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Srinivasa Aiyangar Ramanujan
Early life
Sailed to England
Sailed to India
Landmark paper
Memorializing Ramanujan and his achievements
Ramanujan’s Notebooks
Ramanujan's Magic Square- Video
Srinivasa Aiyangar Ramanujan
Srinivasa Aiyangar Ramanujan (சீனிவாச இராமானுஜன் or ஸ்ரீனிவாஸ ஐயங்கார் ராமானுஜன்) (22 December 1887 – 26
April 1920) was one of the greatest mathematical geniuses of the 20th century.
Srinivasa Ramanujan made significant contribution to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.
He independently discovered results of Gauss, Kummer and others on hyper geometric series.
His work on partial sums and products of hyper geometric series have led to major development in the topic.
His most famous work was on the number p(n) of partitions of an integer n into summands.
Srinivasa Aiyangar Ramanujan (22 December 1887 – 26 April 1920)
Srinivasa Aiyangar Ramanujan is undoubtedly the most celebrated Indian
Mathematical genius. He was the second Indian to be elected Fellow of the Royal Society
in February, 1918. Later that year, he became the first Indian to be elected
Fellow of Trinity College, Cambridge. Ramanujan independently compiled nearly 3900 results (mostly identities and
equations) during his short lifetime. In 1912-1913, he sent samples of his theorems to three academics at
University of Cambridge. Only G. H. Hardy recognized his brilliant work, and he
asked Ramanujan to study under him at Cambridge. Recently, Ramanujan's formulae have found applications in the field
of crystallography and in string theory. The Ramanujan Journal, an international
publication, was launched to publish work in all the areas of mathematics that were influenced by Ramanujan.
On December 26, 2011 Prime Minister Manmohan Singh declared year 2012 as the 'National Mathematical year' as a
tribute to maths wizard Srinivasa Ramanujan. Manmohan Singh also declared December 22, the birthday of Ramanujan, as 'National
Mathematics Day.' He said Ramanujan overcame formidable difficulties to reach the pinnacle
of greatness, illustrating the inadequacy of University evaluation system in the early decades of the last century, while at the same time
showing the system displayed enough flexibility to take care of mavericks like him.He said the country was proud of Ramanujan and Tamil Nadu has a special
claim on him for he was a Tamilian
."Along with CV Raman and Subramanyam Chandrashekhar (both Nobel
laureates), he is among the three great men of science and mathematics that Tamil Nadu and India have given to the world of modern times", he said.
On 22nd December 2012, the world celebrates the 125th birth anniversary of Srinivasa Ramanujan. In his honour, the Indian government declared 2012
as the Year of Mathematics. |
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Early life
Born on December 22, 1887 in the town of Erode in Tamil Nadu, Ramanujan
was largely self-taught and emerged from extreme poverty to become one
of the most influential mathematicians of the 20th century. His father worked in Kumbakonam as
a clerk in a cloth merchant's shop. At the of five Ramanujan went to primary school in Kumbakonam.
From her mother, he learned about tradition, the caste system and puranas. He learned to sing religious songs, to
attend pujas at the temple and eating habits, all of which were necessary for
Ramanujan to be a good Brahmin child. In 1898 at age 10, he entered the Town High School in Kumbakonam.
At the age of 12, he borrowed from a friend a copy of Loney's book on
Plane Trigonometry, published by Cambridge University Press in 1894.This book goes far beyond high school trigonometry and also deals with
the rudiments of calculus. At age of 16 Ramanujan came across the book, A
synopsis of elementary results in pure and applied mathematics written by George
S. Carr. This book was a collection of 5000 theorems, and it introduced Ramanujan to the world of mathematics. The next year, he had independently
developed and investigated the Bernoulli numbers and had calculated Euler's
constant up to 15 decimal places. He was given a scholarship to the Government College in Kumbakonam which he entered in
1904. But he neglected his other subjects at the cost of mathematics and failed in college examination. He dropped out of the college.
In 1903, Ramanujan entered the Government College in
Kumbakonam. Unfortunately, he failed in the examination since he neglected his
non-mathematical subjects. Four years later, he entered another college in Chennai, and the same
thing happened. Finally, in 1912, he secured a job as a clerk in the Madras Port Trust Office. Here, his duties were light and so he could
devote a lot of time to his mathematical discoveries — which he recorded in his now celebrated notebooks. As luck would have it, the manager of
the office, S.N. Aiyar, was also a mathematician who took kindly to Ramanujan and encouraged him in his mathematics. It was he who suggested
to Ramanujan that he write to G.H. Hardy, a famous mathematician at Trinity College, Cambridge University.
On 14 July 1909 Ramanujan marry a ten year old girl S Janaki Ammal. During
this period Ramanujan had his first paper published, a 17-page work on Bernoulli numbers that appeared in 1911 in the Journal of the Indian Mathematical Society. In
1911 Ramanujan approached the founder of the Indian Mathematical Society for advice on a job. He got the job of clerk
at the Madras Port Trust with the help of Indian mathematician Ramachandra Rao.
In his famous 1913 letter to Hardy, Ramanujan attached 120 theorems as a
representative sample of his work. Some of these formulas Hardy had already seen in the course of his own research work. But many of the
other formulas, he had not. It took over two hours for him to analyse
the letter in order to determine if it was written by a crank or a genius. He consulted with his eminent colleague J.E. Littlewood, also of
Trinity College, and together they sat down for three more hours. Finally they concluded that it was the work of a genius. Hardy wrote:
“They must be true, because if they were not true, no one would have had the imagination to invent them.'' With this certificate of approval,
Ramanujan was invited to come to Trinity College to work with Hardy.
Sailed to England
Ramanujan sailed to England in March 1914, just a few months before the
outbreak of the First World War. From 1914 to 1917, Hardy and Ramanujan
collaborated on more than half a dozen research papers. At the same time, Ramanujan published more than 30 research papers in three years.
The most notable of these collaborations involved the partition
function. This function counts the number of ways a natural number can
be decomposed into smaller parts. Hardy and Ramanujan developed a new method, now called the circle method, to derive an asymptotic formula
for this function. If one analyses Ramanujan's first letter to Hardy, we already find a hint of the method in his work done in India while at the
Port Trust Office. This method is now one of the central tools of analytic number theory and is largely responsible for major advances in
the 20th century of notoriously difficult problems such as Goldbach's conjecture, Waring's conjecture and other additive questions. The circle
method and its refinements constitute a very large area of current research and will probably continue to be so in the 21st century.
Another fundamental paper of Hardy and Ramanujan concerns what is now
called the “normal order method.'' This method analyses the behaviour of additive arithmetical functions. In their paper, Hardy and Ramanujan
showed that a random natural number usually has about log log n prime factors. Their paper led to the creation of an entirely new field of
mathematics called probabilistic number theory. In the 20th century, it was largely developed by P. Erdos, M. Kac and J. Kubilius.
Ramanujan was awarded a B.A. degree by research (this degree was later renamed
PhD) in March 1916 for his work on highly composite numbers which was published as a paper in the Journal of the London Mathematical Society. The paper was over
50 pages with different properties of such numbers proven. Hardy remarked that this was one of the most unusual papers seen in Mathematical Research at that
time and that Ramanujan showed extraordinary ingenuity in handling it. On 6 December 1917, he was elected to the London Mathematical Society. He was the
second Indian to become a Fellow of the Royal Society in 1918 and he became one of the youngest Fellows in the entire history of the Royal
Society. He was elected "for his investigation in Elliptic Functions and the Theory of Numbers."
On 13 October 1918, he became the first Indian to be elected a Fellow of Trinity College, Cambridge.
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Sailed to India
Ramanujan fell seriously ill in 1917 and his doctors feared that he would die.
He did improve a little by September but spent most of his time in various nursing homes. By the end of
November 1918 Ramanujan's health had greatly improved. Ramanujan sailed to India on 27 February 1919 arriving on 13 March.
However his health was very poor and, despite medical treatment, he died on April 6, 1920.
Ramanujan's wife died in the late 1980s. She adopted a son only after her husband's death.
Landmark paper
The landmark paper that changed the course of 20th century mathematics
was the one written by Ramanujan in 1916, modestly titled “On certain arithmetical functions.'' In this paper, Ramanujan investigated
the properties of Fourier coefficients of modular forms. At that time the theory of modular forms was not even developed. However, Ramanujan
enunciated three fundamental conjectures that served as a guiding force for the development of the theory. However,
it was the last of the three of Ramanujan's conjectures that created a sensation in 20th century mathematics. This conjecture, later
called Ramanujan's conjecture, came to play a pivotal role in the towering edifice known as the Langlands program, a far-reaching program
articulated by R.P. Langlands in the 1970s.
Ramanujan is generally hailed as an all time great like Euler, Gauss or Jacobi
for his natural mathematical genius. In his book Scientific Edge, noted physicist Jayant Narlikar stated that
"Srinivasa Ramanujan, discovered by the Cambridge mathematician G.H. Hardy,
whose great mathematical findings were beginning to be appreciated from 1915 to 1919. His achievements were to be fully understood much later, well after his
untimely death in 1920. Narlikar also goes on to say that his work was one of the top ten achievements of 20th century Indian science and
"could be considered in the Nobel Prize class"
Memorializing Ramanujan and his achievements
Tamil Nadu celebrates December 22 (Ramanujan's birthday) as 'State IT Day', memorializing both the man and his achievements, as
a native of Tamil Nadu. A stamp picturing Ramanujan was released by the Government of India in 1962 — the 75th anniversary of Ramanujan's birth —
commemorating his achievements in the field of number theory. A prize for young mathematicians from developing countries has been created in
the name of Ramanujan by the International Centre for Theoretical Physics
(ICTP), in cooperation with the International Mathematical Union, who nominate members of the prize committee.
An international feature film on Ramanujan's life will begin shooting in 2007 in Tamil Nadu state and Cambridge.
It is being produced by an Indo-British collaboration; it will be co-directed by Stephen Fry and Dev
Benegal. He was referred to in the film Good Will Hunting as an example of mathematical genius.
He was referred to in the film Good Will Hunting as an example of mathematical genius.
The multi-million dollar film will be shot in Erode and Kumbakonam (where he grew up) in Tamil Nadu, and in Cambridge where he spent five years.
"For me, Ramanujan's work and ideas are the DNA of what powers digital technology today," says
Benegal. "When your automated teller machines divide and arrange your money before coughing it up, they are all using Ramanujan's partition theory."
Spiritually, Ramanujan credited his acumen 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."
He is the subject of David Leavitt's new novel "The Indian Clerk," released September 2007.
His biography was highlighted in the Vernor Vinge book The Peace War as well as Douglas Hofstadter's Gödel, Escher, Bach.
Ramanujan’s Notebooks
Ramanujan developed much of his mathematics in isolation while still in
India, and his works – with chalk and slate because paper was expensive – are contained in three notebooks, totalling about 640 pages in all. A fourth notebook
of 87 unorganised pages, called the ‘Lost Notebook’ was rediscovered in 1976. His works have inspired many, including
Prof. Hardy himself, to explore and create new branches of mathematics. Ramanujan’s Notebooks 1, 2 and 3 were
published as a two volume set, as a photocopy edition of the original manuscripts, in 1957 by TIFR, Mumbai.
Ramanujan's Magic Square- Video
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