S. Ramanujan was a renowned Indian mathematician born in 1887 in Tamil Nadu. He made extensive contributions to mathematical analysis, number theory, infinite series, and continued fractions. Some of his key achievements included developing new theorems regarding partition functions, elliptic functions, highly composite numbers, and discovering the Ramanujan prime and the Ramanujan theta function. Despite his untrained background, he was elected to the Fellowship of the Royal Society due to his exceptional genius and intuition for mathematical discoveries. He collaborated extensively with English mathematician G.H. Hardy and produced nearly 3,900 results, though most were without proof. Ramanujan passed away in 1920 at the young age of 32 due to illness.

1. Contributions Of GreatContributions Of Great
MathematicianMathematician
S.RAMANUJANS.RAMANUJAN

3. History Of S.RAMANUJAN-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.

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 His famous history was :- One day a primary
School teacher of 3rd
form was telling to his
students ‘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 number divided by itself was unity . This
Made a child of that class jump and ask- ‘ is zero
divided by zero also unity?’ If no fruits are
divided nobody , will each get one? This little boy
was none other than RAMANUJAN .

5.  So intelligent that as students of class 3rd
or primary
school.
 Solved all problems of Looney’s Trigonometry
meant for degree classes.
 At the age of seven , he was transferred to Town
High School at Kumbhakonam.
 He held scholarship.
 Stood first in class.
 Popular in mathematics.

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 At the age of 12, he was declared “CHILD
MATHEMATICIAN” by his teachers.
 Entertain his friends with theorem and formulas.
 Recitation of complete list of Sanskrit roots and
repeating value of ∏ and square root of 2, to any
number of decimal places.
 In 1903 , at the age of 15, in VI form he got a book ,
“Carr’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
Mathematical Society”.
 In 1911, at 23 , wrote a long article on some
properties 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
month.
In 1914, invited to Cambridge University,
and in 1916, got Hon. B.A. Degree of
University of Cambridge

10. His Achievements-His Achievements-
1) Divergent Series:- When Dr. Hardy examined his
investigation – “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 highest 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
Eulerian 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
unsolved problems. Good Example is of Gold Bach’s
Theorem which states that every even number is sum
of two prime numbers. Ramanujan discovered
Reimann’s series , concerning prime numbers . For him
every integer was one of his personal friend.

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He detected congruence, symmetries and
relationships and different wonderful
properties.Taxi cab Nowas 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

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

14.  Greatest masters in the field of higher geometric
theories and continued fractions.
 He could work out modular equation, work out
theorems of complex multiplication, mastery of
continued fraction.
 Found for him self functional equation of zeta
function.
 Mathematician whom only first class
mathematicians 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
Fellowship.
 Due to TB, he left for India and died in chetpet ,
Madras .
 On April 26, 1920 at the age of 33.