The Man Who knew Infinity 1*1*1 + 12*12*12 = 1729 = 9*9*9 + 10*10*10

“HE” is between two “MAT” s. His qualification is “ICS”. Who is he….(“MATHEMATICS”)

MATHEMATICS

SRINIVASA AIYANGAR

RAMANUJAN

22-12-1887 to 24-04-1920

MATHEMATICS

Sinivasa Aiyangarr Ramanujan 1887 - 1920

Srinivasa Ramanujan was one of India’s greatest mathematical geniuses.

He made substantial contributions to the analytical theory of numbers and worked on elliptical functions, continued fractions and infinite series.

Srinivasa Aiyangar Ramanujan was born on 22-Dec-1887 in Erode, Kumbakonam, Madras Presidency ( now in Tamilnadu) at the residence of his maternal grandparents .

The house where Ramanujan was born

His mother name was Komalathammal and father was Srinivasa Raghava Aiyangar.

They lived in Sarangapani Street in a traditional home in the town of Kumbakonam.

Ramanujan’s house at Sarangapani street in Kumbakonam……

The house is now runs as Ramanujan’s Muesium…..

Oct.1st 1892, on a Vijayathasami day, he was enrolled in the Thinnai Palli Koodam (Pial school).

In March 1894, he was moved to a Telugu medium school.

From his mother he learned about tradition and puranas. He learned to sing religious songs, to attend pujas at the temple and particular eating habits – all of which are part of Brahmin culture.

At the age of 10, in November 1897, he passed his primary examinations in English, Tamil, geography and arithmetic at the Kangayan Primary School. With his scores, he stood first in the district..

Town Higher Secondary School, Kumbakonam

In 1898, Ramanujan entered Town Higher Secondary School where he encountered formal mathematics for the first time..

He was later lent a book on plane trigonometry written by S. L. Loney. He completely mastered this book by the age of 13 and discovered sophisticated theorems on his own.

The book of Trigonometry by S.L.Loney

He completed mathematical exams in half the allotted time, and showed a familiarity with geometry and infinite series.

In 1903 when he was 16, Ramanujan obtained from a friend a library-loaned copy of a book by. G. S. Carr. The book was titled A Synopsis of Elementary Results in Pure and Applied Mathematics and was a collection of 5000 theorems.

The copy of G.S.Carr’s book….

This book is generally acknowledged as a key element in awakening the genius of Ramanujan.

he graduated from Town Higher Secondary School in 1904.

The certificate of Ramanujan issued in Town High school

Ramanujan was awarded the K. Ranganatha Raoprize for mathematics by the school's headmaster, Krishnaswami Iyer.

After Passing of Madras Matriculation examination joined the F.A., class in the Government Arts College in Kumbakonam. Obtained Junior Subramaniam scholorship.

Ramanujan was so intent on studying mathematics that he could not focus on any other subjects and failed most of them, losing his scholarship in the process.

Government Arts College, Kumbakonam

In August 1905, he ran away from home, heading towards Visakhapatnam and stayed in Rajahmundry for about a month.

At this time his father gave an missing add In the news paper THE HINDU.

He later enrolled at Pachaiyappa's College in Madras

He again excelled in mathematics but performed poorly in other subjects such as physiology.

Ramanujan failed his Fellow of Arts exam in December 1906 and again a year later .

Without a degree, he left college and continued to pursue independent research in mathematics

Pachaiyappa’s College

Adulthood in India:

On 14 July 1909, Ramanujan was married to a ten year old bride, Janakiammal.

Ramanujan

Janaki

After the marriage, Ramanujan developed a hydrocele testis, an abnormal swelling of the tunica vaginalis, an internalmembrane in the testicle.

But his family did not have the money for the operation.

but in January 1910, a doctor volunteered to do the surgery for free.

After his successful surgery, Ramanujan searched for a job, he went door to door around the city of Madras (now Chennai) looking for a clerical position.

To make some money, he tutored somestudents at Presidency College who were preparing for their F.A. exam.

In late 1910, Ramanujan was sick again, He feared for his health..

Told his friend, R. Radakrishna Iyer, to "hand these [Ramanujan's mathematical notebooks] over to Professor Singaravelu Mudaliar [the mathematics professor at Pachaiyappa's College] or to the British professor Edward B. Ross, of the Madras Christian College.

After Ramanujan recovered and got back his notebooks from Iyer.

Attention towards mathematics:

Ramanujan met deputy collector of Tirtukkoilur V.Ramaswamy Aiyer, founder of the Indian Mathematical Society.

V.Ramaswamy Aiyer, The founder of Indian Mathematical Society……

Ramanujan, wishing for a job at the revenue department where Ramaswamy Aiyer worked, showed him his mathematics notebooks.

As Ramaswamy Aiyer later recalled:

“ 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 “.

Ramaswamy Aiyer sent Ramanujan, with letters of introduction, to his mathematician friends in Madras.

Some of these friends looked at his work and gave his letters of introduction to R. Ramachandra Rao, the district collector for Nellore and the secretary of the Indian Mathematical Society.

R. Ramachandra Rao, the district collector for Nellore and the secretary of the Indian Mathematical Society.

Ramachandra Rao was impressed by Ramanujan's research but doubted that it was actually his own work

Rao listened Ramanujan’s elliptic integrals, hyper geometric series, and theory of divergent series.

After that Rao said ultimately "converted" him to a belief in Ramanujan's mathematical brilliance. Rao asked him what do you want.

Ramanujan replied : “I need some work and financial support” Rao consented and sent him to Madras. He continued his mathematical research with Rao's financial aid taking care of his daily needs.

Ramanujan, with the help of Ramaswamy Aiyer, had his work published in the Journal of the Indian Mathematical Society

One of the first problems he posed in the journal was:

√1+2√1+3√1+4√1+… Ramanujan’s answer for this problem is ‘3’ , by

using the following formula.

x+n+a=

x+n+a=Put x=2, n=1, a=0

2+1+0=√1+2√1+3√1+4 √1+…=3𝑓 (𝑛)=𝑛 (𝑛+2 )=𝑛 √(𝑛+2)2=𝑛√𝑛2+4𝑛+4

¿√1+(𝑛+1)(𝑛+3)=𝑛√1+ 𝑓 (𝑛+1)

¿𝑛√1+(𝑛+1)√1+ 𝑓 (𝑛+2)

¿𝑛√1+(𝑛+1)√1+(𝑛+2)√1+…3

1)

2)

In early 1912, he got a temporary job in the Madras Accountant General's office, with a salary of 20 rupees per month..

He lasted it for only a few weeks.

Toward the end of lasting his job he applied for a position under the Chief Accountant of the Madras Port Trust. In a letter dated 9 February 1912.

The Chief Accountant of Madras Port Trust S.Narayana Iyer

wrote in that letter Ramanujan was:

To The Chief Accountant, Port Trust, Madras.

Sir,

I understand there is a clerkship vacant in yo uroffice, and I beg to apply for the same. I have passed the Matriculation Examination and studied up to the F.A. but was prevented from pursuing my studiesfurther owing to several untoward circumstances. I have, however, been devoting all my time toMathematics and developing the subject. I can say I am quite confident I can do justice to my work if Iam appointed to the post. I therefore beg to request that you will be good enough to confer the appointment on me. yours most obediently,

09-Feb-1912.

Contacting English mathematicians

In the spring of 1913, Narayana Iyer, Ramachandra Rao and  E.W. Middlemast tried to present Ramanujan's work to British mathematicians.

One mathematician, M. J. M. Hill of University College London , said that Ramanujan had "a taste for mathematics, and some ability“ but he doesn’t have educational background and foundation needed to be accepted by Mathematicians and refuse him.

With the help of friends, Ramanujan drafted letters to leading mathematicians at Cambridge University.

The first two professors, H. F. Baker and E. W. Hobson, returned Ramanujan's papers without comment.

H.F.Baker E.W.Hobson

On 16 January 1913, Ramanujan wrote to G. H. Hardy

Hardy recognized some of Ramanujan's formulae butothers "seemed scarcely possible to believe".

One of the theorems Hardy found scarcely possible to believe was found on the bottom of page three (valid for 0 < a < b + 1/2):

This result had already been determined by a mathematician named Bauer.

∫0

∞1+𝑥2/(𝑏+1)2

1+𝑥2/(𝑎)2×1+𝑥2/(𝑏+2)2

1+𝑥2/ (𝑎+1)2×…=√𝜋

2×Γ (𝑎+

12)Γ (𝑏+1)Γ (𝑏−𝑎+

12)

Γ (𝑎)Γ (𝑏+ 12)Γ (𝑏−𝑎+1)

The second one was new to Hardy, and was derived from a class of functions called a hypergeometric series.

Compared to Ramanujan's work on integrals, Hardy found these results "much more intriguing“.

Hardy commented that "they [theorems] defeated me completely; I had never seen anything in the least like them before“.

2.

3.

G.H.Hardy English mathematician, Cambridge

University

Well known as Hardy-Ramanujan number 1729

 Hardy concluded that the letters were "certainly the most remarkable I have received" and commented that Ramanujan was "a mathematician of the highest quality, a man of altogether exceptional originality and power".

One colleague, E. H. Neville, later commented that "not one [theorem] could have been set in the most advanced mathematical examination in the world".

On 8 February 1913, Hardy wrote a letter to Ramanujan, expressing his interest for his work.

And contacted the Indian Office to plan for Ramanujan's trip to Cambridge.

Ramanujan refused to leave his country to "go to a foreign land“

Meanwhile, Ramanujan sent a letter packed with theorems to Hardy, writing, "I have found a friend in you who views my labour sympathetically.“

 A former mathematical lecturer at Trinity College, Cambridge, Gilbert Walker, looked at Ramanujan's work and expressed amazement, urging him to spend time at Cambridge.

Hardy enlisted a colleague lecturing in Madras, E. H. Neville, to mentor and bring Ramanujan to England.

Ramanujan's mother had a vivid dream in which the family Goddess, the deity of Namagiri, commanded her "to stand no longer between her son and the fulfillment of his life's purpose".

Ramanujan apparently had now accepted the proposal; as Neville put it, "Ramanujan needed no converting and that his parents' opposition had been withdrawn“

Ramanujan then set sail for England, leaving his wife to stay with his parents in India.

Life in England:

Ramanujan boarded the S.S. Nevasa on 17 March 1914, and at 10 o'clock in the morning, the ship departed from Madras.

He arrived in London on 14 April, with E. H. Neville waiting for him with a car.

Neville took him to his house on Chesterton Road in Cambridge. Ramanujan immediately began his work with Littlewood and Hardy.

Hardy and Ramanujan began to take a look at Ramanujan's notebooks.

Hardy saw that some were wrong, others had already been discovered, while the rest were new breakthroughs.

Ramanujan left a deep impression on Hardy and Littlewood.

Comments about Ramanujan: Littlewood:  "I can believe that he's at least a Jacobi",

G.H.Hardy: "can compare him only with [Leonhard] Euler or Jacobi.“

Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood and published a part of his findings there.

Ramanujan was awarded a Bachelor of Science degree by research (this degree was later renamed PhD) in March 1916 for his work on highly composite numbers.

The first part of which was published as a paper in the Proceedings of the London Mathematical Society.

Hardy remarked that this was one of the most un--usual papers seen in mathematical research. 

On 6 December 1917, he was elected to the London Mathematical Society.

He became a Fellow of the Royal Society in 1918, becoming the second Indian to do so, following Ardaseer Cursetjee in 1841.

 he was one of the youngest Fellows in the history of the Royal Society. He was elected "for his investigation in Elliptic functions and the Theory of Numbers.“

On 13 October 1918, he became the first Indian to be elected a Fellow of Trinity College, Cambridge..

Illness and return to India:

Plagued by health problems throughout his life, living in a country far away from home, and obsessively involvedwith his mathematics, Ramanujan's health worsened in England.

He was diagnosed with tuberculosis and a severe vitamin deficiency and was confined to a sanatorium.

Srinivasa Aiyangar Ramanujan was died on 26- Apr - 1920

22–Dec–1887 to 26–Apr-1920

Hardy-Ramanujan number 1729

The number 1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital to see Ramanujan.

In Hardy’s words “ I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." ”

1*1*1 + 12*12*12 = 1729 =

9*9*9 + 10*10*10

Ramanujan’s family tree..

Sarangapani street, Erode, Kumbakonam

Ramanujan’s statue in his house…..

The cot used by Ramanujan…..

Varanda in his house….

Ramanujan’s mother Komalathammal…

The class room of Ramnujan in Town High School named as Ramanujan hall

1.Landau-Ramanujan constant. theta 2.Mock function. 3.Ramanujan conjecture. 4.Ramanujan prime Ramanujan Soliner constant.

5.Ramanujan’s sum. 6.Rogers-Ramanujan identities. 7.Ramanujan’s Master theorem.

MATHEMATICS

Ramanujan note books

The reprint of Ramanujan’s note book

Ramanujan’s note book with his own hand writing

Ramanujan’s Note books

MATHEMATICS

Chapter 1 MAGIC SQUARES

( In Ramanujan’s note book)

Ramanujan’s Master’s Theorem

The letter written by G.H.Hardy to Ramanujan

The group of mathematical scientists Ramanujan (centre) and G.H.Hardy (3rd from left)

At Trinity College, Cambridge

Trinity College, CambridgeWhere Ramanujan elected as Fellow

Ramanujan’s Museum

NATIONAL MATHEMATICS DAY

05-AUG-2012

MATHEMATICS

National 2012Mathematics Year

Declared byEx. Prime Minister Of India

Dr. Manmohan Singh

Ramanujan postal stamp released in 1962 by our indian govt.

MATHEMATICS

The postal Stamps on Srinivasa Ramanujan released by Our govt.

129th birthday of Ramanujan

Father of Mathematics

K.RANGA DEVI

M.Sc..MBA

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