Srinivasa Ramanujan

Srinivasa Aiyangar Ramanujan (Tamil: ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (December 22, 1887 – April 26, 1920) was a groundbreaking Indian mathematician. A child prodigy, he was largely self-taught in mathematics. Ramanujan is considered one of the world's greatest-ever mathematicians, proving over 3,000 theorems. Ramanujan mainly worked in analytical number theory and is famous for many summation formulas involving constants such as π, prime numbers and the partition function. Often, his formulae were stated without proof and were only later proven to be true. His results inspired a large amount of later research and mathematical papers. In 1997 the Ramanujan Journal was launched to publish work "in areas of mathematics influenced by Ramanujan".

Life

Childhood and early life

Ramanujan was an Indian Tamilian born in 1887 in Erode, Tamil Nadu, India. In 1898 at age 10, he entered the Town High School in Kumbakonam, where he appears to have first encountered formal mathematics. At 11 he had mastered the mathematical knowledge of the lodgers at his home, both students at the Government College, and was loaned books on advanced trigonometry, which he mastered by 13. His biographer reports that by 14 his genius was beginning to show. Not only did he achieve merit certificates and academic awards throughout his school years, he was assisting the school in the logistics of assigning its 1200 students (each with their own needs) to its 35-odd teachers, completing exams in half the allotted time, was already showing his familiarity with infinite series; his peers at the time later commented "We, including teachers, rarely understood him," and "stood in respectful awe" of him. However, Ramanujan could not concentrate on other subjects and failed his high school exams. At this time in his life, he was also quite poor and was often pushed to the point of starvation.

Related Topics:
1887 - Erode - Tamil Nadu - India - 1898 - Kumbakonam - Trigonometry - Theorem

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Adulthood in India

As he was married, he had to find a job. With the packet of his mathematical calculations, he moved around in the city of Chennai on the look out of a clerical job. He finally got a job and was advised by an Englishman to contact researchers in Cambridge.

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As clerk in the Chennai Accountant General's Office, Ramanujan desired the luxury to completely focus on mathematics without having to hold a job. He doggedly solicited support from influential Indian individuals and published several papers in Indian mathematical journals, but was unsuccessful in his attempts to foster sponsorship. At this point of time Sir Ashutosh Mukherjee tried to support his cause.

Related Topics:
Chennai - Ashutosh Mukherjee

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In 1913 Ramanujan enclosed a long list of complex theorems in a letter to three Cambridge academics: H. F. Baker, E. W. Hobson, and G. H. Hardy. Only Hardy, a Fellow of Trinity College, noticed the genius in Ramanujan?s theorems.

Related Topics:
1913 - Cambridge - H. F. Baker - E. W. Hobson - G. H. Hardy - Trinity College

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Upon reading the initial unsolicited missive by an unknown and untrained Indian mathematician, Hardy and his colleague J.E. Littlewood commented that, ?not one could have been set in the most advanced mathematical examination in the world.? Although Hardy was one of the pre-eminent mathematicians of the day and an expert in several of the fields Ramanujan wrote about, he added that many of them "defeated me completely; I had never seen anything in the least like them before."

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As an example of his results, Ramanujan gave the beautiful continued fraction,

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:sqrt{phi+2}- phi = cfrac{e^{-2 pi/5}}{1 + cfrac{e^{-2 pi}}{1 + cfrac{e^{-4 pi}}{1+ cfrac{e^{-6 pi}}{1+,cdots}}}} = 0.2840...

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among others, where phi=(1+ sqrt{5})/2 is the golden ratio.

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Life in England

After some initial skepticism, Hardy replied with comments, requesting proofs for some of the discoveries, and began to make plans to bring Ramanujan to England. As an orthodox Brahmin, Ramanujan consulted the astrological data for his journey, because of religious concerns that he would lose his caste by traveling to foreign shores. Ramanujan's mother had a dream in which the family Goddess told her not to stand in the way of her son's travel, and so he made plans accordingly, although he took pains to keep a proper Brahmin lifestyle as far as he could, when he did.

Related Topics:
Brahmin - Astrological - Caste

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A fruitful collaboration ensued, which Hardy described as "the one romantic incident in my life". Hardy said of Ramanujan's formulas, some of which he could not initially understand, that "a single look at them is enough to show that they could only be written down by a mathematician of the highest class. They must be true, for if they were not true, no one would have had the imagination to invent them." Hardy stated in an interview by Paul Erdős that his own greatest contribution to mathematics was the discovery of Ramanujan, and compared Ramanujan at least to the mathematical giants Euler and Jacobi in terms of genius. Ramanujan was later appointed a Fellow of Trinity, and the highest level of honor in science, a Fellow of the Royal Society (FRS).

Related Topics:
Paul Erdős - Euler - Jacobi - Genius - Royal Society

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Illness and return to India

Plagued by health problems all his life, in a country far from home, and obsessively involved with his studies, Ramanujan's health worsened in England, perhaps exacerbated by stress, and by the scarcity of vegetarian food during the First World War. He was diagnosed with tuberculosis (Henderson, 1996) and a severe vitamin deficiency, though a 1994 analysis of Ramanujan's medical records and symptoms by Dr. D.A.B Young concluded that it was much more likely he had hepatic amoebiasis, a parasitic infection of the liver. This is also supported by the fact that Ramanujan spent time in Madras, a coastal city where the disease was widespread. It was a difficult disease to diagnose, but once diagnosed was readily curable (Berndt, 1998). He returned to India in 1919 and died soon after in Kumbakonam, his final gift to the world being the discovery of 'mock Theta functions'. His wife S. Janaki Ammal lived outside Chennai (formerly Madras) until her death in 1994. Janaki had been nine when they were married, a fairly common practice in India at the time. (Henderson, 1996)

Related Topics:
Stress - Vegetarian food - First World War - Tuberculosis - 1996 - 1994 - Amoebiasis - Madras - 1998 - 1919 - Kumbakonam - 'mock Theta functions'

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Spiritual life

Ramanujan lived as a Tamil Brahmin all his life. Views of his actual beliefs vary: his first Indian biographers described him as rigorously orthodox, whereas G. H. Hardy (a militant atheist) believed him to be essentially agnostic as far as metaphysical matters were concerned.

Related Topics:
G. H. Hardy - Atheist

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Hardy reported a statement of Ramanujan's to the effect that all religions are equally correct. Kanigel's biography states that Ramanujan would probably not have shown Hardy his religious side anyway; on the other hand Kanigel paints a generally negative picture of Hardy.

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Ramanujan credited his understanding to his family Goddess, Namagiri, and looked to her for inspiration in his work. He often said, "An equation for me has no meaning, unless it represents a thought of God."

Related Topics:
Goddess - Namagiri

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