Srinivasa Ramanujan, an Indian mathematician, made groundbreaking contributions to various fields in mathematics despite having no formal training in the subject. His work primarily spanned number theory, continued fractions, infinite series, and mathematical analysis. One of his most famous contributions is the Ramanujan prime, which has implications in number theory and the distribution of prime numbers.

Ramanujan’s collaborations with British mathematician G.H. Hardy led to the formulation of the Hardy-Ramanujan asymptotic formula, which provides an approximation for the partition function, an essential concept in number theory and combinatorics. He also developed the Ramanujan theta function, contributing significantly to the theory of modular forms and partitions.

In addition to these, Ramanujan is known for his intuitive grasp of continued fractions and for generating rapidly converging infinite series for computing π. His work on mock theta functions, introduced in his last letter to Hardy, opened new areas of research and had a profound impact on modern mathematics, including fields like string theory in physics.

Ramanujan’s notebooks, filled with thousands of results, many without proofs, continue to inspire and challenge mathematicians to this day, demonstrating his extraordinary creativity and insight into the depths of mathematical structures.