Other notable contributions by Ramanujan include hypergeometric series, the Riemann series, the elliptic integrals, the theory of divergent series, and the functional equations of the zeta function. Ramanujan theta function is used to determine the critical dimensions in Bosonic string theory, superstring theory, and M-theory. Theta function was studied by extensively Ramanujan who came up with the Ramanujan theta function, that generalizes the form of Jacobi theta functions and also captures general properties. German mathematician Carl Gustav Jacob Jacobi invented several closely related theta functions known as Jacobi theta functions. Theta Function: Theta function is a special function of several complex variables. This method contributed significantly to solving the notorious complex problems of the 20th century, such as Waring's conjecture and other additional questions. Ramanujan number: 1729 is known as the Ramanujan number which is the sum of the cubes of two numbers 10 and 9.Ĭircle Method: Ramanujan, along with GH Hardy, invented the circle method which gave the first approximations of the partition of numbers beyond 200. Mock theta function: He elaborated on the mock theta function, a concept in the field of modular forms of mathematics. His contribution to game theory is purely based on intuition and natural talent and is unmatched to this day. Game theory: Ramanujan discovered a long list of new ideas for solving many challenging mathematical problems that have given great impetus to the development of game theory. Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics. Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today. Ramanujan's contribution extends to mathematical fields such as complex analysis, number theory, infinite series, and continued fractions. Ramanujan’s major contributions to mathematics: In 1918, Ramanujan became the second Indian to be included as a Fellow of the Royal Society. He was mentored at Cambridge by GH Hardy, a well-known British mathematician who encouraged him to publish his findings in a number of papers. Srinivasa Ramanujan began developing his theories in mathematics and published his first paper in 1911. Rao was initially sceptical of Ramanujan, but he eventually recognised his abilities and supported him financially. Ramachandra Rao, secretary of the Indian Mathematical Society. He drifted through poverty until 1910 when he was interviewed by R. It was around this time that he began his famous notebooks. Another attempt at college in Madras (now Chennai) ended in failure when he failed his First Arts exam. He received a college scholarship in 1904, but he quickly lost it by failing in nonmathematical subjects. Despite being a mathematical prodigy, Ramanujan's career did not begin well. Every year, Ramanujan’s birth anniversary on December 22 is observed as National Mathematics Day.īorn in Erode, Tamil Nadu, India, Ramanujan demonstrated an exceptional intuitive grasp of mathematics at a young age. With its humble and sometimes difficult start, his life story is just as fascinating as his incredible work. Most of his mathematical discoveries were based only on intuition and were ultimately proven correct. Surprisingly, he never received any formal mathematics training. Leaving this world at the youthful age of 32, Ramanujan made significant contributions to mathematics that only a few others could match in their lifetime. Srinivasa Ramanujan (1887-1920), the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including mathematical analysis, infinite series, continued fractions, number theory, and game theory is recognized as one of history's greatest mathematicians.
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