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Saturday, 2 June 2018

You Must Experience Who Is Indian Genius : Ramanujan || Srinivasa Ramanujan

   Indian Genius : Srinivasa Ramanujan


Srinivasa Ramanujan famous Indian mathematician :-

  • Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functionscontinued fractions, and infinite series.
  • Srinivasa Ramanujan ( 22 December 1887  in Erode, located in Tamil Nadu. - 26 April 1920 ) was an Indian mathematician who lived during British Rule in India. 33 years 
  • Indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function.
  • He was also to become a master of the book in 13 years of short life and he himself discovered many theorems. At the age of 14, he was given a Merit Certificate for his contribution.
  • In 1905, Srinivasa Ramanujan / Srinivasa Ramanujan joined the entrance examination of the University of Madras, but he failed in all the other subjects except mathematics. After some time, in 1906 and 1907, Ramanujan again gave a private examination of class XII and failed.
  • Ramanujan failed two time in 12th.
  • Ramanujan never received a college degree.
  • Seeing his achievements, the number 1729 is known as Hardy-Ramanujan number.
Hardy-Ramanujan number  Story  : -

Hardy left the cab. He was visiting an ill Ramanujan at Putney. Ramanujan asked about his trip. Hardy remarked the ride was dull; even the taxi number, 1729, was dull to the number theorist. He hoped the number’s dullness wasn’t an omen predicting Ramanujan’s declining health. “No Hardy,” Ramanujan replied, “it is a very interesting number.” The integer 1729 is actually the smallest number expressible as the sum of two positive cubes in two different ways. Indeed 1729 = 13 + 123 = 93 + 103.

The mathematicians Srinivasa Iyengar Ramanujan and G.H. Hardy comprise the characters of this story. Ramanujan’s casual discovery of the smallest so-called taxicab number was no fluke. Ramanujan and Hardy’s most famous result was an asymptotic formula for the number of partitions of a positive integer. A partition of a number n is a way of writing n as the sum of positive integers. Reordering terms doesn’t change a partition. Thus the partitions of 5 are 5, 4 + 1, 3 + 2, 3 + 1 + 1, 2 + 1 + 1 + 1, and 1 + 1 + 1 + 1 + 1; hence 5 has 7 seven partitions. Counting the partitions becomes difficult as n grows. Ramanujan had made several conjectures based on numerical evidence, and Hardy credits many of the needed insights to Ramanujan. The formula is complicated and counter-intuitive. It involves values of √3, π, and e, all very strange numbers for a counting formula. Near his death, Ramanujan discovered mock theta functions, which mathematicians are still “rediscovering” today.

These are only the achievements of later Ramanujan. The early life of Ramanujan is even more surprising. He spent his childhood in the poor south Indian town, Kumbakonam. In school, he scored top marks. He probed college students for mathematical knowledge by age 11. When he was 13, he comprehended S.L. Loney’s advanced trigonometry book. He could solve cubic and quartic equations—the latter method he found himself—and finished math tests in half the allotted time. If asked, he could recite the digits of π and e to any number of digits. He borrowed G.S. Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics by age 16 and worked through its many theorems. By 17, he independently investigated the Bernoulli numbers, a set of numbers intimately connected to number theory.
So How did Ramanujan do it? No brilliant teacher—excluding Hardy and J.E. Littlewood when Ramanujan was already an adult—taught Ramanujan. The odds were against Ramanujan from the start. Ramanujan often used slate instead of paper because paper was expensive; he even erased slate with his elbows, since finding a rag would take too long. He lost his first college scholarship by neglecting his every subject that wasn’t math. The first two English mathematicians he sent letters to request publication did not respond; was it luck that Hardy did?
Ramanujan credits Namagiri, a family deity, for his mathematics. He claimed the goddess would write mathematics on his tongue, that dreams and visions would reveal the secrets of math to him.
Ramanujan was undoubtedly religious. Before leaving India, he respected all the holy customs of his caste: he shaved his forehead, tied his hair into a knot, wore a red U with a white slash on his forehead, and refused to eat any meat. In the Sarangapani temple, Ramanujan would work on his math in his tattered notebook.
Hardy, the ardent atheist, didn’t believe that gods communicated with Ramanujan. He thought flashes of insight were just more common in Ramanujan than in most other mathematicians. Sure, Ramanujan had his religious quirks, but they were just quirks.
Looking at Ramanujan’s work, I find it hard to deny that some god aided the man. I cannot even imagine Ramanujan’s impact had he lived longer or had better teachers.


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