S. Ramanujan

Srinivasa Ramanujan (1887–1920) was an Indian mathematician who made remarkable contributions to various fields of mathematics, including mathematical analysis, number theory, infinite series, and continued fractions. Despite having little formal training in pure mathematics, Ramanujan displayed an extraordinary intuitive grasp of numbers and mathematical concepts.

Early Life and Education:

Born in Erode, Tamil Nadu, India, Ramanujan grew up in a humble household. He was a prodigious talent who taught himself advanced mathematics from old textbooks, such as G.S. Carr's "A Synopsis of Elementary Results in Pure and Applied Mathematics." His self-directed studies led him to discover complex mathematical theorems independently.

Collaboration with G.H. Hardy:

In 1913, Ramanujan began a correspondence with British mathematician G.H. Hardy, sending him a letter filled with several of his own theorems and formulas. Impressed by Ramanujan's brilliance, Hardy invited him to Trinity College at the University of Cambridge. Their collaboration proved highly productive, leading to significant advancements in several areas of mathematics.

Contributions to Mathematics:

Ramanujan compiled nearly 3,900 results, including identities and equations. Some of his most notable contributions include:

• Ramanujan Prime: A concept in number theory that generalizes the idea of prime numbers.


• Ramanujan Theta Function: Functions that play a significant role in the theory of modular forms and have applications in areas like string theory.


• Partition Function: Work on partitions of numbers, leading to profound results in combinatorics.


• Mock Theta Functions: Introduced the concept, which later became important in the field of q-series and modular forms.

Many of his discoveries were ahead of his time and have inspired extensive research. His intuitive approach often led to results without formal proofs, some of which were validated by mathematicians decades later.

Legacy and Recognition:

Ramanujan returned to India in 1919 due to ill health and passed away in 1920 at the young age of 32. His legacy endures, and he is celebrated as one of the greatest mathematicians in history. Institutions like the Ramanujan Institute for Advanced Study in Mathematics and various scholarships and awards have been established in his honor.

His life has been the subject of books and films, notably "The Man Who Knew Infinity," which highlight his exceptional intellect and the challenges he faced.

Impact on Modern Mathematics:

Ramanujan's work continues to have a significant impact on modern mathematics and physics, particularly in areas like number theory, cryptography, and string theory. His notebooks, filled with unpublished results, remain a source of inspiration and study for mathematicians worldwide.