Who Was The Pioneer Of The Kerala School Of Mathematics?


Who Was The Pioneer Of The Kerala School Of Mathematics
Mādhava of Sangamagrāma Mādhava of Sangamagrāma (Mādhavan) (c.1340 – c.1425) was an Indian mathematician and astronomer who is considered as the founder of the Kerala school of astronomy and mathematics.
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Who established Kerala School of Mathematics?

From Wikipedia, the free encyclopedia

Kerala school of astronomy and mathematics
Chain of teachers of the Kerala school
Central and Northern Kerala, India
Type Astronomy, Mathematics, Science
Founder Madhava of Sangamagrama

The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar,

The school flourished between the 14th and 16th centuries and its original discoveries seem to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship.

The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa ( c. 1530 ), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha,
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Who is the father of Kerala mathematics?

Madhava – Biography Born 1350 Died 1425 India Summary Madhava was a mathematician from South India. He made some important advances in infinite series including finding the expansions for trigonometric functions. Madhava of Sangamagramma was born near Cochin on the coast in the Kerala state in southwestern India.

It is only due to research into Keralese mathematics over the last twenty-five years that the remarkable contributions of Madhava have come to light. In Rajagopal and Rangachari put his achievement into context when they write:- took the decisive step onwards from the finite procedures of ancient mathematics to treat their limit-passage to infinity, which is the kernel of modern classical analysis.

All the mathematical writings of Madhava have been lost, although some of his texts on astronomy have survived. However his brilliant work in mathematics has been largely discovered by the reports of other Keralese mathematicians such as who lived about 100 years later.

  1. Madhava discovered the series equivalent to the expansions of sin x x x, cos x x x, and arctan x x x around 1400, which is over two hundred years before they were rediscovered in Europe.
  2. Details appear in a number of works written by his followers such as Mahajyanayana prakara which means Method of computing the great sines,

In fact this work had been claimed by some historians such as Sarma ( see for example ) to be by Madhava himself but this seems highly unlikely and it is now accepted by most historians to be a 16 th century work by a follower of Madhava. This is discussed in detail in,

  • Wrote Yukti-Bhasa in Malayalam, the regional language of Kerala, around 1550,
  • In Gupta gives a translation of the text and this is also given in and a number of other sources.
  • Describes Madhava’s series as follows:- The first term is the product of the given sine and radius of the desired arc divided by the cosine of the arc.

The succeeding terms are obtained by a process of iteration when the first term is repeatedly multiplied by the square of the sine and divided by the square of the cosine. All the terms are then divided by the odd numbers 1, 3, 5,, The arc is obtained by adding and subtracting respectively the terms of odd rank and those of even rank.

It is laid down that the sine of the arc or that of its complement whichever is the smaller should be taken here as the given sine. Otherwise the terms obtained by this above iteration will not tend to the vanishing magnitude. This is a remarkable passage describing Madhava’s series, but remember that even this passage by was written more than 100 years before rediscovered this series expansion.

Perhaps we should write down in modern symbols exactly what the series is that Madhava has found. The first thing to note is that the Indian meaning for sine of θ would be written in our notation as r sin ⁡ θ r \sin \theta r sin θ and the Indian cosine of would be r cos ⁡ θ r \cos \theta r cos θ in our notation, where r r r is the radius.

  • Thus the series is r θ = r r sin ⁡ θ r cos ⁡ θ − r r sin ⁡ θ ) 3 3 r ( r cos ⁡ θ ) 3 + r r sin ⁡ θ ) 5 5 r ( r cos ⁡ θ ) 5 − r r sin ⁡ θ ) 7 7 r ( r cos ⁡ θ ) 7 +,
  • R \theta = r\Large\frac \normalsize – r\Large\frac } }\normalsize + r\Large\frac } }\normalsize- r\Large\frac } }\normalsize +,
  • R θ = r r c o s θ r s i n θ ​ − r 3 r ( r c o s θ ) 3 r s i n θ ) 3 ​ + r 5 r ( r c o s θ ) 5 r s i n θ ) 5 ​ − r 7 r ( r c o s θ ) 7 r s i n θ ) 7 ​ +,

putting tan ⁡ = sin ⁡ cos ⁡ \tan = \Large \frac tan = c o s s i n ​ and cancelling r r r gives θ = tan ⁡ θ − 1 3 tan ⁡ 3 θ + 1 5 tan ⁡ 5 θ −, \theta = \tan \theta – \large\frac \normalsize \tan^ \theta + \large\frac \normalsize \tan^ \theta -, θ = tan θ − 3 1 ​ tan 3 θ + 5 1 ​ tan 5 θ −,

Which is equivalent to ‘s series tan ⁡ − 1 θ = θ − 1 3 θ 3 + 1 5 θ 5 −, \tan^ \theta = \theta – \large\frac \normalsize \theta^ + \large\frac \normalsize \theta^ -, tan − 1 θ = θ − 3 1 ​ θ 3 + 5 1 ​ θ 5 −, Now Madhava put q = π 4 q = \large\frac \normalsize q = 4 π ​ into his series to obtain π 4 = 1 − 1 3 + 1 5 −,

\large\frac \normalsize = 1 – \large\frac \normalsize + \large\frac \normalsize -,4 π ​ = 1 − 3 1 ​ + 5 1 ​ −, and he also put θ = π / 6 \theta = \pi/6 θ = π / 6 into his series to obtain π = 12 ( 1 − 1 3 × 3 + 1 5 × 3 2 − 1 7 × 3 3 +,,) \pi = \sqrt (1 – \large\frac \normalsize + \large\frac }\normalsize – \large\frac }\normalsize +,) π = 1 2 ​ ( 1 − 3 × 3 1 ​ + 5 × 3 2 1 ​ − 7 × 3 3 1 ​ +,

  • We know that Madhava obtained an approximation for π correct to 11 decimal places when he gave π = 3.14159265359 \pi = 3.14159265359 π = 3,1 4 1 5 9 2 6 5 3 5 9 which can be obtained from the last of Madhava’s series above by taking 21 terms.
  • In Gupta gives a translation of the Sanskrit text giving Madhava’s approximation of π correct to 11 places.

Perhaps even more impressive is the fact that Madhava gave a remainder term for his series which improved the approximation. He improved the approximation of the series for π 4 \large\frac \normalsize 4 π ​ by adding a correction term R n R_ R n ​ to obtain π 4 = 1 − 1 3 + 1 5 −,

.1 2 n − 1 ± R n \large\frac \normalsize = 1 – \large\frac \normalsize + \large\frac \normalsize -, \large\frac \normalsize ± R_ 4 π ​ = 1 − 3 1 ​ + 5 1 ​ −,,2 n − 1 1 ​ ± R n ​ Madhava gave three forms of R n R_ R n ​ which improved the approximation, namely R n = 1 4 n R_ = \large\frac R n ​ = 4 n 1 ​ or R n = n 4 n 2 + 1 R_ = \large\frac + 1} R n ​ = 4 n 2 + 1 n ​ or R n = n 2 + 1 4 n 3 + 5 n R_ = \large\frac + 1} + 5n} R n ​ = 4 n 3 + 5 n n 2 + 1 ​,

There has been a lot of work done in trying to reconstruct how Madhava might have found his correction terms. The most convincing is that they come as the first three convergents of a continued fraction which can itself be derived from the standard Indian approximation to π namely 62832 20000 \large\frac \normalsize 2 0 0 0 0 6 2 8 3 2 ​,

Madhava also gave a table of almost accurate values of half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle. It is thought that the way that he found these highly accurate tables was to use the equivalent of the series expansions sin ⁡ θ = θ − 1 3 ! θ 3 + 1 5 ! θ 5 −,

\sin \theta = \theta – \large\frac \normalsize \theta^ + \large\frac \normalsize \theta^ -, sin θ = θ − 3 ! 1 ​ θ 3 + 5 ! 1 ​ θ 5 −, cos ⁡ θ = 1 − 1 2 ! θ 2 + 1 4 ! θ 4 −, \cos \theta = 1 – \large\frac \normalsize \theta^ + \large\frac \normalsize \theta^ -,

Cos θ = 1 − 2 ! 1 ​ θ 2 + 4 ! 1 ​ θ 4 −, in Yukti-Bhasa gave an explanation of how Madhava found his series expansions around 1400 which are equivalent to these modern versions rediscovered by around 1676, Historians have claimed that the method used by Madhava amounts to term by term integration. Rajagopal’s claim that Madhava took the decisive step towards modern classical analysis seems very fair given his remarkable achievements.

In the same vein Joseph writes in :- We may consider Madhava to have been the founder of mathematical analysis. Some of his discoveries in this field show him to have possessed extraordinary intuition, making him almost the equal of the more recent intuitive genius, who spent his childhood and youth at Kumbakonam, not far from Madhava’s birthplace.

G G Joseph, The crest of the peacock ( London, 1991), K V Sarma, A History of the Kerala School of Hindu Astronomy ( Hoshiarpur, 1972), A K Bag, Madhava’s sine and cosine series, Indian J. History Sci.11 (1) (1976), 54 – 57, D Gold and D Pingree, A hitherto unknown Sanskrit work concerning Madhava’s derivation of the power series for sine and cosine, Historia Sci. No.42 (1991), 49 – 65, R C Gupta, Madhava’s and other medieval Indian values of pi, Math. Education 9 (3) (1975), B 45 -B 48, R C Gupta, Madhava’s power series computation of the sine, Ganita 27 (1 – 2) (1976), 19 – 24, R C Gupta, Madhava’s rule for finding angle between the ecliptic and the horizon and Aryabhata’s knowledge of it, in History of oriental astronomy, New Delhi, 1985 ( Cambridge, 1987), 197 – 202, R C Gupta, On the remainder term in the Madhava-Leibniz’s series, Ganita Bharati 14 (1 – 4) (1992), 68 – 71, R C Gupta, The Madhava-Gregory series, Math. Education 7 (1973), B 67 -B 70, T Hayashi, T Kusuba and M Yano, The correction of the Madhava series for the circumference of a circle, Centaurus 33 (2 – 3) (1990), 149 – 174, C T Rajagopal and M S Rangachari, On an untapped source of medieval Keralese mathematics, Arch. History Exact Sci.18 (1978), 89 – 102, C T Rajagopal and M S Rangachari, On medieval Keralese mathematics, Arch. History Exact Sci.35 (1986), 91 – 99,

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Other pages about Madhava: Written by J J O’Connor and E F Robertson Last Update November 2000 : Madhava – Biography
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Who was the greatest mathematician in Kerala?

Madhava of Sangamagrama (c.1350-1425)

Madhava sometimes called the greatest mathematician-astronomer of medieval India, He came from the town of Sangamagrama in Kerala, near the southern tip of India, and founded the Kerala School of Astronomy and Mathematics in the late 14th Century. Although almost all of Madhava’s original work is lost, he is referred to in the work of later Kerala mathematicians as the source for several infinite series expansions (including the sine, cosine, tangent and arctangent functions and the value of π ), representing the first steps from the traditional finite processes of algebra to considerations of the infinite, with its implications for the future development of calculus and mathematical analysis.
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What is the history of Kerala School of Mathematics?

Kerala School of Mathematics was founded with the vision of establishing a centre of excellence for research in Mathematics and to revive the glory of a school by a similar name which flourished between the fourteenth and sixteenth century in Kerala.
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Did Kerala invent calculus?

Science Researchers from the universities of Manchester and Exeter say a group of scholars and mathematicians in 14th century India identified one of the basic components of calculus. Researchers in England may have finally settled the centuries-old debate over who gets credit for the creation of calculus.

  • For years, English scientist Isaac Newton and German philosopher Gottfried Leibniz both claimed credit for inventing the mathematical system sometime around the end of the seventeenth century.
  • Now, a team from the universities of Manchester and Exeter says it knows where the true credit lies — and it’s with someone else completely.

The “Kerala school,” a little-known group of scholars and mathematicians in fourteenth century India, identified the “infinite series” — one of the basic components of calculus — around 1350. Dr. George Gheverghese Joseph, a member of the research team, says the findings should not diminish Newton or Leibniz, but rather exalt the non-European thinkers whose contributions are often ignored.

“The beginnings of modern maths is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten,” he said. “The brilliance of Newton’s work at the end of the seventeenth century stands undiminished — especially when it came to the algorithms of calculus.

“But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus — infinite series.” He argues that imperialist attitudes are to blame for suppressing the true story behind the discovery of calculus.

“There were many reasons why the contribution of the Kerala school has not been acknowledged,” he said. “A prime reason is neglect of scientific ideas emanating from the Non-European world, a legacy of European colonialism and beyond.” However, he concedes there are other factors also in play. “There is also little knowledge of the medieval form of the local language of Kerala, Malayalam, in which some of most seminal texts, such as the Yuktibhasa, from much of the documentation of this remarkable mathematics is written,” he admits.

Joseph made the discovery while conducting research for the as-yet unpublished third edition of his best-selling book The Crest of the Peacock: the Non-European Roots of Mathematics.
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Who is the father of mathematical school?

Archimedes is considered the father of mathematics because of his notable inventions in mathematics and science. He was in the service of King Hiero II of Syracuse.
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Who invented mathematics first in India?

Famous Indian Mathematicians and their Contributions – 1. Bhaskara

He is also known as Bhaskaracharya. He was born in 1114. He was the one who acknowledged that any number divided by zero is infinity and that the sum of any number and infinity is also infinity. The famous book “Siddhanta Siromani” was written by him.

2. Aryabhata

He was born in 476 CE at Kusumapura. He was regarded as the first of the major mathematician-astronomers from the classical age. Aryabhaṭiya and Arya-Siddhanta were his known works. He worked on the ‘place value system’ using letters to signify numbers and stating qualities. He discovered the position of the 9 planets and found that these planets revolve around the sun. He also described the number of days in a year to be 365.

3. Brahmagupta

He was born in 598 CE near present-day Rajasthan. The most important contribution of Brahmagupta to mathematics was introducing the concept and computing methods of zero (0).

4. Srinivasa Ramanujan

He was born on 1887. His important contributions to this field are

Hardy-Ramanujan-Littlewood circle method in number theory Roger-Ramanujan’s identities in the partition of numbers Work on the algebra of inequalities Elliptic functions Continued fractions Partial sums and products of hypergeometric series

5.P.C. Mahalanobis

P.C. Mahalanobis was born in 1893. He is known for

Mahalanobis distance Feldman–Mahalanobis model

6. Calyampudi Radhakrishna Rao

R Rao was born in 1920. He is a well-known statistician. He is famous for his ‘Theory of estimation’. He is known for

Cramer–Rao bound Rao–Blackwell theorem Orthogonal arrays Score test

7.D.R. Kaprekar

D.R. Kaprekar was a recreational mathematician. He discovered several results in number theory, comprising a class of numbers and a constant named after him.

8. Satyendranath Bose

He was born in 1894. He is known for his collaboration with Albert Einstein. He is best known for his work on quantum mechanics. He famous contributions are

Bose-Einstein correlations Bose-Einstein condensate Bose-Einstein distribution Bose-Einstein statistics Boson Bose gas Photon gas Ideal Bose equation of state.

9. Shakuntala Devi

Known as the ‘Human Computer’ she was famous for solving the most complex maths equations without needing calculators. She was famous for setting many world records in mathematics with her superior intellect

10. Narendra Karamkar

Best known for his work regarding polynomial algorithms. He is listed as an ISI highly cited researcher. Narendra Karamkar one of the first provably polynomial time algorithms for linear programming, which is generally referred to as an interior point method. The algorithm is a cornerstone in the field of Linear Programming.

Professor of history of science, Doshisha University, Kyoto, Japan. Aryabhata, also called Aryabhata I or Aryabhata the Elder, (born 476, possibly Ashmaka or Kusumapura, India), astronomer and the earliest Indian mathematician whose work and history are available to modern scholars.

Aspirants can read other related articles linked in the table below:UPSC Preparation:

: Indian Mathematicians and their Contributions
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Is Ramanujan born in Kerala?

Srinivasa Ramanujan was born in December 22 nd, 1887 in Irod Nagar of Tamilnadu.
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Who is the father of Indian mathematics in India?

Aryabhatta is the father of Indian mathematics. Aryabhatta’s major work: Spherical trigonometry, plane trigonometry. Determined the value of π correct to four decimal places.
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Who is the No 1 mathematicians of India?

Srinivasa Ramanujan : India’s greatest mathematician.
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Who is India’s greatest mathematical genius?

What is Srinivasa Ramanujan remembered for? – Srinivasa Ramanujan, (born December 22, 1887, Erode, India—died April 26, 1920, Kumbakonam), Indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function.

  • When he was 15 years old, he obtained a copy of George Shoobridge Carr’s Synopsis of Elementary Results in Pure and Applied Mathematics, 2 vol.
  • 1880–86).
  • This collection of thousands of theorems, many presented with only the briefest of proofs and with no material newer than 1860, aroused his genius.

Having verified the results in Carr’s book, Ramanujan went beyond it, developing his own theorems and ideas. In 1903 he secured a scholarship to the University of Madras but lost it the following year because he neglected all other studies in pursuit of mathematics, Who Was The Pioneer Of The Kerala School Of Mathematics Britannica Quiz Numbers and Mathematics Ramanujan continued his work, without employment and living in the poorest circumstances. After marrying in 1909 he began a search for permanent employment that culminated in an interview with a government official, Ramachandra Rao.

  1. Impressed by Ramanujan’s mathematical prowess, Rao supported his research for a time, but Ramanujan, unwilling to exist on charity, obtained a clerical post with the Madras Port Trust.
  2. In 1911 Ramanujan published the first of his papers in the Journal of the Indian Mathematical Society,
  3. His genius slowly gained recognition, and in 1913 he began a correspondence with the British mathematician Godfrey H.

Hardy that led to a special scholarship from the University of Madras and a grant from Trinity College, Cambridge, Overcoming his religious objections, Ramanujan traveled to England in 1914, where Hardy tutored him and collaborated with him in some research.

Ramanujan’s knowledge of mathematics (most of which he had worked out for himself) was startling. Although he was almost completely unaware of modern developments in mathematics, his mastery of continued fractions was unequaled by any living mathematician. He worked out the Riemann series, the elliptic integrals, hypergeometric series, the functional equations of the zeta function, and his own theory of divergent series, in which he found a value for the sum of such series using a technique he invented that came to be called Ramanujan summation.

On the other hand, he knew nothing of doubly periodic functions, the classical theory of quadratic forms, or Cauchy’s theorem, and he had only the most nebulous idea of what constitutes a mathematical proof. Though brilliant, many of his theorems on the theory of prime numbers were wrong.

  • In England Ramanujan made further advances, especially in the partition of numbers (the number of ways that a positive integer can be expressed as the sum of positive integers; e.g., 4 can be expressed as 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1).
  • His papers were published in English and European journals, and in 1918 he was elected to the Royal Society of London,

In 1917 Ramanujan had contracted tuberculosis, but his condition improved sufficiently for him to return to India in 1919. He died the following year, generally unknown to the world at large but recognized by mathematicians as a phenomenal genius, without peer since Leonhard Euler (1707–83) and Carl Jacobi (1804–51).
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Who was the No 1 mathematician?

1. Pythagoras – The life of the famous Greek Pythagoras is somewhat mysterious. Probably born the son of a seal engraver on the island of Samos, Pythagoras has been attributed with many scientific and mathematical discoveries in antiquity. Student Read : What Can You Do With A Maths Degree? This includes the Pythagorean theorem currently annoying schoolchildren across the world, the Theory of Proportions, the sphericity of the Earth and the discovery that the morning and evening stars are, in fact, the planet Venus.
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Who is the father of education in Kerala?

Jewel Tom Mathew – This video is about sree narayana Guru who is known as the father of kerala renissance. This is first part and in this part i will explain about his birth, family, education, quotes, meetings with other prominent renissence leaders etc.
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Who started education in Kerala?

Archbishop Bernadine Baccinelli OCD The importance and antiquity of education in Kerala are underscored by the state’s ranking as among the most literate in the country. The educational transformation of Kerala was triggered by the efforts of the Church Mission Society missionaries, who were the pioneers that promoted mass education in Kerala, in the early decades of the 19th century.

  1. The local dynastic precursors of modern-day Kerala —primarily the Travancore Royal Family, the Nair Service Society, Sree Narayana Dharma Paripalana Yogam (SNDP Yogam) and Muslim Educational Society (MES) —also made significant contribution to the progress on education in Kerala.
  2. Local schools were known by the general word kalaris, some of which taught martial arts, but other village schools run by Ezhuthachans were for imparting general education.

Christian missionaries and British rule brought the modern school education system to Kerala. Ezhuthu palli was the name used in earlier times. The word was derived from the schools run by the Buddhist monasteries. For centuries villages used to setup an ezhuthupally or ashan pallikoodam with one or two teachers.

  1. Students used to go this school from nearby areas and learn languages, literature, mathematics, grammar etc.
  2. After completing this students may continue study about specific subjects such as ayurveda, astrology, accounting etc.
  3. Censuses during 1800 shows that Travancore, Cochin, Kannur areas have many such schools.

Even name list of ashans were used to be published along with the census.
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Why Kerala is first in education?

Kerala was declared a Fully Literate State in 1991 and is the only state in India where over 90% of the people can read and write, thanks to the free and compulsory education provided to all children up to the age of 14 years. Apart from this, the Kerala government is taking every possible step to improve the quality and standard of education.

Education, in its broadest sense, refers to the ways in which people learn skills and gain knowledge and understanding about the world, and about themselves.A Literate is any person who is able to read and write on his own and Literacy is the ability to read and write or is the quality of being literate.

Kerala stands first among other Indian states in literacy.Recognizing the need for a literate population and provision of elementary education as a crucial input for nation building, the state government with the backing of the central government, launched a number of plans and programmes over the past years to encourage elementary education in Kerala.
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Did Muslims invent calculus?

Some examples of the complex symmetries used in Islamic temple decoration

The Islamic Empire established across Persia, the Middle East, Central Asia, North Africa, Iberia and parts of India from the 8th Century onwards made significant contributions towards mathematics. They were able to draw on and fuse together the mathematical developments of both Greece and India,

One consequence of the Islamic prohibition on depicting the human form was the extensive use of complex geometric patterns to decorate their buildings, raising mathematics to the form of an art. In fact, over time, Muslim artists discovered all the different forms of symmetry that can be depicted on a 2-dimensional surface.

The Qu’ran itself encouraged the accumulation of knowledge, and a Golden Age of Islamic science and mathematics flourished throughout the medieval period from the 9th to 15th Centuries. The House of Wisdom was set up in Baghdad around 810, and work started almost immediately on translating the major Greek and Indian mathematical and astronomy works into Arabic.

The outstanding Persian mathematician Muhammad Al-Khwarizmi was an early Director of the House of Wisdom in the 9th Century, and one of the greatest of early Muslim mathematicians. Perhaps Al-Khwarizmi ‘s most important contribution to mathematics was his strong advocacy of the Hindu numerical system (1 – 9 and 0), which he recognized as having the power and efficiency needed to revolutionize Islamic (and, later, Western) mathematics, and which was soon adopted by the entire Islamic world, and later by Europe as well.

Al-Khwarizmi ‘s other important contribution was algebra, and he introduced the fundamental algebraic methods of “reduction” and “balancing” and provided an exhaustive account of solving polynomial equations up to the second degree. In this way, he helped create the powerful abstract mathematical language still used across the world today, and allowed a much more general way of analyzing problems other than just the specific problems previously considered by the Indians and Chinese,

Binomial Theorem

The 10th Century Persian mathematician Muhammad Al-Karaji worked to extend algebra still further, freeing it from its geometrical heritage, and introduced the theory of algebraic calculus. Al-Karaji was the first to use the method of proof by mathematical induction to prove his results, by proving that the first statement in an infinite sequence of statements is true, and then proving that, if any one statement in the sequence is true, then so is the next one.
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Who is invented Kerala?

Kerala is first mentioned (as Keralaputra) in a 3rd-century- bce rock inscription left by the Mauryan emperor Ashoka, In the last centuries bce this region became famous among the Greeks and Romans for its spices (especially pepper). During the first five centuries ce the region was a part of Tamilakam—the territory of the Tamils —and thus was sometimes partially controlled by the eastern Pandya and Chola dynasties, as well as by the Cheras.

In the 1st century Jewish immigrants arrived, and, according to local Christian tradition, St. Thomas the Apostle visited Kerala in the same century ( see St. Thomas Christians ). Much of Kerala’s history from the 6th to the 8th century is obscure, but it is known that Arab traders introduced Islam later in the period.

Under the Kulashekhara dynasty ( c.800–1102), Malayalam emerged as a distinct language, and Hinduism became prominent. The Cholas often controlled Kerala during the 11th and 12th centuries. By the beginning of the 14th century, Ravi Varma Kulashekhara of the Venad kingdom established a short-lived supremacy over southern India,

After his death, Kerala became a conglomeration of warring chieftaincies, among which the most important were Calicut (now Kozhikode ) in the north and Venad in the south. The era of foreign intervention began in 1498, when Vasco da Gama landed near Calicut. In the 16th century the Portuguese superseded the Arab traders and dominated the commerce of the Malabar Coast,

Their attempt to establish sovereignty was thwarted by the zamorin (hereditary ruler) of Calicut. The Dutch ousted the Portuguese in the 17th century. Marthanda Varma ascended the Venad throne in 1729 and crushed Dutch expansionist designs at the Battle of Kolachel 12 years later.

Marthanda Varma then adopted a European mode of martial discipline and expanded the Venad domain to encompass what became the southern state of Travancore, His alliance in 1757 with the raja of the central state of Cochin ( Kochi ), against the zamorin, enabled Cochin to survive. By 1806, however, Cochin and Travancore, as well as the Malabar Coast in the north, had become subject states under the British Madras Presidency.

Two years after India’s independence was achieved in 1947, Cochin and Travancore were united as Travancore-Cochin state. The present state of Kerala was constituted on a linguistic basis in 1956 when the Malabar Coast and the Kasargod taluka (administrative subdivision) of South Kanara were added to Travancore-Cochin.
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Who is the first scientist from Kerala?

From Wikipedia, the free encyclopedia

Nambi Narayanan
Narayanan in 2017
Born 12 December 1941 (age 81) Nagercoil, Kanniyakumari District, Tamil Nadu
  • Princeton University ( MSE )
  • Thiagarajar College of Engineering, Madurai ( B. Tech )
Occupation Aerospace engineer
Awards Padma Bhushan (2019)

S. Nambi Narayanan (born 12 December 1941) is an Indian aerospace scientist who worked for the Indian Space Research Organisation (ISRO) and contributed significantly to the Indian space program by developing the Vikas rocket engine, He led the team which acquired technology from the French for the Vikas engine used in the first Polar Satellite Launch Vehicle (PSLV) that India launched.

As a senior official at the ISRO, he was in charge of the cryogenics division. He was awarded the Padma Bhushan, India’s third-highest civilian award, in March 2019. In 1994, he was arrested on trumped up charges of espionage, being subjected to physical abuse while in the custody of the Kerala Police,

The charges against him were found to be baseless by the Central Bureau of Investigation (CBI) in April 1996. As a result, the Supreme Court of India dismissed all charges against him and prohibited the Government of Kerala from continuing its investigation on technical grounds.

  • In 2018, a Supreme Court bench headed by then Chief Justice Dipak Misra, awarded Narayanan a compensation of ₹ 50 lakh (equivalent to ₹ 57 lakh or US$71,000 in 2020).
  • Additionally, the Government of Kerala then awarded him further compensation to the tune of ₹ 1.3 crore (equivalent to ₹ 1.5 crore or US$190,000 in 2020) in 2019.

The film Rocketry: The Nambi Effect, based on his life, starring and directed by R. Madhavan, was released in July 2022.
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Who found 0 in India?

Zero as a symbol and a value – The first time we have a record of zero being understood as both a symbol and as a value in its own right was in India. About 650 AD the mathematician Brahmagupta, amongst others, used small dots under numbers to represent a zero.

  • The dots were known as ‘sunya’, which means empty, as well as ‘kha’, which means place.
  • So their version of zero was seen as having a null value as well as being a placeholder.
  • Brahmagupta was also the first to show how zero could be reached via addition and subtraction and the results of operations with zero.
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He did however get it wrong when it came to dividing by zero! We know about this largely because of the Bakhshali manuscript, an ancient Indian text filled with mathematics and text in Sanskrit form. It was discovered by a local farmer in 1881 and was originally thought to be from the ninth century but a few years ago carbon dating showed the oldest pages to be from sometime between 224 AD to 383 AD.
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Who was the creator of math?

Archimedes’ Legacy of Honour – Archimedes’ contributions to the fields of math, physics, astronomy, and philosophy have been outstanding. Math and science historians universally agree on the fact that Archimedes was the greatest mathematician of antiquity.
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When was Kerala school of astronomy and mathematics founded?

Babylonian – Babylonian mathematics refers to any mathematics of the peoples of Mesopotamia (modern Iraq ) from the days of the early Sumerians through the Hellenistic period almost to the dawn of Christianity, The majority of Babylonian mathematical work comes from two widely separated periods: The first few hundred years of the second millennium BC (Old Babylonian period), and the last few centuries of the first millennium BC ( Seleucid period). Geometry problem on a clay tablet belonging to a school for scribes; Susa, first half of the 2nd millennium BCE In contrast to the sparsity of sources in Egyptian mathematics, knowledge of Babylonian mathematics is derived from more than 400 clay tablets unearthed since the 1850s.

Written in Cuneiform script, tablets were inscribed whilst the clay was moist, and baked hard in an oven or by the heat of the sun. Some of these appear to be graded homework. The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia.

They developed a complex system of metrology from 3000 BC. From around 2500 BC onward, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period. The Babylonian mathematical tablet Plimpton 322, dated to 1800 BC. Babylonian mathematics were written using a sexagesimal (base-60) numeral system, From this derives the modern-day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 × 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree.

It is likely the sexagesimal system was chosen because 60 can be evenly divided by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a place-value system, where digits written in the left column represented larger values, much as in the decimal system.

The power of the Babylonian notational system lay in that it could be used to represent fractions as easily as whole numbers; thus multiplying two numbers that contained fractions was no different from multiplying integers, similar to modern notation.

The notational system of the Babylonians was the best of any civilization until the Renaissance, and its power allowed it to achieve remarkable computational accuracy; for example, the Babylonian tablet YBC 7289 gives an approximation of √ 2 accurate to five decimal places. The Babylonians lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context.

By the Seleucid period, the Babylonians had developed a zero symbol as a placeholder for empty positions; however it was only used for intermediate positions. This zero sign does not appear in terminal positions, thus the Babylonians came close but did not develop a true place value system.

Other topics covered by Babylonian mathematics include fractions, algebra, quadratic and cubic equations, and the calculation of regular numbers, and their reciprocal pairs, The tablets also include multiplication tables and methods for solving linear, quadratic equations and cubic equations, a remarkable achievement for the time.

Tablets from the Old Babylonian period also contain the earliest known statement of the Pythagorean theorem, However, as with Egyptian mathematics, Babylonian mathematics shows no awareness of the difference between exact and approximate solutions, or the solvability of a problem, and most importantly, no explicit statement of the need for proofs or logical principles.
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What is the contribution of Kerala school of mathematics?

Kerala School of Mathematics Kerala School of Mathematics may refer to:

, a school that existed in Kerala, India between 14th and 16th century CE and had produced pioneering mathematical research such as on Infinite series (well before the development of the theory of modern calculus in Europe), in Kunnamangalam near Kozhikode, Kerala, India

Topics referred to by the same term This page lists articles about schools, colleges, or other educational institutions which are associated with the same title. If an led you here, you may wish to change the link to point directly to the intended article. Retrieved from “” : Kerala School of Mathematics
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Who started first Sanskrit school in Kerala?

Education – Kuriakose Chavara started an institution for Sanskrit studies at Mannanam in 1846. A tutor belonging to the Variar community was brought from Thrissur, to teach at this Sanskrit institution. After establishing the Sanskrit institution in Mannanam, Chavara took the initiative to start a school in a nearby village called Arpookara.

On this Parappurath Varkey wrote in the Chronicles of the Mannanam monastery: “While the work on the Mannanam School began, a place on the Arpookara Thuruthumali hill was located to build a Chapel and school for the converts from the Pulaya caste.” Chavara was the first Indian who not only dared to admit the untouchables to schools but also provided them with Sanskrit education which was forbidden to the lower castes, thereby challenging social bans based on caste, as early as the former part of the 19th century.

It was during this time Bishop Bernadine Baccinelly issued a circular in 1856 which would act as the root cause of tremendous growth of education and hundred percent literacy in Kerala. Kuriakose Chavara was the motivator for such a movement and he successfully convinced Bishop Bernadine to issue a circular, apparently as an order.

It was a warning circular which stated, “each parish should establish educational institutions, or else they will be debarred from the communion”. The schools in Kerala are commonly called Pallikudams (school attached to Church (Palli)) because of this circular. Kuriakose Chavara took great interest in implementing the circular.

He delegated the members of his Congregation to ensure the implementation of the order in the circular and to actively take up educational activities. Each monastery was to oversee these activities of the parish churches in its neighbourhood.
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Who is the famous maths scientists in Kerala?

Mathematicians of Kerala – Part II This is the second article in the series Narayana Pandit (c.1340-1400), the earliest of the notable Keralese mathematicians, is known to have definitely written two works, an arithmetical treatise called Ganita Kaumudi and an algebraic treatise called Bijganita Vatamsa,

  • He was strongly influenced by the work of Bhaskara II, which proves work from the classic period was known to Keralese mathematicians and was thus influential in the continued progress of the subject.
  • Due to this influence Narayana is also thought to be the author of an elaborate commentary of Bhaskara II’s Lilavati, titled Karmapradipika (or Karma-Paddhati ).

It has been suggested that this work was written in conjunction with another scholar, Sankara Variyar, while others attribute the work to Madhava. Although the Karmapradipika contains very little original work, seven different methods for squaring numbers are found within it, a contribution that is wholly original to the author.

Narayana’s other major works contain a variety of mathematical developments, including a rule to calculate approximate values of square roots, using the second order indeterminate equation Nx 2 + 1 = y 2 (Pell’s equation). Mathematical operations with zero, several geometrical rules and discussion of magic squares and similar figures are other contributions of note.

Evidence also exists that Narayana made minor contributions to the ideas of differential calculus found in Bhaskara II’s work. R Gupta has also brought to light Narayana’s contributions to the topic of cyclic quadrilaterals. Subsequent developments of this topic, found in the works of Sankara Variyar and Ganesa interestingly show the influence of work of Brahmagupta.

  1. Paramesvara (c.1370-1460) is known to have been a pupil of Narayana Pandit, and also Madhava of Sangamagramma, who is thought to have been a significant influence.
  2. He wrote commentaries on the work of Bhaskara I, Aryabhata I and Bhaskara II, and his contributions to mathematics include an outstanding version of the mean value theorem.

Furthermore Paramesvara gave a mean value type formula for inverse interpolation of sine, and is thought to have been the first mathematician to give the radius of circle with inscribed cyclic quadrilateral, an expression that is normally attributed to Lhuilier (1782).

In turn, Nilakantha Somayaji (1444-1544) was a disciple of Paramesvara and was educated by his son Damodra. In his most notable work Tantra Samgraha (which ‘spawned’ a later anonymous commentary Tantrasangraha-vyakhya and a further commentary by the name Yuktidipaika, written in 1501) he elaborates and extends the contributions of Madhava.

Sadly none of his mathematical works are extant, however it can be determined that he was a mathematician of some note. Nilakantha was also the author of Aryabhatiya-bhasa a commentary of the Aryabhatiya, Of great significance is the presence of mathematical proof (inductive) in Nilakantha’s work. 3, and remarkably good rational approximations of p (using another Madhava series) are of great interest. Various results regarding infinite geometrically progressing convergent series are also attributed to Nilakantha. Citabhanu (1475-1550) has yet to find a place in books on Bharatiya mathematics.

His work on the solution of equations is quoted in a work called Kriya-krama-kari, by the scholar Sankara Variar, who is also relatively little known (although R Gupta mentions a further text, written by him). Jyesthadeva (c.1500-1575) was a member of the Kerala School, which was founded on the work of Madhava, Nilakantha, Paramesvara and others.

His key work was the Yukti-bhasa (written in Malayalam). Similarly to the work of Nilakantha, it is almost unique in the history of Bharatiya mathematics, in that it contains both proofs of theorems and derivations of rules. He also studied various topics found in many previous Bharatiya works, including integer solutions of systems of first degree equations solved using kuttaka,
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