This document discusses the life and work of mathematician Srinivasa Ramanujan. It notes that he made significant contributions to number theory, infinite series, and continued fractions despite having no formal training. Some of his accomplishments included formulating the Ramanujan prime and summation, discovering identities and equations in partitions and mock theta functions, and developing Ramanujan-Sato series. The document also describes how he was mentored by G.H. Hardy and elected to prestigious mathematical societies before his untimely death at age 32.

1. Annabel Catherine Juliana J.
Stella Matutina College of Education
History of Ramanujan
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2.  Quotes
 Introduction
 Honors
 Ramanujan Prime
 Number Theory
Magic Square
Partition
 Taxicab Number
 Ramanujan Summation
 Nested and De-Nested
 Ramanujan Sato Series
 Conclusion
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8.  Srinivasa Ramanujan Iyenger was an Indian Mathematics.
 One of the most talented mathematicians in recent
history.
 Had no formal training in mathematics.
 Made a large contribution to
1 Number Theory
2 Infinite Series
3 Continued Fractions.
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9.  Srinivasa Ramanujan was mentored by G.H.Hardy
in the early 1910’s.After getting his degree
at cambridge, Ramanujan did his own work.
 He compiled over 3500 identities and
equations in his life. Some of the identities
were found in his “Lost Notebooks.”
 His formulas are now being used in
Crystallography and String Theory.
 In 2011, Ramanujan’s birthday was
made an annual“National Mathematics Day”
by Prime Minister Dr.Manmohan Singh.
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10.  In March 1916, Graduated Bachelor of Science degree by research.
(later called PhD)
 In1917, Elected to London Mathematics Society.
 In 1918, become a Fellow of the Royal society.
 Again in 1918, Fellow of Trinity College, Cambridge.
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11.  Ramanjuan prime is a prime number that satisfies a result
proven by Srinivasa Ramanujan relating to the prime-
counting function.
 In 1919,Ramanujan published a new proof of Bertrand’s
postulate which as he notes, was first proved by chebyshen.
 Ramanujan primes are the least integers Rn for which there
are at least n primes between x and x/2.
 The first prime of Ramanujan are 2,11,17,29,41.
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13. MAGIC SQUARE
 Ramanujan created a super magic square.
 The top row is his birthdate (December 22,1887).
 This is not the super magic squares because not only
do the rows ,columns and diagonals add up to the
same number, but the four corners, the four middle
squares(17,9,24,89),the first and last rows two
middle numbers(12,18,86,23) and the first and last
columns two middle numbers(88,10,25,16) all add up
to the sum of 139.
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15. The magic squares form the nucleus of the theory
of partitions developed by Srinivasa Ramanujan.
 His fascination for magic squares led him in his later
life to work on this theory.
 Let p(n) denote the partition function n.
For example,
1 has the partition 1;
2 has the partition 2, 1+1;
3 has the partition 3,2+1,1+1+1. and so on….
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16. For example,
6 has the partition 6,
5+1,4+2,4+1+1,3+3,3+2+1,3+1+1+1,2+2+2,
2+2+1+1,2+1+1+1+1,1+1+1+1+1+1.
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18. A Taxi Cab Number is the smallest number that can be
expressed as the sum of 2 positive cubes in ‘n’ distinct
way.
 It has nothing to do with TAXIS, but the name comes
from a well-known conversation
that took place between 2
famous mathematician
G.H.Hardy
Srinivasa Ramanujan
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19.  One day G.H.Hardy went to visit a friend,
the brilliant young Indian Mathematician
Srinivasa Ramanujan, who was ill. Both men
were mathematics and liked to think about
numbers.
 When Ramanujan heard that Hardy had come
in a taxi he asked what the number of the taxi was.
 Hardy said that it was a boring number 1729.
Ramanujan explained that it was the
“(Smallest Number that could be expressed
by the sum of 2 cubes in 2 different ways).”
 1729 is called “Hardy-Ramanujan Numbers
or Taxi Number.
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20.  Ramanujan Summation is a
technique invented by the
mathematician Srinivasa
Ramanujan for assigning
a value to divergent
infinite series.
 It states that if you add
all the natural numbers
that is 1,2,3,4, and
so on to infinity you will
find that is equal to -1/12.
(i.e)
1+2+3+4+----+infinity= -1/12.
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22.  Rewriting a nested radical in this way is
called denesting.
 This is not always possible and even when
possible, it is often difficult.
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23.  A Ramanujan – Sato Series generalizes
Ramanujan’s pi formulas such as
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24.  He discovered mock theta function in the last year
of his life. For many years these functions were a
mystery, but they are now known to be the
holomorphic parts of harmonic weak mass forms.
 Of ramanujan’s published papers -37 in total –
professor Bruce C. Berndt reveals that “ a huge
portions of his work was left behind in three
notebooks and a lost notebook”.
 Srinivasa Ramanujan was died on 26 April 1920.(at
aged 32)
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25. THANK YOU
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