Contribution of srinivasa ramanujan to mathematics?
Srinivasa Ramanujan (1887-1920) hailed as an all-time great
mathematician, like Euler, Gauss or Jacobi, for his natural genius,
has left behind 4000 original theorems, despite his lack of formal
education and a short life-span. In his formative years, after
having failed in his F.A. (First examination in Arts) class at
College, he ran from pillar to post in search of a benefactor. It
is during this period, 1903-1914, he kept a record of the final
results of his original research work in the form of entries in two
large-sized Note Books. These were the ones which he showed to
Dewan Bahadur Ramachandra Rao (Collector of Nellore), V. Ramaswamy
Iyer (Founder of Indian Mathematical Society), R. Narayana Iyer
(Treasurer of IMS and Manager, Madras Port Trust), and to several
others to convince them of his abilities as a Mathematician. The
orchestrated efforts of his admirers, culminated in the
encouragement he received from Prof. G.H. Hardy of Trinity College,
Cambridge, whose warm response to the historic letter of Ramanujan
which contained about 100 theorems, resulted in inducing the Madras
University, to its lasting credit, to rise to the occasion thrice -
in offering him the first research scholarship of the University in
May 1913 ; then in offering him a scholarship of 250 pounds a year
for five years with 100 pounds for passage by ship and for initial
outfit to go to England in 1914 ; and finally, by granting
Ramanujan 250 pounds a year as an allowance for 5 years commencing
from April 1919 soon after his triumphant return from Cambridge
``with a scientific standing and reputation such as no Indian has
enjoyed before''.
Ramanujan was awarded in 1916 the B.A. Degree by research of the
Cambridge University. He was elected a Fellow of the Royal Society
of London in Feb. 1918 being a ``Research student in Mathematics
Distinguished as a pure mathematician particularly for his
investigations in elliptic functions and the theory of numbers''
and he was elected to a Trinity College Fellowship, in Oct. 1918 (-
a prize fellowship worth 250 pounds a year for six years with no
duties or condition, which he was not destined to avail of). The
``Collected Papers of Ramanujan'' was edited by Profs. G.H.Hardy,
P.V. Seshu Aiyar and B.M. Wilson and first published by Cambridge
University Press in 1927 (later by Chelsea, 1962 ; and by Narosa,
1987), seven years after his death. His `Lost' Notebook found in
the estate of Prof. G.N. Watson in the spring of 1976 by Prof.
George Andrews of Pennsylvania State University, and its facsimile
edition was brought out by Narosa Publishing House in 1987, on the
occasion of Ramanujan's birth centenary. His bust was commissioned
by Professors R. Askey, S. Chandrasekhar, G.E. Andrews, Bruce C.
Berndt (`the gang of four'!) and `more than one hundred
mathematicians and scientists who contributed money for the bust'
sculpted by Paul Granlund in 1984 and another was commissioned for
the Ramanujan Institute of the University of Madras, by Mr.
Masilamani in 1994. His original Note Books have been edited in a
series of five volumes by Bruce C. Berndt (``Ramanujan Note
Books'', Springer, Parts I to V, 1985 onwards), who devoted his
attention to each and every one of the three to four thousand
theorems. Robert Kanigel recently wrote a delightfully readable
biography entitled : ``The Man who knew Infinity : a life of the
Genius Ramanujan'' (Scribners 1991; Rupa & Co. 1993). Truly,
the life of Ramanujan in the words of C.P. Snow: ``is an admirable
story and one which showers credit on nearly everyone''.
During his five year stay in Cambridge, which unfortunately
overlapped with the first World War years, he published 21 papers,
five of which were in collaboration with Prof. G.H. Hardy and these
as well as his earlier publications before he set sail to England
are all contained in the ``Collected Papers of Srinivasa
Ramanujan'', referred earlier. It is important to note that though
Ramanujan took his ``Note Books'' with him he had no time to delve
deep into them. The 600 formulae he jotted down on loose sheets of
paper during the one year he was in India, after his meritorious
stay at Cambridge, are the contents of the `Lost' Note Book found
by Andrews in 1976. He was ailing throughout that one year after
his return from England (March 1919 - April 26, 1920). The last and
only letter he wrote to Hardy, from India, after his return, in
Jan. 1920, four months before his demise, contained no news about
his declining health but only information about his latest work :
``I discovered very interesting functions recently which I call
`Mock' theta-functions. Unlike the `False' theta-functions (studied
partially by Prof. Rogers in his interesting paper) they enter into
mathematics as beautifully as ordinary theta-functions. I am
sending you with this letter some examples ... ''. The following
observation of Richard Askey is noteworthy: ``Try to imagine the
quality of Ramanujan's mind, one which drove him to work
unceasingly while deathly ill, and one great enough to grow deeper
while his body became weaker. I stand in awe of his
accomplishments; understanding is beyond me. We would admire any
mathematician whose life's work was half of what Ramanujan found in
the last year of his life while he was dying''.
As for his place in the world of Mathematics, we quote Bruce C
Berndt: ``Paul Erdos has passed on to us Hardy's personal ratings
of mathematicians. Suppose that we rate mathematicians on the basis
of pure talent on a scale from 0 to 100, Hardy gave himself a score
of 25, Littlewood 30, Hilbert 80 and Ramanujan 100''. G.H.Hardy, in
1923, edited Chapter XII of Ramanujan's second Notebook on
Hypergeometric series which contained 47 main theorems, many of
them followed by a number of corollaries and particular cases. This
work had taken him so many weeks that he felt that if he were to
edit the entire Notebooks ``it will take the whole of my lifetime.
I cannot do my own work. This would not be proper.'' He urged
Indian authorities and G.N.Watson and B.M. Wilson to edit the
Notebooks. Watson and Wilson divided the task of editing the
Notebooks - Chapters 2 to 13 were to be edited by Wilson and
Chapters 14 to 21 by Watson. Unfortunately, the premature death of
Wilson, in 1935, at the age of 38, aborted this effort. In 1957,
with monetary assistance from Sir Dadabai Naoroji Trust, at the
instance of Professors Homi J Bhabha and K. Chandrasekaran, the
Tata institute of Fundamental Research published a facsimile
edition of the Notebooks of Ramanujan in two volumes, with just an
introductory para about them. The formidable task of truly editing
the Notebooks was taken up in right earnest by Professor Bruce C.
Berndt of the University of Illinois, in May 1977 and his dedicated
efforts for nearly two decades has resulted in the Ramanujan's
Notebooks published by Springer-Verlag in five Parts, the first of
which appeared in 1985. The three original Ramanujan Notebooks are
with the Library of the University of Madras, some of the
correspondence, papers/letters on or about Ramanujan are with the
National Archives at New Delhi and the Tamil Nadu Archives, and a
large number of his letters and connected papers/correspondence and
notes by Hardy, Watson, Wilson are with the Wren Library of Trinity
College, Cambridge. ``Ramanujan : Letters and Commentary'', by
Bruce C. Berndt and Robert A. Rankin (published jointly by the
American Mathematical Society and London Math. Society, 1995) is a
recent publication. The Ramanujan Institute for Advanced Study in
Mathematics of the University of Madras is situated at a short
distance from the famed Marina Beach and is close to the
Administrative Buildings of the University and its Library. The
bust of Ramanujan made by Mr. Masilamani is housed in the Ramanujan
Institute. In 1992, the Ramanujan Museum was started in the Avvai
Kalai Kazhagam in Royapuram. Mrs. Janakiammal Ramanujan, the widow
of Ramanujan, lived for several decades in Triplicane, close to the
University's Marina Campus and died on April 13, 1994. A bust of
Ramanujan, sculpted by Paul Granlund was presented to her and it is
now with her adopted son Mr. W. Narayanan, living in
Triplicane.
by The Institute of Mathematical Sciences, Madras...