modern mathematics.

Abstract

We briefly review some of Ramanujan's contributions to mathematics, including his $1/\pi$ series, his work on modular forms, and his work on partitions. We briefly review his life, including his collaboration with Hardy. Finally, we give a brief summary of what any prospective mathematician should know about Ramanujan's work in number theory, including the rich relationship between his work on partitions and his work on modular forms. The title of this paper is a reference to a direct quote from Ramanujan himself: an equation means nothing to me unless it expresses a thought of God.