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SRINIVASA
RAMANUJAN
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
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
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.
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
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
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
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
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
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 -
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
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
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
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.”
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
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
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
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
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
De Basanti actor Siddharth. Titled The First Class Man,
RAMANUJAN – RARE
MATHEMATICAL GENIUS
THANK YOU!!
Made By
DEV YADAV