maths

1. S Ramanujan

2. Ramanujan House Kumbakonam

3. S Ramanujan
Srinivasa Ramanujan Aiyangar,
December 22, 1887: born in Erode, India
April 26, 1920: died in Kumbakonam
In 1900 he began to work on his own on mathematics
Summing geometric and arithmetic series.
A great Indian mathematician who made substantial
contributions to mathematical analysis, number theory, infinite
series, and continued fractions, including solutions to
mathematical problems then considered unsolvable even
though he had almost no formal training in pure mathematics.

4. Early age brilliance
• By the age of11years, he had exhausted the mathematical
knowledgeof two college studentswho were lodgers at his home.
He was later lent a book written by S. L. Loney on advanced
trigonometry.He mastered this by the age of 13 while discovering
sophisticated theorems on his own.
• By 14, he received merit certificates and academic awards that
continued throughout his school career, and he assisted the school
in the logistics of assigning its 1,200 students(each with differing
needs) to its approximately 35 teachers.He completed
mathematical exams in half the allottedtime, and showed a
familiarity with geometry and infinite series.
• Ramanujan was shown how to solve cubic equationsin 1902. He
wouldlater develop his own method to solve the quartic.
• In 1903, he tried to solvethe quintic, not knowing that it
was impossible to solve with radicals.

5. • In 1903 (December) and 1905: Fails the university exam
• 1904: he begun to undertake deep research, he investigated
series 1/n as n is from 1 to infinity.
• 1911: first mathematical paper.
• Journal of Indian Mathematical Society (1912) - published
problems solved by Ramanujan

6. Letter of Ramanujan to Hardy
(January 16, 1913)
I have had no university education but I have undergone the
ordinary school course. After leaving school I have been
employing the spare time at my disposal to work at
mathematics. I have not trodden through the conventional
regular course which is followed in a university course, but I
am striking out a new path for myself. I have made a special
investigation of divergent series in general and the results I
get are termed by the local mathematicians as “startling”. He
attached his workings with this letter.

7. Godfrey Harold Hardy (1877 –
1947)

8. Answer from Hardy
(February 8, 1913)
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. Your results seem to me to fall
into roughly three classes:
(1) there are a number of results that are already known,
or easily deducible from known theorems;
(2) there are results which, so far as I know, are new and
interesting, but interesting rather from their curiosity and
apparent difficulty than their importance;
(3) there are results which appear to be new and

9. Thank You