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