Ramanujan: The Man Who Knew Infinity

A tiny peek into the life of the GREAT mathematician from India.(Includes pics of some other great mathematician.)
(28 slides long)

1. S RINIVASA I YENGAR R AMANUJAN The Man Who Knew Infinity – How Indian Genius Ramanujan Rose From Zero to Wow the Math World

2. 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 SRINIVASA IYENGAR RAMANUJAN

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 unfavourable 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. Searched 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

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 In early 1912 he got a job in the Madras Accountant Generals office with a salary of Rs 20 per month.

8. 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”.

11. Some of them were – Relating to infinite series

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. Hardy believed that Ramanujan’s theorems must be true otherwise no one could have imagined to invent them Hardy considered to be “a mathematician of the highest, 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 With his parents supporting him he agreed to the proposal this time

14. RAMANUJAN’S HONOURS Awarded BA degree by research (later called PhD) in March 1916 6 December 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

15. 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

16. Contributions of ramanujan

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

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

24. ROYAL SOCEITY LONDON CAMBRIDGE UNIVERSITY TRINITY COLLEGE, CAMBRIDGE RAMANUJAN’S HOUSE

25. The GANG OF FOUR R. ASKEY SUBRAHMANYAM CHANDRASHEKHAR G.E. ANDREWS BRUCE C. BERNDT

26. DEWAN BAHADUR RAMCHANDRA RAO EULER G.H. HARDY V.RAMASWAMY IYER SESHU IYER GAUSS ROBERT KANIGEL JANAKI AMMAL

27. THANK YOU