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Srinivasa Ramanujan

Srinivasa Ramanujan

Indian mathematician who was self-

taught and had an uncannymathematical manipulative ability



Ramanujan

C



Ramanujan

Born 22 December 1887 Erode,

Died April 1920 Chetput,

Residence Kumbakonam ,

Tamil Nadu

Fields Mathematics



Family

Father

K. Srinivasa Iyengar

Mother

Komalatammal

Spouse

S Janaki Ammal

The family home is nowa museum



Known for

LandauRamanujan constant

Mock theta functions

Ramanujan conjecture

Ramanujan prime



Known for

Ramanujan theta function

Rumanian's sum

RamanujanSoldner constant

RogersRamanujan identities



Early hood

He lent a book on advanced trigonometry

written by S. L. Loney. He completely

mastered this book by the age of 13 and

discovered sophisticated theorems on his

own.

By 14, he was receiving merit certificates and

academic awards and showed a familiaritywith infinite series.



When he was 16, Ramanujan came across the

book A Synopsis of Elementary Results in Pure and Applied Mathematics by George S. Carr. This book

was a collection of 5000 theorems, and it

introduced Ramanujan to the world of mathematics.

By 17 he had independently developed and

investigated theBernoulli numbers and had

calculated Euler's constant up to 15 decimalplaces



he was awarded the K. Ranganatha Rao prize

for mathematics by the school's headmaster,

Krishnaswami Iyer. Iyer introduced Ramanujan

as an outstanding student who deserved

scores higher than the maximum possible

marks.

He received a scholarship to study atGovernment College in Kumbakonam



Ramanujan was so intent on studying

mathematics that he could not focus on any

other subjects and failed most of them, losinghis scholarship in the process .

In August 1905he ran away from home,

heading towards Visakhapatnam. He laterenrolled at Pachaiyappa's College in Madras.

He again excelled in mathematics but

performed poorly in other subjects such as

physiology and failed in fine arts



Ramanujan had an intimate familiarity with

numbers, and excelled especially in number

theory and modular function theory.

He sent letters to three mathematicians in England

containing some of his results. While two of the threereturned the letters unopened



HardyG. H. Hardy

recognized

Rumanian's

intrinsicmathematical

ability and

arranged for himto come to

Cambridge



In Cambridge University

Because of his lack of formal training,Ramanujan sometimes did not differentiatebetween formal proof and apparent truth

based on intuitive or numerical evidence. Although his intuition and computationalability allowed him to determine and statehighly original and unconventional results

which continued to defy formal proof untilrecently (Berndt 1985-1997), Ramanujan didoccasionally state incorrect results.



Mathematical achievements

Ramanujan's talent suggested a plethora of formulae that could then be investigated indepth later. It is said that Ramanujan's

discoveries are unusually rich and that there isoften more in it than what initially meets theeye. As a by-product, new directions of research were opened up

One of his remarkable capabilities was therapid solution for problems.



Ramanujan's series for converges extraordinarily

rapidly (exponentially) and forms the basis of someof the fastest algorithms currently used to calculate.

He discovered mock theta functions in the last yearof his life. For many years these functions were a

mystery .

In 1918, Hardy and Ramanujan studied the partitionfunction P(n) extensively and gave a non-convergentasymptotic series that permits exact computation of

the number of partitions of an integer.



1729=13+123=93+103

During an illness in England, Hardy visitedRamanujan in the hospital. When Hardy remarked that he had taken taxi

number 1729, a singularly unexceptional number,Ramanujan immediately responded that thisnumber was actually quite remarkable that

It is the smallest integer that can be

represented in two ways by the sum of two cubes



Unfortunately, Ramanujan's health

deteriorated rapidly in England, due perhaps

to the unfamiliar climate, food, and to the

isolation which Ramanujan felt as the sole

Indian in a culture which was largely foreign to

him. Ramanujan was sent home to recuperate

in 1919, but tragically died the next year atthe very young age of 32.



Recognition

A stamp picturing

Ramanujan was

released by

the Government of India in 1962 the

75thanniversary of

Ramanujan's birth

commemorating hisachievements in the

field of number theory.



Recognition

Every year on Ramanujan's birth day IndianInstitute of Technology-Madras,Chennai (IITMadras) pays tribute to Ramanujan by

conducting a National Symposium OnMathematicalMethods and Applications(NSMMA)

SASTRA Ramanujan Prize of $10,000 to begiven annually to a mathematician notexceeding the age of 32



Selected publications by Ramanujan

Srinivasa Ramanujan, G. H. Hardy, P. V. Seshu

Aiyar, B. M. Wilson, Bruce C. Berndt

(2000). Collected Papers of Srinivasa Ramanujan.

This book was originally published in 1927 after

Ramanujan's death. It contains the 37 papers

published in professional journals by Ramanujanduring his lifetime. The third re-print contains

additional commentary by Bruce C. Berndt.



S. Ramanujan (1957). Notebooks (2 Volumes). Bombay: Tata Institute of FundamentalResearch.

These books contain photo copies of the

original notebooks as written by Ramanujan. S. Ramanujan (1988). The Lost Notebook and

Other Unpublished Papers. New Delhi Narosa.

This book contains photo copies of the pages of the "Lost Notebook".

Problems posed by Ramanujan, Journal of theIndian Mathematical Society

Documents

srinivasa ramanujan 2