Srinivasa Ramanujan

Srinivasa Ramanujan’s work has found application in physics and engineering. He developed rapidly as a mathematician under the guidance of G. H. Hardy, who brought him to Cambridge University in 1916. He published more than 340 mathematical papers spanning various mathematical areas.

Ramanujan is now recognised as one of the greatest Indian mathematicians ever and one of the most influential mathematicians. He was selected as a Fellow of the Royal Society in 1914 at the unusually young age of 26. He died at 32 from diabetes, Vitamin deficiency, and Tuberculosis complications. This article will learn about Srinivasa Ramanujan’s journey to becoming a famous Indian Mathematician and his mathematical analysis.

Srinivasa Ramanujan Early Life

Srinivasa Ramanujan (1887 – 1920) was an Indian mathematician who, with almost no formal training in mathematics, made extraordinary contributions to number theory, mathematical analysis, infinite series, and continued fractions. He had no traditional degree or education but significantly contributed to mathematics. His mathematical equations are hard to solve. No one discovers his derivations properly, and they got only the formulas or some distorted number of equations.

Ramanujan had a brief life span of only 32 years. He died of TB at the age of 32; but left a collection of papers that contained more than 3,000 formulas and identities, many of which are yet to be proved by other mathematicians. Many of the formulas in this collection were so complex that they had been rejected by many eminent mathematicians of his time, including Hardy and Littlewood.

Srinivasa Ramanujan’s Contribution

Ramanujan’s mathematical discoveries were made independently from any formal training in pure mathematics, and he even made several conjectures which were unproven at the time. While some of his results were proven by others, many remain true but as yet unproven. He has also given several mathematical identities, such as the Reimann series, elliptic integrals, hypergeometric series, and zeta function.

Ramanujan memorised formulas and their values for many special functions (such as elliptic integrals) that were not available in texts. He developed new analytical capabilities, which allowed him to compute complicated values of these functions and generalisations of some functions like gamma function, zeta function, and beta function, which came to be known as Ramanujan’s formulas.

Srinivasa Ramanujan was a mathematician living in Madras (now Chennai) and worked on number theory, continued fractions, and infinite series. He was self-taught and had no formal training in pure mathematics. Most of his contributions are in the form of identities and equations, and he invented a summation process called Ramanujan Summation. He made a significant contribution to the infinite series. Srinivasa Ramanujan, discovered in 1729, is called the magic number.

Srinivasa Ramanujan’s First Paper

He studied independently and significantly contributed to mathematical analysis, number theory, infinite series, and continued fractions. His work on the idea of primes is considered one of the most outstanding achievements in the history of mathematics. He also made significant contributions to analytical continuation. He had an uncanny ability to make conjectures without proof and provide guarantees later on with great ease.

When he was only 19 years old, his first paper was published, which contained several results that no one had proved before him or even thought about.

In 1913 he sent another paper titled “Modular Equations” to G H Hardy, a Cambridge University, UK professor. Still, Hardy did not think much about it initially since it contained just three pages. Later, when Hardy read more papers by Ramanujan, he realised that he had something extraordinary on his hands.

Ramanujan’s notebooks contained formulas and results in number theory, trigonometry, and continued fractions that he claimed to have discovered through his efforts. He recalled the procedures discussed in Hardy-Littlewood’s research paper on partitions from memory, which led G. H. Hardy asked him if he could prove any of them. In his reply, Ramanujan stated that he had already established everything in the paper except for the “trivial” case n = 1.

Ramanujan’s first result published in a European journal was a formula for pi (π). He sent his first letter to G. H. Hardy at Trinity College Cambridge in 1913, containing several procedures which would later become known as “Ramanujan’s tau function”. He also sent Hardy an article entitled “Modular Equations And Approximations To Pi”, which included more than 100 pages of calculations related to π.

Conclusion

Srinivasa Ramanujan initially developed his skills by studying advanced trigonometry and calculus textbooks. He is still regarded as one of the most talented Indian mathematicians, having contributed thousands of new results based on his research. His work has many gaps and errors; some can be proven incorrect. However, he provided many examples of solutions to problems that had stumped mathematicians for centuries. Some were eventually proven wrong, but others were subsequently proven correct by other mathematicians or are still being investigated today. In this article, you learned about Srinivasa Ramanujan’s journey to becoming a famous Indian Mathematician and his mathematical analysis.