1) Srinivasa Ramanujan was one of India's greatest mathematical geniuses who made substantial contributions to analytical number theory, elliptic functions, and infinite series. 2) He was mostly self-taught and showed extraordinary talent from a young age, mastering advanced mathematical concepts from books he received. 3) Ramanujan struggled for recognition in India but eventually his work was brought to the attention of the English mathematician G.H. Hardy, who helped arrange for Ramanujan to travel to Cambridge University in 1914 where he spent five productive years collaborating before falling ill and returning to India, where he passed away in 1920.

1. The Man Who knew Infinity1*1*1 + 12*12*12 = 1729 =
9*9*9 + 10*10*10

2. 
“HE” is between two “MAT” s. His
qualification is “ICS”. Who is
he….(“MATHEMATICS”)

3. SRINIVASA AIYANGAR
RAMANUJAN 22-12-1887
to 24-04-1920

4. Sinivasa Aiyangarr
Ramanujan
1887 - 1920

5.  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.

6.  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.

7.  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…..

8. 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..

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

10. 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.

11.  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.

12.  he graduated from Town Higher Secondary School in 1904.
The certificate of Ramanujan issued
in Town High school

13.  Ramanujan was awarded the K. Ranganatha Rao
prize 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.

14. Government Arts College, Kumbakonam

15.  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.

16.  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

17. Adulthood in India:
 On 14 July 1909, Ramanujan was
married to a
ten year old bride, Janakiammal.
Ramanujan Janaki

18.  After the marriage, Ramanujan developed a hydrocele
testis, an abnormal swelling of the tunica vaginalis, an
internal
membrane 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 some
students at Presidency College who were preparing for
their F.A. exam.

19.  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.

20. 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.

21. 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.

22. 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

23.  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.

24.  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= 𝑎𝑥 + (𝑛 + 𝑎)2+𝑥 𝑎 𝑥 + 𝑛 + (𝑛 + 𝑎)2+(𝑥 + 𝑛) …

25. x+n+a= 𝑎𝑥 + (𝑛 + 𝑎)2+𝑥 𝑎 𝑥 + 𝑛 + (𝑛 + 𝑎)2+(𝑥 + 𝑛) …
Put x=2, n=1, a=0
2 + 1 + 0 = 1 + 2 1 + 3 1 + 4 1 + ⋯ = 3
𝑓 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 + ⋯
𝐹𝑜𝑟 𝑛 = 1
3 = 1 + 2 1 + 3 1 + 4 1 + ⋯
1)
2)

26.  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

27. 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 studies
further owing to several untoward
circumstances. I have, however, been devoting
all my time to
Mathematics and developing the subject. I can
say I am quite confident I can do justice to my
work if I
am appointed to the post. I therefore beg to
request that you will be good enough to confer
the appointment on me.
yours most
09-Feb-
1912.

28. 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.

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

30.  On 16 January 1913, Ramanujan wrote to G. H. Hardy
 Hardy recognized some of Ramanujan's formulae but
others "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 + 1
2)Γ(𝑏 + 1)Γ(𝑏 − 𝑎 + 1
2)
Γ(𝑎)Γ(𝑏 + 1
2
)Γ(𝑏 − 𝑎 + 1)

31.  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. 1 − 5
1
2
3
+ 9
1×3
2×4
3
− 13
1×3×5
2×4×6
3
+ ⋯ =
2
𝜋
3. 1 + 9
1
4
4
+ 17
1×5
4×8
4
+ 25
1×5×9
4×8×12
4
+ ⋯ =
2
3
2
𝜋
1
2Γ2 3
4

32. G.H.Hardy
English mathematician, Cambridge University
Well known as Hardy-Ramanujan number 1729

33.  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.

34. 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.

35.  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.

36. 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.

37.  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.

38.  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.

39.  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..

40. Illness and return to India:
 Plagued by health problems throughout his life, living in
a country far away from home, and obsessively involved
with 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

41. 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." ”

42. 1*1*1 + 12*12*12 = 1729 = 9*9*9
+ 10*10*10

43. Ramanujan’s family tree..

44. Sarangapani street, Erode, Kumbakonam

45. Ramanujan’s statue in
his house…..
The cot used by
Ramanujan…..
Varanda in his house….
Ramanujan’s
mother
Komalathammal…

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

47.  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.

48. Ramanujan note books
The reprint of Ramanujan’s
note book
Ramanujan’s note book with his
own hand writing

49. Ramanujan’s Note
books

51. Chapter 1
MAGIC SQUARES
( In Ramanujan’s note book)

52. Ramanujan’s
Master’s Theorem

53. The letter written by G.H.Hardy to Ramanujan

54. The group of mathematical scientists Ramanujan (centre) and G.H.Hardy (3rd
from left)
At Trinity College, Cambridge

55. Trinity College, Cambridge
Where Ramanujan elected as Fellow

56. Ramanujan’s Museum

57.  NATIONAL MATHEMATICS
DAY 05-
AUG-2012

58. National 2012
Mathematics Year
Declared by
Ex. Prime Minister Of India

59. 
Ramanujan postal stamp released in 1962 by
our indian govt.

60. The postal Stamps on Srinivasa Ramanujan released by Our
govt.