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Ramanujan
The Forgotten, but Un-Deniable Genius
Sheer intuitive brilliance coupled
to long, hard hours on his slate made up for most of his educational lapse. This ‘poor and solitary Hindu pitting his
brains against the accumulated wisdom of Europe’ as Hardy called him, had rediscovered a century of mathematics and
made new discoveries that would captivate mathematicians for next century.
Robert Kanigel author of - The Man who Knew Infinity : A
Life of the Genius Ramanujan
As Robert Kanigel wrote:
"Ramanujan's life can be made to serve as parable for almost any lesson you want to draw
from it. Few can say much about his work, and yet something in the story of his struggle for the chance to pursue his work
on his own terms compels the imagination, leaving Ramanujan a symbol for genius, for the obstacles it faces, for the burden
it bears, for the pleasure it takes in its own existence."
The Birth
Srinivasa Ramanujan Iyengar was born on December 22, 1887 to K.Srinivasa
Iyengar and Komlatammal, in Erode (about 400 km from Chennai, formerly called Madras) where his mother's parent's lived.
Ramanujan's Mother - Komalatammal
After one year he was brought to his father's town, Kumbakonam
Schooling and College
In 1897 Ramanujan passed his primary education, scoring first
in the district. He then joined the Town High School.
While at school he came across a book titled - "A Synopsis
of Elementary Results in Pure and Applied Mathematics"by George Shoobridge Carr (the title did not reflect the book's
content).
Carr had compressed a huge mass of mathematics that was known in the late 19th century into a compilation of
about 5000 equations in algebra, calculus, trigonometry and analytical geometry with abridges demonstrations of the propositions,
within 2 volumes. Ramanujan had the first volume.
The book was not a classic but had positive features. According to Kanigel, "one strength of Carr’s book was
a movement, a flow to the formulas seemingly laid down one after another in artless profusion that gave the book a sly seductive
logic of its own."
The English mathematician Godfrey Harold Hardy once wrote about the book as - "He (Carr) is now completely
forgotten, even in his college, except in so far as Ramanujan kept his name alive. The book is not in any sense a great one,
but Ramanujan made it famous and there is no doubt it influenced him (Ramanujan) profoundly"
But the book greatly influenced his career nobody knows exactly how, but the book ignited a burst of fiercely single-minded
intellectual activity.
Carr did not provide any elaborate demonstrations or step to step proofs, he simply gave some hints
to proceed in the right way.
E.H.Neville Another English mathematician E.H.Neville wrote - "In proving one formula, as he (Ramanujan) worked through Carr’s
synopsis, he discovered many others, and he began the practice of compiling a notebook."
Between 1903 and 1914 Ramanujan
had 3 notebooks.
After school, his total concentration was focussed on mathematics.
In 1904, he entered Kumbakonam's Government College
as F.A student with scholarship.
But, because of his total concentration in mathematics, he first failed in Kumbakonam's
Government College. He tried once again in Madras from Pachaiyappa's College, but failed again.
This with added financial
constraints led him to discontinue his formal education.
The Stuggle
Part-1
Now Ramanujan made up his mind to pursue mathematics forgetting everything else. But he had to work under extreme hardship,
he could not even buy enough paper to record proofs of his results.
Once he confided to his friends, "when food is problem, how can I find money for paper? I may require
four reams of paper every month"
In fact Ramanujan was in a very precarious situation. He had lost his scholarship. He had failed in examination. What is
more, he failed to prove a good tutor in the subject which he loved most.
Part-2
Ramaswami Iyer, a middle level Government servant founded the Indian Mathematical Society in 1906. Ramaswami Iyer met
Ramanujan sometime in late 1910 and introduced Ramanujan to his mathematical friends in Madras, one of them was P.V.Seshu
Iyer (who had taught Ramanujan at the Government College).
These introductions to government officials helped Ramanujan get a clerikal job in Madras Port Trust, joining from March
1, 1912. But this was to be for a short period of 14 months as his life altering moment was soon to come.
The Letter
On January 16, 1913 25 year old Ramanujan with no formal education wrote a letter to the leading British mathematician
Godfrey Harold Hardy who championed in pure mathematics with no interest in the applied aspects. He discovered one of the
fundamental results in population genetics which explains the properties of dominant, and recessive genes in large mixed population,
but he regarded the work as unimportant.
Godfrey Harold Hardy
The letter from Ramanujan ran into eleven pages, filled with theorems of divergent series but did not send proofs for
his theorems, requesting for advice and help to get his results published.
Ramanujan wrote : "I beg to introduce myself to you as a clerk in the Accounts Department of the Port
Trust Office at Madras on a salary of only £ 20 per annum. I have had no university education but I have undergone the ordinary
school course. After leaving school I have been employing the spare time at my disposal to work at mathematics. I have not
trodden through the conventional regular course which is followed in a university course, but I am striking out a new path
for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local
mathematicians as "startling". I would request you to go through the enclosed papers. Being poor, if you are convinced that
there is anything of value I would like to have my theorems published. I have not given the actual investigations nor the
expressions that I get but I have indicated the lines on which I proceed. Being inexperienced I would very highly value any
advice you give me"
Ramanujan had sent similar letters to two other established Cambridge mathematicians, H.F.Baker and E.W.Hobson, which was
not even opened by them.
Though Hardy read the letter, but was not impressed with the contents at first glance of the letter.
So, Hardy left the letter aside and got engaged in his daily routine but on one evening Hardy re-examined Ramanujan's theorems
and also requested his colleague, John Edensor Littlewood (1885-1977) to examine the theorems
The result analysing the theorems was, awe amongst the mathematical peers for this unknown mathematician. Everyone in Cambridge
concerned in mathematics came to know about the letter. Some even said - "at least another Jacobi in making had been found
out"
Karl Gustav Jacob Jacobi
Bertrand Arthur William Russell (1872-1970) wrote to Lady Ottoline Morell - "I found Hardy and Littlewood in a state of
wild excitement because they believe, they have discovered a second Newton, a Hindu Clerk in Madras.... He wrote to Hardy
telling of some results he has got, which Hardy thinks quite wonderful."
Bertrand Arthur William Russell
The Reply
Hardy sent 3 letters to Ramanujan in the next 3 months after recieving Ramanujan's letter.
Hardy was cautious in the initial response.
Quote from the letter on 8 February 1913 -
"I was exceedingly
interested by your letter and by the theorems which you state. You will however understand that, before I can judge properly
of the value of what you have done it is essential that I should see proofs of some of your assertions.... I hope very much
that you will send me as quickly as possible at any rate a few of your proofs, and follow this more at your leisure by more
detailed account of your work on primer and divergent series. It seems to me quite likely that you have done a good deal of
work worth publication; and if you can produce satisfactory demonstration I should be very glad to do what I can to secure
it"
Hardy's Plan
Hardy started taking steps for bringing Ramanujan to England first by contacting the Indian Office in London.
As the news was out about the new mathematical star, Francis Spring convinced Gilbert Walker to look through Ramanujan's
notebooks. Gilbert Walker was the Head of Indian Meteorological Department in Simla, who was not a pure mathematician but
was a former Fellow and mathematics lecturer at Trinity College, Cambridge.
This led to Gilbert Walker writing to the Registrar of Madras University, to award the first research scolarship of Madras
University to Ramanujan.
The letter from Gilbert Walker to the Registrar - "The character of the work that I saw impressed me
as comparable in originality with that of a Mathematical Fellow in a Cambridge College; it appears to lack, however, as might
be expected in the circumstances, the completeness and precision necessary before the universal validity of the results could
be accepted. I have not specialised in the branches of pure mathematics at which he worked, and could not therefore form a
reliable estimate of his abilities, which might be of an order to bring him a European reputation. But it was perfectly clear
to me that the University would be justified in enabling S. Ramanujan for a few years at least to spend the whole of his time
on mathematics without any anxiety as to his livelihood"
A New World
Ramanujan was apprehensive and not very eager to travel abroad, but eventually left Madras by S.S.Navesa on 17 March,
1914 for Cambridge on 18 April, 1914
Ramanujan was awarded B.A degree in 1916 March for his work on "Highly Composite Numbers" which was published as
a paper in Journal of London Mathematical Society. He was the second Indian to become a Fellow of the Royal Society in October,
1918 elected by Trinity College, Cambridge for - "for his investigation in Elliptic Functions and the Theory
of Numbers"
He became one of the youngest Fellows in the entire Royal Society history.
Ramanujan's Works
Though what Ramanujan did will be fully understood only by very few, it is worth noting what Godfrey Harold Hardy said
about the works of any pure mathematician -
"What we do may be small, but it has certain character of permanence and to have produced anything of
the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something beyond
the powers of the vast majority of men"
Ramanujan worked mostly on the purest realm of mathematics - under the heading "The Number Theory". The number
theory is the abstract study of structures of number systems and properties of positive integers, which included theorems
about prime numbers.
Number theory includes -
analytic number theory originated by Leonhard Euler (1707-1789);
Leonhard Euler
Geometric theory, which uses geometrical methods like Cartesian co-ordinates, vectors and matrices;
Probabilistic number theory based on probability theory.
About Ramanujan's work, Hardy said -
"Opinions may differ as to the importance of Ramanujan’s work, the kind of standard by which it
should be judged and the influence which it is likely to have on the mathematics of the future. It has not the simplicity
and the inevitableness of the greatest work; it would be greater if it were less strange. One gift it shows which no one will
deny - profound and invincible originality"
One of the greatest number theorist, Atle Selberg from Norway said about Ramanujan's work -
"Ramanujan’s recognition of the multiplicative properties of the coefficients of modular forms
that we now refer to as cusp forms and his conjectures formulated in this connection and their later generalization, have
come to play a more central role in the mathematics of today, serving as a kind of focus for the attention of quite a large
group of the best mathematicians of our time. Other discoveries like the mock-theta functions are only in the very early stages
of being understood and no one can yet assess their real importance. So the final verdict is certainly not in, and it may
not be in for a long time, but the estimates of Ramanujan’s nature in mathematics certainly have been growing over the
years. There is doubt no about that"
Why Ramanujan is still respected and revered amongst the mathematical communities is not merely for the hardship he had
to cross for his first love in life, mathematics, but because of his unique approach to mathematical calculation.
As Hardy observed Ramanujan's technique -
"Ramanujan combined a power of generalization, a feeling for form and a capacity for rapid modification
of his hypotheses, that were often really startling, and made him, in his peculiar field, without a rival in his day"
Hard Work+Passion = Genius = Ramanujan
On the basis of his work alone he was a mathematical genius, working hard like any other great mathematician but had no
special powers.
As Hardy said -
"I have often been asked whether Ramanujan had any special secret; whether his methods differed in kind
from those of other mathematicians; whether there was anything really abnormal in his mode of thought. I cannot answer these
questions with any confidence or conviction; but I do not believe it. My belief that all mathematicians think, at bottom,
in the same kind of way, and that Ramanujan was no exception"
Ramanujan's Untimely Death
Ramanujan though was getting his mathematical recognition in England, because of the cultural divide like the food (he
was a Brahmin-a strict vegetarian hindu) and the people, where they were more reserved unlike the people in his hometown.
The main person he could converse was with Hardy, but he too was a eccentric character which was known even by his Cambridge
collegues.
So eventually, his stay in England made him physically unwell (because he skipped most of his meal) and mentally depressed.
Finally, he requested Hardy that he wanted to go back to his hometown.
In Kumbakonam, on 26th April 1920 Ramanujan died of tuberculosis. He was only 32 years old.
Even days after he came
back and days before his death, Ramanujan was still doing his mathematics eagerly.
Janaki - Ramanujan's Wife
Ramanujan's wife, Janaki said -
"It was always maths ... Four days before he died he was scribbling"
Of the untimely and most particularly unfortunate circumstances of Ramanujan's Death, TIMES Magazine rightly wrote -
"There is something peculiarly sad in the spectacle of genius dying young, dying with the first sweets of recognition
and success tasted, but before the full recognition of powers that lie within"
The only Ramanujan Museum in India, founded by Shri P. K. Srinivasan, a mathematics teacher, opened from March 1993 in
the Avvai Academy, Royapuram, Madras.
 Statue by American Architect Paul Grandlund
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 Postage Stamp released by Govt.of India in 1962 |
The Presumptous Facts
Speculations of Ramanujan's achievements had he not have had such an untimely death has been compared with the the cases of
other great mathematicians like -
Niels Henrik Abel (1809-1829) - who solved one of the great mathematical problems of his day by finding a general solution
for a class equation called "quintiles" (he solved it by proving that such a solution was impossible).
 Niels Henrik Abel |
 Evarista Galois |
And Evarista Galois (1811-1832) - who pioneered the branch of modern mathematics called "group theory".
But as any mathematican will approach a problem, speculations are futile.
As someone once wrote -
"Ramanujan did mathematics for its own sake, for the thrill that he got in
seeing and discovering unusual relationships between various mathematical objects"
Today Ramanujan’s work has some applications in particle physics or in the calculation of pi up to a very large number
of decimal places. His work on Rieman’s Zeta Function has been applied to the pyrometry, the investigations of the temperature
of furnaces. His work on the Partition Numbers resulted in two applications - new fuels and fabrics like nylons. But then
highlighting the importance of the application side Ramanujan’s work is really not very important.
Ramanujan's Struggle Still Not Acknowledged
Even after more than 90 years of the death of Ramanujan the situation is not very different as far the rigidity of the education
system is concerned.
Even today a ‘Ramanujan’ is not likely to get a chance to pursue his career. This situation remains very
much similar as described by JBS Haldane (1982-1964), a British born geneticist and philosopher who spent last part of his
life in India.
Haldane said :-
"Today in India Ramanujan could not get even a lectureship in a rural college because he had no degree.
Much less could he get a post through the Union Public Service Commission. This fact is a disgrace to India. I am aware that
he was offered a chair in India after becoming a Fellow of the Royal Society. But it is scandalous that India’s great
men should have to wait for foreign recognition. If Ramanujan’s work had been recognised in India as early it was in
England, he might never have emigrated and might be alive today. We can cast the blame for Ramanujan’s non-recognition
on the British Raj. We cannot do so when similar cases occur today...
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