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 pure mathematics. He was born in 1887 in India and showed an extraordinary aptitude for mathematics from a young age. Ramanujan struggled to get recognition until he was introduced to the English mathematician G.H. Hardy through letters containing his original research. Hardy arranged for Ramanujan to work at Cambridge University where he spent the last years of his life conducting groundbreaking mathematical research before passing away in 1920 at the young age of 32. Ramanujan made substantial contributions to mathematical functions and analysis and continues to have a significant impact on mathematics despite his short life

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
J.E.Littlewood

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 [Leonhard]
Euler or Jacobi”
 Ramanujan spent nearly 5 years in Cambridge

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
 "An equation for me has no meaning, unless it
represents a thought of God.”

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 Bruce Berndt
created papers from his work

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 discoveries

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 around Ramanujan
 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’ the main
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 Numb3rs is
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!! 
Made By
DEV YADAV