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 toMathematical Analysis,
Number Theory, InfiniteSeries 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.
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 ofIndian
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
7. •Published his work in Journal of Indian Mathematical
SocietyFirst problem which he posed
√1+2√1+3√1+......
•He then formulated an equation to solve the infinitely
nested radicals problem.
X + n + a = √ ax + (n+a)² + x√a(x + n) + (n+a)² + (x +
n)√···
•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
“seemedare scarcely possible to believe some of are
11. • Hardy believed that Ramanujan’s theorems must be true
otherwise no one could have imagined to invent them
• Hardy considered him to be “a mathematician of the highest
quality,a man of altogether exceptional originality and
power”
• Hardy’s one colleague E.H.Neville commented that “not one
[theorem] could have been set in the most advanced
mathematical examination in the world”
• Hardy invited Ramanujan to Cambridge university but
Ramanujan refused
• Hardy then enlisted E.H.Neville to bring Ramanujan to
England
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”
13. RAMANUJAN’S HONOURS
•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
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
itrepresents 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
•1729 =13 +123 = 93 + 103.
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, andinduction, 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
