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Why Is Srinivasa Ramanujan Famous

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Srinivasa Ramanujan is famous for his remarkable and original contributions to mathematics, particularly in the fields of number theory, mathematical analysis, infinite series, and continued fractions[1][4]. He developed many results and formulas—often with little formal training—that were both groundbreaking and highly unconventional, including the Ramanujan prime, Ramanujan theta function, and novel formulas for the computation of π (pi)[3][5]. His work on the partition function and congruences transformed 20th-century mathematics and inspired continued research into these areas[1][6].

Some highlights of his contributions include:

  • Infinite series and continued fractions: Developed advanced formulas for hypergeometric series and infinite series, including efficient series for calculating π[1][3].
  • The theory of partitions: Made pioneering discoveries in partition theory (ways of expressing an integer as the sum of positive integers) and derived profound results and congruences influencing modern number theory[1][2][6].
  • Mock theta functions: Introduced new classes of mathematical functions, which have become central to areas of modern number theory and modular forms[1].
  • Ramanujan-Hardy collaboration: Worked with British mathematician G. H. Hardy, leading to deep theorems in prime number theory, the study of the Riemann zeta function, and analytical formulae for partitions[1][4][6].
  • Unique intuition: Proposed numerous formulas based on intuition, some later proved correct, which opened new directions in mathematical research[3][7].
  • Ramanujan number (1729): Identified the number 1729 as the smallest number expressible as the sum of two cubes in two different ways, now known as the “Ramanujan-Hardy number”[1].
  • Influence despite adversity: Achieved all this despite minimal formal training and limited access to up-to-date mathematical literature, demonstrating exceptional creativity and insight[2][4].
  • Lasting legacy: Left behind notebooks containing thousands of results, many of which mathematicians are still studying and discovering to this day[6].

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