S. Ramanujan was a renowned Indian mathematician who made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training. He was born in 1887 in Tamil Nadu, India and showed remarkable mathematical abilities from a very young age. Although he struggled to receive formal education, he independently discovered deep mathematical identities and functions. His work attracted the attention of mathematicians in England and he was elected to the London Mathematical Society. However, his health declined and he ultimately passed away in 1920 at the young age of 32.

1. Contributions Of Great Mathemati
cian
S.RAMANUJAN
‫رامانجن‬ ‫ايس‬

3. History Of S.RAMANUJAN-
 Born on December 22 , 1887.
 In a village in Madras State, at Erode, in Tanjore District.
 In a poor HINDU BRAHMIN family.
 Full name is “SRINIVAS RAMANUJAN AYYANGER”.
 Son of Srinivas Iyenger.
 Accountant to a cloth merchant at KUMBHAKONAM. Daughter of petty
official ( Amin ) in District Munsif’s court at Erode.
 Daughter of petty official ( Amin ) in District Munsif’s court at Erode.
 First went to school at the age of 7.

4. --------------------------------------------
 His famous history was :- One day a primary S
chool teacher of 3rd form was telling to his studen
ts ‘If three fruits are divided among three persons,
each would get one , even would get one , even if
1000 fruits are divided among 1000 persons each
would get one ‘. Thus , generalized that any num
ber divided by itself was unity . This Made a child
of that class jump and ask- ‘ is zero divided by zer
o also unity?’ If no fruits are divided nobody , wi
ll each get one? This little boy was none other tha
n RAMANUJAN .

5.  So intelligent that as students of class 3rd or primary
school.
 Solved all problems of Looney’s Trigonometry mean
t for degree classes.
 At the age of seven , he was transferred to Town Hig
h School at Kumbhakonam.
 He held scholarship.
 Stood first in class.
 Popular in mathematics.

6. -------------------------------------------
 At the age of 12, he was declared “CHILD MATHEMA
TICIAN” by his teachers.
 Entertain his friends with theorem and formulas.
 Recitation of complete list of Sanskrit roots and repeatin
g value of ∏ and square root of 2, to any number of dec
imal places.
 In 1903 , at the age of 15, in VI form he got a book , “Ca
rr’s Synopsis”.
 “Pure and Applied Mathematics”

7.  Gained first class in matriculation in December 1903
.
 Secured Subramanian’s scholarship.
 Joined first examination in Arts (F.A).
 Tried thrice for F.A.
 In 1909, he got married to Janaki ammal.
 Got job as clerk.
 Office of Madras port trust.
Born 4 November 1897
Tellicherry,Kerala
Died February 1984 (aged 87)
Nationality Indian
Fields Botany, Cytology
Institutions University Botany,,Laboratory
Madras
Alma mater University of Michigan

8.  Published his work in “Journal of Indian Mathe
matical Society”.
 In 1911, at 23 , wrote a long article on some pro
perties of “Bernoullis Numbers”.
 Correspondence with Prof.J.H Hardy.
 Attached 120 theorems to the first letter.

9. In 1912, Mr. Walker, held high post under
the Government.
Obtained, scholarship of Rs. 75/- per mont
h.
In 1914, invited to Cambridge University,
and in 1916, got Hon. B.A. Degree of Uni
versity of Cambridge

10. His Achievements-
1) Divergent Series:- When Dr. Hardy examined his in
vestigation – “I had never seen anything the least like
them before. A single look at them is enough to show
that this could only be written by Mathematician of h
ighest class”.
2) Hyper Geometric series and continued Fraction:
He was compared with Euler and Jacobi.
3) Definite Integrals

11. -----------------
4)Elliptic Functions
5)Partition functions
6)Fractional Differentiation: He gave a meaning to Euleri
an second integral for all values of n .He proved x ⁿ−‫ا‬ e
−ͯ = Gamma is true for all Gamma.
7)Theory of Numbers: The modern theory of numbers is
most difficult branch of mathematician .It has many u
nsolved problems. Good Example is of Gold Bach’s Th
eorem which states that every even number is sum of t
wo prime numbers. Ramanujan discovered Reimann’s s
eries , concerning prime numbers . For him every integ
er was one of his personal friend.

12. ------
He detected congruence, symmetries and relations
hips and different wonderful properties.Taxi cab No
was an interesting number to him.
1729 = 1³+12³ = 9³ + 10³
8. Partition of whole numbers: Take case of 3. It can
be written as…
3+0,1+2,1+1+1
He developed a formula
, for partition of any number
which can be made to yield the
required result by a series of
successive approximation.

13. 9). Highly Composite Numbers : Highly composite num
ber is opposite of prime numbers. Prime number has two
divisions, itself and unity . A highly composite number h
as more divisions than any preceding number like: 2,4,6,
12,24,36,48,60,120,etc.He studied the structure ,distribu
tion and special forms of highly composite numbers. Har
dy says – “Elementary analysis of highly composite num
bers is most remarkable and shows very clearly Ramanu
jan’s extra-ordinary mastery over algebra of inequalities
”.

14.  Greatest masters in the field of higher geometric th
eories and continued fractions.
 He could work out modular equation, work out theo
rems of complex multiplication, mastery of continu
ed fraction.
 Found for him self functional equation of zeta funct
ion.
 Mathematician whom only first class mathematicia
ns follow.

15.  England honoured by Royal Society and Trinity
fellowship.
 Did not receive any honour from India.
 In spring of 1917, he first appeared tobe unwell.
 Active work for Royal Society and Trinity Fello
wship.
 Due to TB, he left for India and died in chetpet ,
Madras .
 On April 26, 1920 at the age of 33.

16. Made by :-
Yash Prakash
Karjekar,
Std-8th, Div-B,
Roll.No-35.