Great mathematician

Great mathematician

2. Index
•Aryabhatta
•Srinivasa Ramanujam
•Bhaskaracharya
•Shakuntala Devi
•Brahmagupta
•Narayana Pandit

3. Aryabhatta
Aryabhatta came to this world on the 476 A.D at Patliputra Aryabhatta came to this world on the 476 A.D at Patliputra
in Magadha which is known as the modern Patna in Bihar. in Magadha which is known as the modern Patna in Bihar.
Some people were saying that he was born in the South of Some people were saying that he was born in the South of
India mostly Kerala. But it cannot be disproved that he was India mostly Kerala. But it cannot be disproved that he was
not born in Patlipura and then travelled to Magadha where he not born in Patlipura and then travelled to Magadha where he
was educated and established a coaching centre. His first name was educated and established a coaching centre. His first name
is “Arya” which is a South Indian name and “Bhatt” or is “Arya” which is a South Indian name and “Bhatt” or
“Bhatta” a normal north Indian name which could be seen “Bhatta” a normal north Indian name which could be seen
among the trader people in India.among the trader people in India.
No matter where he could be originated from, people cannot No matter where he could be originated from, people cannot
dispute that he resided in Patliputra because he wrote one of dispute that he resided in Patliputra because he wrote one of
his popular “Aryabhatta-siddhanta” but “Aryabhatiya” was his popular “Aryabhatta-siddhanta” but “Aryabhatiya” was
much more popular than the former. much more popular than the former.
Aryabhatta do for his survival. His writing consists of Aryabhatta do for his survival. His writing consists of
mathematical theory and astronomical theory which was viewed mathematical theory and astronomical theory which was viewed
to be perfect in modern mathematics. For example, it was to be perfect in modern mathematics. For example, it was
written in his theory that when you add 4 to 100 and multiply written in his theory that when you add 4 to 100 and multiply
the result with 8, then add the answer to 62,000 and divide it the result with 8, then add the answer to 62,000 and divide it
by 20000, the result will be the same thing as the circumference by 20000, the result will be the same thing as the circumference
with diameter twenty thousand. The calculation of 3.1416 is with diameter twenty thousand. The calculation of 3.1416 is
nearly the same with the true value of Pi which is 3.14159. nearly the same with the true value of Pi which is 3.14159.
Aryabhatta’s strongest contribution was zero. Another aspect of Aryabhatta’s strongest contribution was zero. Another aspect of
mathematics that he worked upon is arithmetic, algebra, mathematics that he worked upon is arithmetic, algebra,
quadratic equations, trigonometry and sine table. quadratic equations, trigonometry and sine table.

4. Aryabhatta was aware that the earth rotates on its axis. The earth Aryabhatta was aware that the earth rotates on its axis. The earth
rotates round the sun and the moon moves round the earth. He rotates round the sun and the moon moves round the earth. He
discovered the 9 planets position and related them to their rotation discovered the 9 planets position and related them to their rotation
round the sun. Aryabhatta said the light received from planets and round the sun. Aryabhatta said the light received from planets and
the moon is gotten from sun. He also made mention on the eclipse the moon is gotten from sun. He also made mention on the eclipse
of the sun, moon, day and night, earth contours and the 365 days of the sun, moon, day and night, earth contours and the 365 days
of the year as the exact length of the year. Aryabhatta also of the year as the exact length of the year. Aryabhatta also
revealed that the earth circumference is 24835 miles when revealed that the earth circumference is 24835 miles when
compared to the modern day calculation which is 24900 miles.compared to the modern day calculation which is 24900 miles.
Aryabhatta have unusually great intelligence and well skilled in Aryabhatta have unusually great intelligence and well skilled in
the sense that all his theories has became wonders to some the sense that all his theories has became wonders to some
mathematicians of the present age. The Greeks and the Arabs mathematicians of the present age. The Greeks and the Arabs
developed some of his works to suit their present demands. developed some of his works to suit their present demands.
Aryabhatta was the first inventor of the earth sphericity and also Aryabhatta was the first inventor of the earth sphericity and also
discovered that earth rotates round the sun. He was the one that discovered that earth rotates round the sun. He was the one that
created the formula (a + b)2 = a2 + b2 + 2abcreated the formula (a + b)2 = a2 + b2 + 2ab

5. Srinivasa Ramanujam
•Ramanujam was born on Ramanujam was born on
December 27, 1887, in December 27, 1887, in
Erode.Erode.
•He was a very great and He was a very great and
famous mathematician.famous mathematician.
•He made contributions He made contributions
to the analytical theory to the analytical theory
of numbers.of numbers.
•His father worked in His father worked in
Kumbakonam as a clerk Kumbakonam as a clerk
in a cloth merchant's in a cloth merchant's
shop. shop.
•When he was nearly five When he was nearly five
years old, Ramanujayears old, Ramanujamm
entered the primary entered the primary
schoolschool..

6. •Ramanujan was Ramanujan was
appointed to the post appointed to the post
of clerk and began of clerk and began
his duties on 1 his duties on 1
March 1912.March 1912.
•Ramanujan was Ramanujan was
quite lucky to have a quite lucky to have a
number of people number of people
working round him working round him
with training in with training in
mathematics.mathematics.
•He died on 26He died on 26
thth
April April
1920 in 1920 in
Kumbakonam.Kumbakonam.
•Ramanujan continued Ramanujan continued
to develop his to develop his
mathematical ideas mathematical ideas
and began to pose and began to pose
problems and solve problems and solve
problems in the problems in the
Journal of the Indian Journal of the Indian
Mathematical Society.Mathematical Society.
•He developed relations He developed relations
between elliptic between elliptic
modular equations in modular equations in
1910.1910.
•In 1912 Ramanujan In 1912 Ramanujan
applied for the post of applied for the post of
clerk in the accounts clerk in the accounts
section of the Madras section of the Madras
Port Trust.Port Trust.

7. Bhaskaracharya
•Bhaskaracharya otherwise known as Bhaskara is probably Bhaskaracharya otherwise known as Bhaskara is probably
the most well known mathematician of ancient Indian the most well known mathematician of ancient Indian
today. Bhaskara was born in 1114 A.D. according to a today. Bhaskara was born in 1114 A.D. according to a
statement he recorded in one of his own works. He was statement he recorded in one of his own works. He was
from Bijjada Bida near the Sahyadri mountains. Bijjada from Bijjada Bida near the Sahyadri mountains. Bijjada
Bida is thought to be present day Bijapur in Mysore Bida is thought to be present day Bijapur in Mysore
state. Bhaskara wrote his famous Siddhanta Siroman in state. Bhaskara wrote his famous Siddhanta Siroman in
the year 1150 A.D. It is divided into four parts; Lilavati the year 1150 A.D. It is divided into four parts; Lilavati
(arithmetic), Bijaganita (algebra), Goladhyaya (celestial (arithmetic), Bijaganita (algebra), Goladhyaya (celestial
globe), and Grahaganita (mathematics of the planets). globe), and Grahaganita (mathematics of the planets).
Much of Bhaskara's work in the Lilavati and Bijaganita Much of Bhaskara's work in the Lilavati and Bijaganita
was derived from earlier mathematicians; hence it is not was derived from earlier mathematicians; hence it is not
surprising that Bhaskara is best in dealing with surprising that Bhaskara is best in dealing with
indeterminate analysis. In connection with the Pell indeterminate analysis. In connection with the Pell
equation, x^2=1+61y^2, nearly solved by Brahmagupta, equation, x^2=1+61y^2, nearly solved by Brahmagupta,
Bhaskara gave a method (Chakravala process) for solving Bhaskara gave a method (Chakravala process) for solving
the equation.the equation.
•O girl! out of a group of swans, 7/2 times the square root O girl! out of a group of swans, 7/2 times the square root
of the number are playing on the shore of a tank. The two of the number are playing on the shore of a tank. The two
remaining ones are playing with amorous fight, in the remaining ones are playing with amorous fight, in the
water. What is the total number of swans?water. What is the total number of swans?
•Teaching and learning mathematics was in Bhaskara's Teaching and learning mathematics was in Bhaskara's
blood. He learnt mathematics from his father, a blood. He learnt mathematics from his father, a
mathematician, and he himself passed his knowledge to mathematician, and he himself passed his knowledge to
his son Loksamudra. To return to the timeline click here: his son Loksamudra. To return to the timeline click here:
timeline.timeline.

8. •A very great mathematician and an A very great mathematician and an
astronomer of the Kaliyuga's 43rd century astronomer of the Kaliyuga's 43rd century
( i.e. 12th century A.D ) Bhaskaracharya ( i.e. 12th century A.D ) Bhaskaracharya
was the head of the observatory at Ujjain. was the head of the observatory at Ujjain.
There are two famous works of his on There are two famous works of his on
Mathematical Astronomy - Siddhanta-Mathematical Astronomy - Siddhanta-
Siromani and Karana-Kutuhala. Besides his Siromani and Karana-Kutuhala. Besides his
work on Algebra, Lilavati Bija Ganita too work on Algebra, Lilavati Bija Ganita too
is famous. The law of Gravitation, in clear is famous. The law of Gravitation, in clear
tems, had been propounded by tems, had been propounded by
Bhaskaracharya 500 years before it was Bhaskaracharya 500 years before it was
rediscovered by Newton. Centuries before rediscovered by Newton. Centuries before
him there had been another mathematician him there had been another mathematician
Bhaskaracharya also in Bharat ( India ).Bhaskaracharya also in Bharat ( India ).
•The subjects of his six works include The subjects of his six works include
arithmetic, algebra, trigonometry, calculus, arithmetic, algebra, trigonometry, calculus,
geometry, astronomy. There is a seventh geometry, astronomy. There is a seventh
book attributed to him which is thought to book attributed to him which is thought to
be a forgery. Bhaskaracharya discovered the be a forgery. Bhaskaracharya discovered the
concept of differentials, and contributed a concept of differentials, and contributed a
greater understanding of number systems greater understanding of number systems
and advanced methods of equation solving. and advanced methods of equation solving.
He was able to accurately calculate the He was able to accurately calculate the
sidreal year, or the time it takes for the sidreal year, or the time it takes for the
earth to orbit the sun. There is but a scant earth to orbit the sun. There is but a scant
difference in his figure of 365.2588 days difference in his figure of 365.2588 days
and the modern figure of 365.2596 days.and the modern figure of 365.2596 days.

9. Shakuntala Devi
•Shakuntala Devi is a calculating prodigy who was born on Shakuntala Devi is a calculating prodigy who was born on
November 4, 1939 in Bangalore, India. Her father worked in a November 4, 1939 in Bangalore, India. Her father worked in a
\"Brahmin circus\" as a trapeze and tightrope performer, and \"Brahmin circus\" as a trapeze and tightrope performer, and
later as a lion tamer and a human cannonball. Her calculating later as a lion tamer and a human cannonball. Her calculating
gifts first demonstrated themselves while she was doing card gifts first demonstrated themselves while she was doing card
tricks with her father when she was three. They report tricks with her father when she was three. They report
she \"beat\" them by memorization of cards rather than by she \"beat\" them by memorization of cards rather than by
sleight of hand. By age six she demonstrated her calculation sleight of hand. By age six she demonstrated her calculation
and memorization abilities at the University of Mysore. At and memorization abilities at the University of Mysore. At
the age of eight she had success at Annamalai University by the age of eight she had success at Annamalai University by
doing the same. Unlike many other calculating prodigies, for doing the same. Unlike many other calculating prodigies, for
example Truman Henry Safford, her abilities did not wane in example Truman Henry Safford, her abilities did not wane in
adulthood. In 1977 she extracted the 23rd root of a 201-digit adulthood. In 1977 she extracted the 23rd root of a 201-digit
number mentally. On June 18, 1980 she demonstrated the number mentally. On June 18, 1980 she demonstrated the
multiplication of two 13-digit numbers 7,686,369,774,870 x multiplication of two 13-digit numbers 7,686,369,774,870 x
2,465,099,745,779 picked at random by the Computer 2,465,099,745,779 picked at random by the Computer
Department of Imperial College, London. She answered the Department of Imperial College, London. She answered the
question in 28 seconds. However, this time is more likely the question in 28 seconds. However, this time is more likely the
time for dictating the answer (a 26-digit number) than the time for dictating the answer (a 26-digit number) than the
time for the mental calculation (the time of 28 seconds was time for the mental calculation (the time of 28 seconds was
quoted on her own website). Her correct answer was quoted on her own website). Her correct answer was
18,947,668,177,995,426,462,773,730. 18,947,668,177,995,426,462,773,730.

10. •This event is mentioned on page 26 of the This event is mentioned on page 26 of the
1995 Guinness Book of Records ISBN 1995 Guinness Book of Records ISBN
0-553-56942-2. In 1977, she published the 0-553-56942-2. In 1977, she published the
first study of homosexuality in first study of homosexuality in
India.According to Subhash Chandra's review India.According to Subhash Chandra's review
of Ana Garcia-Arroyo's book The Construction of Ana Garcia-Arroyo's book The Construction
of Queer Culture in India: Pioneers and of Queer Culture in India: Pioneers and
Landmarks,For Garcia-Arroyo the beginning Landmarks,For Garcia-Arroyo the beginning
of the debate on homosexuality in the of the debate on homosexuality in the
twentieth century is made with Shakuntala twentieth century is made with Shakuntala
Devi's book The World of Homosexuals Devi's book The World of Homosexuals
published in 1977. [...] Shakuntala Devi's (the published in 1977. [...] Shakuntala Devi's (the
famous mathematician) book appeared. This famous mathematician) book appeared. This
book went almost unnoticed, and did not book went almost unnoticed, and did not
contribute to queer discourse or movement. contribute to queer discourse or movement.
[...] The reason for this book not making its [...] The reason for this book not making its
mark was becauseShakuntala Devi was famous mark was becauseShakuntala Devi was famous
for her mathematical wizardry and nothing of for her mathematical wizardry and nothing of
substantial import in the field of substantial import in the field of
homosexuality was expected from her. Another homosexuality was expected from her. Another
factor for the indifference meted out to the factor for the indifference meted out to the
book could perhaps be a calculated silence book could perhaps be a calculated silence
because the cultural situation in India was because the cultural situation in India was
inhospitable for an open and elaborate inhospitable for an open and elaborate
discussion on this issue. In 2006 she has discussion on this issue. In 2006 she has
released a new book called In the Wonderland released a new book called In the Wonderland
of Numbers with Orient Paperbacks which of Numbers with Orient Paperbacks which
talks about a girl Neha and her fascination talks about a girl Neha and her fascination
for numbers. for numbers.

11. Brahmagupta
•Brahmagupta, whose father was Jisnugupta, wrote Brahmagupta, whose father was Jisnugupta, wrote
important works on mathematics and astronomy. In important works on mathematics and astronomy. In
particular he wrote particular he wrote BrahmasphutasiddhantaBrahmasphutasiddhanta (The  (The
Opening of the Universe), in 628. The work was written Opening of the Universe), in 628. The work was written
in 25 chapters and Brahmagupta tells us in the text that in 25 chapters and Brahmagupta tells us in the text that
he wrote it at Bhillamala which today is the city of he wrote it at Bhillamala which today is the city of
Bhinmal. This was the capital of the lands ruled by the Bhinmal. This was the capital of the lands ruled by the
Gurjara dynasty.Gurjara dynasty.
•Brahmagupta became the head of the astronomical Brahmagupta became the head of the astronomical
observatory at Ujjain which was the foremost observatory at Ujjain which was the foremost
mathematical centre of ancient India at this time. mathematical centre of ancient India at this time.
Outstanding mathematicians such as Outstanding mathematicians such as VarahamihiraVarahamihira had  had
worked there and built up a strong school of worked there and built up a strong school of
mathematical astronomy.mathematical astronomy.
•In addition to In addition to
the the BrahmasphutasiddhantaBrahmasphutasiddhanta Brahmagupta wrote a  Brahmagupta wrote a
second work on mathematics and astronomy which is second work on mathematics and astronomy which is
the the KhandakhadyakaKhandakhadyaka written in 665 when he was 67  written in 665 when he was 67
years old. We look below at some of the remarkable ideas years old. We look below at some of the remarkable ideas
which Brahmagupta's two treatises contain. First let us which Brahmagupta's two treatises contain. First let us
give an overview of their contents.give an overview of their contents.

12. •The The BrahmasphutasiddhantaBrahmasphutasiddhanta contains  contains
twenty-five chapters but the first ten of twenty-five chapters but the first ten of
these chapters seem to form what many these chapters seem to form what many
historians believe was a first version of historians believe was a first version of
Brahmagupta's work and some Brahmagupta's work and some
manuscripts exist which contain only manuscripts exist which contain only
these chapters. These ten chapters are these chapters. These ten chapters are
arranged in topics which are typical of arranged in topics which are typical of
Indian mathematical astronomy texts of Indian mathematical astronomy texts of
the period. The topics covered are: mean the period. The topics covered are: mean
longitudes of the planets; true longitudes longitudes of the planets; true longitudes
of the planets; the three problems of of the planets; the three problems of
diurnal rotation; lunar eclipses; solar diurnal rotation; lunar eclipses; solar
eclipses; risings and settings; the moon's eclipses; risings and settings; the moon's
crescent; the moon's crescent; the moon's
shadow; conjunctions of the planets with shadow; conjunctions of the planets with
each other; and conjunctions of the each other; and conjunctions of the
planets with the fixed stars.planets with the fixed stars.
•The remaining fifteen chapters seem to The remaining fifteen chapters seem to
form a second work which is major form a second work which is major
addendum to the original treatise. The addendum to the original treatise. The
chapters are: examination of previous chapters are: examination of previous
treatises on astronomy; on mathematics; treatises on astronomy; on mathematics;
additions to chapter 1; additions to additions to chapter 1; additions to
chapter 2; additions to chapter 3; chapter 2; additions to chapter 3;
additions to chapter 4 and 5; additions to additions to chapter 4 and 5; additions to
chapter 7; on algebra; on the gnomon; on chapter 7; on algebra; on the gnomon; on
meters; on the sphere; on instruments; meters; on the sphere; on instruments;
summary of contents; versified tablessummary of contents; versified tables

13. Narayana Pandit
•Narayana was the son of Nrsimha (sometimes written Narasimha). We Narayana was the son of Nrsimha (sometimes written Narasimha). We
know that he wrote his most famous work know that he wrote his most famous work Ganita KaumudiGanita Kaumudi on  on
arithmetic in 1356 but little else is known of him. His mathematical arithmetic in 1356 but little else is known of him. His mathematical
writings show that he was strongly influenced by writings show that he was strongly influenced by Bhaskara IIBhaskara II and he  and he
wrote a commentary on the wrote a commentary on the LilavatiLilavati of  of Bhaskara IIBhaskara II
called called Karmapradipika.Karmapradipika. Some historians dispute that Narayana is the  Some historians dispute that Narayana is the
author of this commentary which they attribute to author of this commentary which they attribute to MadhavaMadhava..
•In the In the Ganita KaumudiGanita Kaumudi Narayana considers the mathematical  Narayana considers the mathematical
operation on numbers. Like many other Indian writers of arithmetics operation on numbers. Like many other Indian writers of arithmetics
before him he considered an algorithm for multiplying numbers and he before him he considered an algorithm for multiplying numbers and he
then looked at the special case of squaring numbers. One of the unusual then looked at the special case of squaring numbers. One of the unusual
features of Narayana's work features of Narayana's work KarmapradipikaKarmapradipika is that he gave seven  is that he gave seven
methods of squaring numbers which are not found in the work of other methods of squaring numbers which are not found in the work of other
Indian mathematicians.Indian mathematicians.
•He discussed another standard topic for Indian mathematicians namely He discussed another standard topic for Indian mathematicians namely
that of finding triangles whose sides had integral values. In particular that of finding triangles whose sides had integral values. In particular
he gave a rule of finding integral triangles whose sides differ by one he gave a rule of finding integral triangles whose sides differ by one
unit of length and which contain a pair of right-angled triangles having unit of length and which contain a pair of right-angled triangles having
integral sides with a common integral height. In terms of geometry integral sides with a common integral height. In terms of geometry
Narayana gave a rule for a segment of a circle. NarayanaNarayana gave a rule for a segment of a circle. Narayana

14. •Narayana also gave a rule to Narayana also gave a rule to
calculate approximate values of a calculate approximate values of a
square root. He did this by using an square root. He did this by using an
indeterminate equation of the second indeterminate equation of the second
order, order, NxNx2 + 1 = 2 + 1 = yy2, where2, whereNN is the  is the
number whose square root is to be number whose square root is to be
calculated. If calculated. If xx and  and yy are a pair of  are a pair of
roots of this equation roots of this equation
with with xx <  < yy then √ then √NN is approximately  is approximately
equal to equal to yy//xx. To illustrate this . To illustrate this
method Narayana takes method Narayana takes NN = 10. He  = 10. He
then finds the solutions then finds the solutions xx = 6,  = 6, yy = 19  = 19
which give the approximation 19/6 = which give the approximation 19/6 =
3.1666666666666666667, which is 3.1666666666666666667, which is
correct to 2 decimal places. Narayana correct to 2 decimal places. Narayana
then gives the solutions then gives the solutions xx = 228,  = 228, yy =  =
721 which give the approximation 721 which give the approximation
721/228 = 3.1622807017543859649, 721/228 = 3.1622807017543859649,
correct to four places. Finally correct to four places. Finally
Narayana gives the pair of Narayana gives the pair of
solutions solutions xx = 8658,  = 8658, yy = 227379  = 227379
which give the approximation which give the approximation
227379/8658 = 227379/8658 =
3.1622776622776622777, correct to 3.1622776622776622777, correct to
eight decimal places. Note for eight decimal places. Note for
comparison that √10 is, correct to 20 comparison that √10 is, correct to 20
places, 3.1622776601683793320 places, 3.1622776601683793320