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Srinivasa Ramanujan
Srinivasa Ramanujan
Indian mathematician who was self-
taught and had an uncannymathematical manipulative ability
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Ramanujan
C
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Ramanujan
Born 22 December 1887 Erode,
Died April 1920 Chetput,
Residence Kumbakonam ,
Tamil Nadu
Fields Mathematics
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Family
Father
K. Srinivasa Iyengar
Mother
Komalatammal
Spouse
S Janaki Ammal
The family home is nowa museum
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Known for
LandauRamanujan constant
Mock theta functions
Ramanujan conjecture
Ramanujan prime
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Known for
Ramanujan theta function
Rumanian's sum
RamanujanSoldner constant
RogersRamanujan identities
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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.
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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
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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
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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
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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
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HardyG. H. Hardy
recognized
Rumanian's
intrinsicmathematical
ability and
arranged for himto come to
Cambridge
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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.
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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.
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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.
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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
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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.
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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.
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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
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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.
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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