Srinivasa Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having no formal training in mathematics. He was born in 1887 in India and showed an early aptitude for mathematics. Ramanujan's genius was recognized by English mathematician G.H. Hardy, who brought him to Cambridge University. There, Ramanujan continued his groundbreaking mathematical research but fell ill and returned to India, dying in 1920 at the age of 32. Ramanujan made major discoveries that have influenced mathematics and he is now celebrated as one of history's greatest mathematical minds.

1. SRINIVASA
RAMANUJAN

2. SRINIVASA IYENGAR RAMANUJAN
Born - 22 December 1887
Kumbakonam, Madras
Presidency British India
Died - 26 April 1920
Chetput, Madras, British India
College - Government Arts College
Pachaiyappa’s College
Cambridge University
Academic Advisors -
G.H.Hardy

3. RAMAJUNA – THE MATHEMATICIAN
 No formal training in Mathematics
 Made extraordinary contributions to
Mathematical Analysis, Number Theory,
Infinite Series and Continued Fractions.
 Expert in Trigonometry at age 12
 Discovered theorems of his own
 Fellow of the Royal Society and Trinity
College, Cambridge

4. EARLY LIFE
 Born in Erode to K. Srinivasa Iyengar
and Komalatmmal
 Lived in Sarangapani Street in
Kumbakonam
 Went school first on 1.10.1892.
 Had to switch primary school 3 times
due to circumstances.
 Completed Math exam in half the allotted
time.
 A synopsis of Elementary Results in Pure
and Applied Mathematics. Book
acknowledged in awakening the genius
of Ramanujan.
 Left college without a degree and
pursued research in Mathematics.

5. ADULTHOOD IN INDIA
 Married to a 9 year old bride Janaki
Ammal on 14 July 1909
 Went door to door for job
 Tutored college students

6. ATTENTION FROM MATHEMATICIANS
 Met V. Ramaswamy Aiyer, founder of
Indian Mathematical Society
 I was struck by the extraordinary
mathematical results contained in it
[the notebooks]. I had no mind to
smother his genius by an
appointment in the lowest rungs of
the revenue department
 Introduced to R. Ramachandra
Rao, secretary of the Indian
Mathematical Society
 Impressed by Ramanujan but doubted
his integrity.
 Continued Mathematical Research
with
Rao’s financial help
R.Ramachandra
Rao

7.  Published his work in Journal of Indian Mathematical Society
 First problem which he posed
 He then formulated an equation to solve the infinitely nested
radicals problem.
Wrote his 1st formal paper for the journal on the properties
of Bernoulli Numbers

8.  In early 1912 he got a job in the Madras
Accountant Generals office with a salary of Rs
20 per month.
 Later he applied for a position under the
Chief Accountant of the Madras Port Trust
 Accepted as a Class III, Grade IV
accounting clerk making 30 rupees per
month
 Spent spare time doing Mathematical Research

9. CONTACTING ENGLISH
MATHEMATICIANS
 M. J. M. Hill of University College London
argued that though Ramanujan had taste for
Mathematics he lacked the proper
educational background and foundation
 He refused to take Ramanujan as student
 But gave him professional advice on his work

10. INTRODUCTION WITH
G.H.HARDY
 G.H. Hardy was an academician at Cambridge
University
 He was a prominent English mathematician, known for
his achievements in number theory and mathematical
analysis.
 Later on Ramanujan wrote to G.H.Hardy
 Hardy recognised some of his formulae but other
“seemed scarcely possible to believe”. Some of them
were –
Relating to infinite series -

11. 
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12. LIFE IN ENGLAND
 Ramanujan boarded the S.S.Nevasa on 17 March
1914
and arrived in London on 14th April
 Ramanujan began working with Hardy and
Littlewood
 Hardy received 120 theorems from him in 1st 2
letters
but there were many more results in his notebook
 After working with Ramanujan Littlewood
commented, "I can believe that he's at least a
Jacobi”
 Hardy said he "can compare him only with

13.  Awarded BA degree by
research (later called PhD)
in March 1916
 6.12.1917 – Elected to
London Mathematical
Society
 Became a ‘Fellow of The
Royal Society’ in 1918
 Became the first Indian to be
elected a Fellow of Trinity
College, Cambridge
RAMANUJAN’S HONOURS

14. ILLNESS & RETURN TO INDIA
 Ramanujan's health worsened in England
 Diagnosed with Tuberculosis and Vitamin
deficiency
 Returned to Kumbakonam in 1919 and died
soon thereafter at the age of 32
 In 1994 Dr. D.A.B. Young analysed his
records and
concluded he had hepatic amoebiasis

15. PERSONALITY AND SPIRITUAL LIFE
 A person with a somewhat shy and quiet
disposition
 A dignified man with pleasant manners
 Ramanujan credited his success to his family
Goddess, Namagiri of Namakkal
 He claimed to receive visions of scrolls of
complex
mathematical content unfolding before his eyes
 "Anequation for me has no meaning, unless it
represents a thought ofGod.”

16. RAMANUJAN’S NOTEBOOKS
 Recorded his work in 4 notebooks of
loose
leaf paper
 Results were written without derivation
 Mathematician Bruce C. Berndt says
that Ramanujan was able to make
the proofs but chose not to.
 Might have worked on slate
 Or may be influenced by G.S Carr’s
book
which stated results without proofs
 Mathematicians such as Hardy,
G.N. Watson, B.M. Wilson and

17. RAMANUJAN - HARDY NUMBER
1729
 Hardy arrived in a cab numbered 1729
 He commented that the number was
uninteresting
 Instantly Ramanujan claimed that it was the
smallest natural number which can be
written as sum of cubes in 2 ways

18. OTHER MATHEMATICIANS’ VIEWS
OF RAMANUJAN
 J.H. Hardy was highly impressed by
Ramanujan
 Hardy said that the solutions were "arrived at
by a process of mingled argument, intuition,
and induction, of which he was entirely
unable to give any coherent account”
 On the basis of pure talent Hardy rated
himself a score of 25 out of 100, J.E.
Littlewood 30, David Hilbert 80 and
Ramanujan 100 !
 Physicist Jayant Narlikar
appreciated Ramanujan’s

19. RECOGNITION
 Tamil Nadu celebrates 22 December as ‘State IT
Day’
 Stamp released by the Govt. in 1962
 22nd December celebrated as Ramanujan Day in
Govt Arts College, Kumbakonam
 National Symposium On Mathematical Methods
and
Applications (NSMMA)
 SASTRA Ramanujan Prize

20. IN POPULAR CULTURE
 A play ‘First Class Man’ is centered aroundRamanujan
 Book by Robert Kanigel titled ‘The Man Who Knew
Infinity: A Life of the Genius Ramanujan’ is his
biography
 In the famous film ‘Good Will Hunting’ themain
character is compared to Ramanujan
 ‘A Disappearing Number’, a show by British Stage
Production is about Ramanujan and Hardy
 Character Amita Ramanujan in the show Numb3rsis
named after him
 Roger Spottiswoode is working on a movie on
mathematical genius Srinivasa Ramanujan starring Rang

21. RAMANUJAN – RARE
MATHEMATICAL GENIUS

22. THANK YOU