Shrinivasa Ramanujan was a renowned Indian mathematician born in 1887 in Tamil Nadu. He made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions despite having little formal training in pure mathematics. Some of his key accomplishments included formulating the Ramanujan prime, the Ramanujan theta function, and pioneering work on mock modular forms and partition theory. He collaborated with English mathematician G.H. Hardy and produced nearly 3,900 results, though he unfortunately died young in 1920 at the age of 32. Ramanujan is celebrated annually in India and considered one of the greatest mathematicians of all time.

1. SHRINIVASA
RAMANUJAM
E.PARKAVI,
II B.SC MATHEMATICS.

2. • BORN : 22 December 1887
Erode, Madras Presidency.
• DIED : 26 April 1920,
Chetput, Madras presidency..
BASIC INTRODUCTION OF RAMANNUJAM

3. BASIC INTRODUCTION
Father: Kuppuswamy Srinivasa Iyengar,
Clerical Assistant to a cloth Merchant.
Mother: Komalathammal, Homemaker.
Spouse: Janaki Ammal.
Residence: Kumbakonam.
Alma Matter: Government arts college,
Pachaiyappa college.
Advisors: G.H. Hardy, J.E. Littlewood

4. CHILD HOOD
• Ramanujam exhausted maths of two college students by age 11 . Also ,he
mastered trigonometry book written by S.S. Lonely by age 13.
• When he graduated in 1904, he was awarded K. Ranganatha Rao prize for
mathematics by school’s head master.
• He received a scholarship to study at Government Arts College, but failed
to receive scholarship due to his poor performance in other subjects, except
maths.
• Again he enrolled in Pachaiyappa’s college in Madras. But he failed in
fellow of arts in 1906 and again a year later. He went on to individual
research in maths.

5. Adult hood
• He got a temporary job in Madras Accountant General’s
office,after that he was accepted as a clerk in Chief Accountant
of the Madras Port Trust. He did easily what he was given and
he spent his spare time with mathematical research,which his
boss encouraged him about.
• Since he has showed his supernatural talent by himself,again
people around him tried to connect him with big English
matematicians .About Ramanujan G.H. Hardy thought at first
it could be fraud because most of Ramanujan’s works were
impossible to believe.But eventually,they were convinced and
interested in his talent

6. Ramanujam Relation With God

7. His Best Known Results

8. Relation with Hardy
• G. H. Hardy , J.E. Littlewood who were great
mathematicians of that time invited Ramanujam to
England.
• Hardy, together with Littlewood, studied the long list of
unproved theorems which Ramanujan enclosed with his
letter. On 8 February he replied to Ramanujan.

9. Reply to Ramanujam
• I was exceedingly interested by your letter and by
the theorems which you state. You will however
understand that, before I can judge properly of the
value of what you have done, it is essential that I
should see proofs of some of your assertions

10. Little Woods Difficulty
• Littlewood was asked to help teach Ramanujan rigorous
mathematical methods. However he said
• ... that it was extremely difficult because every time some
matter, which it was thought that Ramanujan needed to
know, was mentioned, Ramanujan's response was an
avalanche of original ideas which made it almost
impossible for Littlewood to persist in his original
intention.

11. 1729 Man

12. RAMANUJAM’S MAGIC SQUARE

13. Ramanujam’s Prime Number Theorem
• Suppose that in some neighborhood of ,
• for some function (say analytic or integrable) . Then

14. PRIME NUMBER THEOREM
• These functions form a forward/inverse transform pair.
For example, taking for all give
• and
• which is simply the usual integral formula for the gamma function.
• Ramanujan used this theorem to generate amazing identities by
substituting particular values for

15. OTHER WORKS OF RAMANUJAM
• In 1900, he worked on his own math summing
zgeometric and arithmetic series.
• He solved cubic equations. (1902)
ax3
+ bx2
+ cx + d = 0
• He went on finding his own method of solving quartic
equation.
ax4
+ bx3
+ cx2
+ dx + e = 0
• He also worked on hyper geometric series.
• He also, Investigated the relation between series and
integrals.
• Despite many brilliant results, some of his theorems on
primes were completely wrong.

16. GETTING DEGREE IN ENGLAND

17. RETURN TO INDIA
• Ramanujam Always Suffered From Health
Problems Due To Stress, Lack Of Vegetarian
Food And Cimate In England.
• Ramanujam returned to India in 1919 and died
despite medical treatment in 1920.

18. Birthday celebration of India
• 22 december celebrated as state IT day in
Tamilnadu for his achievements.

19. Stamp released for him to mark his 75th
birthday

20. Recognition By Indian Governemnt
• 2012 is celebrated as mathematical year
to mark his 125th year birth anniversary.