Nilakantha Somayaji
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Kelallur Nilakantha Somayaji ' onMouseout='HidePop("87595")' href="/topics/Hindi">Hindi
: नीलकण्ठ सोमयाजि) (1444–1544) (also referred to as Kelallur Comatiri) was a major mathematician
and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha
completed in 1501. He had also composed an elaborate commentary on Aryabhatiya
called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra
and spherical geometry
. Grahapareeksakrama is a manual on making observations in astronomy based on instruments of the time.
In one of his works titled Siddhanta-darpana and also in his own commentary on Siddhanta-darpana, Nilakantha Somayaji has stated that he was born on Kali-day
1,660,181 which works out to 14 th June 1444 CE. A contemporary reference to Nilakantha Somayaji in a Malayalam work on astrology
implies that Somayaji lived to a ripe old age even to become a centenarian. Sankara Variar
, a pupil of Nilakantha Somayaji, in his commentary on Tantrasamgraha
titled Tantrasamgraha-vyakhya, points out that the first and last verses of Tantrasamgraha
contain chronograms specifying the Kali-days
of the commencement
(1,680,548) and of completion (1,680,553) of Somayaji's magnum opus Tantrasamgraha
. Both these days occur in 1500 CE.
In Aryabhatiya
-bhashya, Nilakantha Somayaji has stated that he was the son of Jatavedas and he had a brother named Sankara. Somayaji has further stated that he was a Bhatta belonging to the Gargya-gotra
and was a follower of Asvalayana-sutra
of Rigveda
. References in his own Laghuramayana indicate that Nilakantha Somayaji was a member of the Kelallur family (Sanskritised as Kerala-sad-grama) residing at Kundagrama, now known as Trikkandiyur near modern Tirur
in Kerala
. His wife was named Arya and he had two sons Rama and Dakshinamurti.
Nilakantha Somayaji studied vedanta
and some aspects of astronomy under one Ravi. However, It was Damodara
, son of Kerala-drgganita author Paramesvara, who initiated him into the science of astronomy and instructed him in the basic principles of mathematical computations. The great Malayalam poet Thunchaththu Ramanujan Ezhuthachan
is said to have been a student of Nilakantha Somayaji.
The epithet Somayaji is a title assigned to or assumed by a Namputiri who has performed the vedic ritual of Somayajna. So it could be surmised that Nilakantha Somayaji had also performed a Somayajna ritual and assumed the title of a Somayaji in later life. In colloquial Malayalam usage the word Somayaji has been corrupted to Comatiri.
In his writings he refers to a Mimamsa authority, quotes extensively from Pingala's chandas-sutra, scriptures, Dharmasastras, Bhagavata and Vishnupurana also. Sundararaja , a contemporary Tamil astronomer, refers to Nilakantha as sad-darshani-parangata, one who had mastered the six systems of Indian philosophy.
's model for the planets Mercury
and Venus
. His equation of the centre
for these planets remained the most accurate until the time of Johannes Kepler
in the 17th century.
In his Aryabhatiyabhasya, a commentary on Aryabhata's Aryabhatiya
, Nilakantha developed a computational system for a partially heliocentric
planetary model in which Mercury, Venus, Mars
, Jupiter
and Saturn
orbit the Sun
, which in turn orbits the Earth
, similar to the Tychonic system
later proposed by Tycho Brahe
in the late 16th century. Most astronomers of the Kerala school who followed him accepted this planetary model.
Hindi
Standard Hindi, or more precisely Modern Standard Hindi, also known as Manak Hindi , High Hindi, Nagari Hindi, and Literary Hindi, is a standardized and sanskritized register of the Hindustani language derived from the Khariboli dialect of Delhi...
: नीलकण्ठ सोमयाजि) (1444–1544) (also referred to as Kelallur Comatiri) was a major mathematician
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics , important contributions were made by scholars like Aryabhata, Brahmagupta, and Bhaskara II. The decimal number system in use today was first...
and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha
Tantrasamgraha
Tantrasamgraha is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics....
completed in 1501. He had also composed an elaborate commentary on Aryabhatiya
Aryabhatiya
Āryabhaṭīya or Āryabhaṭīyaṃ, a Sanskrit astronomical treatise, is the magnum opus and only extant work of the 5th century Indian mathematician, Āryabhaṭa.- Structure and style:...
called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
and spherical geometry
Spherical geometry
Spherical geometry is the geometry of the two-dimensional surface of a sphere. It is an example of a geometry which is not Euclidean. Two practical applications of the principles of spherical geometry are to navigation and astronomy....
. Grahapareeksakrama is a manual on making observations in astronomy based on instruments of the time.
Biographical details
Nilakantha Somayaji was one of the very few authors of the scholarly traditions of India who had cared to record details about his own life and times. So fortunately a few accurate particulars about Nilakantha Somayaji are known.In one of his works titled Siddhanta-darpana and also in his own commentary on Siddhanta-darpana, Nilakantha Somayaji has stated that he was born on Kali-day
Kali Yuga
Kali Yuga is the last of the four stages that the world goes through as part of the cycle of yugas described in the Indian scriptures. The other ages are Satya Yuga, Treta Yuga and Dvapara Yuga...
1,660,181 which works out to 14 th June 1444 CE. A contemporary reference to Nilakantha Somayaji in a Malayalam work on astrology
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
implies that Somayaji lived to a ripe old age even to become a centenarian. Sankara Variar
Sankara Variar
Sankara Variar was an astronomer-mathematician of the Kerala school of astronomy and mathematics who lived during the sixteenth century CE...
, a pupil of Nilakantha Somayaji, in his commentary on Tantrasamgraha
Tantrasamgraha
Tantrasamgraha is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics....
titled Tantrasamgraha-vyakhya, points out that the first and last verses of Tantrasamgraha
Tantrasamgraha
Tantrasamgraha is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics....
contain chronograms specifying the Kali-days
Kali Yuga
Kali Yuga is the last of the four stages that the world goes through as part of the cycle of yugas described in the Indian scriptures. The other ages are Satya Yuga, Treta Yuga and Dvapara Yuga...
of the commencement
(1,680,548) and of completion (1,680,553) of Somayaji's magnum opus Tantrasamgraha
Tantrasamgraha
Tantrasamgraha is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics....
. Both these days occur in 1500 CE.
In Aryabhatiya
Aryabhatiya
Āryabhaṭīya or Āryabhaṭīyaṃ, a Sanskrit astronomical treatise, is the magnum opus and only extant work of the 5th century Indian mathematician, Āryabhaṭa.- Structure and style:...
-bhashya, Nilakantha Somayaji has stated that he was the son of Jatavedas and he had a brother named Sankara. Somayaji has further stated that he was a Bhatta belonging to the Gargya-gotra
Brahmin gotra system
The word "gotra" means "lineage" in the Sanskrit language. Among those of the Brahmin caste, gotras are reckoned patrilineally. Each gotra takes the name of a famous Rishi or sage who was the patrilineal forebearer of that clan...
and was a follower of Asvalayana-sutra
Shakha
A shakha , is a Hindu theological school that specializes in learning certain Vedic texts, or else the traditional texts followed by such a school. An individual follower of a particular school or recension is called a ...
of Rigveda
Rigveda
The Rigveda is an ancient Indian sacred collection of Vedic Sanskrit hymns...
. References in his own Laghuramayana indicate that Nilakantha Somayaji was a member of the Kelallur family (Sanskritised as Kerala-sad-grama) residing at Kundagrama, now known as Trikkandiyur near modern Tirur
Tirur
Tirur is a town and a municipality in Malappuram district in the Indian state of Kerala spread over an area of 16.55 km2 . It is birth place of Thunchathu Ramanujan Ezhuthachan, the father of Malayalam literature. Thunchan Parambu is highly venerated and its sand is believed to be sacred. The...
in Kerala
Kerala
or Keralam is an Indian state located on the Malabar coast of south-west India. It was created on 1 November 1956 by the States Reorganisation Act by combining various Malayalam speaking regions....
. His wife was named Arya and he had two sons Rama and Dakshinamurti.
Nilakantha Somayaji studied vedanta
Vedanta
Vedānta was originally a word used in Hindu philosophy as a synonym for that part of the Veda texts known also as the Upanishads. The name is a morphophonological form of Veda-anta = "Veda-end" = "the appendix to the Vedic hymns." It is also speculated that "Vedānta" means "the purpose or goal...
and some aspects of astronomy under one Ravi. However, It was Damodara
Damodara
Vatasseri Damodara Nambudiri was an astronomer-mathematician of the Kerala school of astronomy and mathematics who flourished during the fifteenth century CE. He was a son of Vatasseri Paramesvara who developed the drigganita system of astronomical computations...
, son of Kerala-drgganita author Paramesvara, who initiated him into the science of astronomy and instructed him in the basic principles of mathematical computations. The great Malayalam poet Thunchaththu Ramanujan Ezhuthachan
Thunchaththu Ramanujan Ezhuthachan
Thunjathu Ramanujan Ezhuthachan was an Indian poet from around the 16th century, known as the father of the Malayalam language — the principal language of the Indian state of Kerala, spoken by 36 million people in the world...
is said to have been a student of Nilakantha Somayaji.
The epithet Somayaji is a title assigned to or assumed by a Namputiri who has performed the vedic ritual of Somayajna. So it could be surmised that Nilakantha Somayaji had also performed a Somayajna ritual and assumed the title of a Somayaji in later life. In colloquial Malayalam usage the word Somayaji has been corrupted to Comatiri.
Nilakantha Somayaji as a polymath
Nilakantha's writings substantiate his knowledge of several branches of Indian philosophy and culture. It is said that he could refer to a Mimamsa authority to establish his view-point in a debate and with equal felicity apply a grammatical dictum to the same purpose.In his writings he refers to a Mimamsa authority, quotes extensively from Pingala's chandas-sutra, scriptures, Dharmasastras, Bhagavata and Vishnupurana also. Sundararaja , a contemporary Tamil astronomer, refers to Nilakantha as sad-darshani-parangata, one who had mastered the six systems of Indian philosophy.
Astronomy
In his Tantrasangraha, Nilakantha revised AryabhataAryabhata
Aryabhata was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy...
's model for the planets Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...
and Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...
. His equation of the centre
Center of mass
In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...
for these planets remained the most accurate until the time of Johannes Kepler
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...
in the 17th century.
In his Aryabhatiyabhasya, a commentary on Aryabhata's Aryabhatiya
Aryabhatiya
Āryabhaṭīya or Āryabhaṭīyaṃ, a Sanskrit astronomical treatise, is the magnum opus and only extant work of the 5th century Indian mathematician, Āryabhaṭa.- Structure and style:...
, Nilakantha developed a computational system for a partially heliocentric
Heliocentrism
Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around a stationary Sun at the center of the universe. The word comes from the Greek . Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center...
planetary model in which Mercury, Venus, Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...
, Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...
and Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...
orbit the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
, which in turn orbits the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
, similar to the Tychonic system
Tychonic system
The Tychonic system was a model of the solar system published by Tycho Brahe in the late 16th century which combined what he saw as the mathematical benefits of the Copernican system with the philosophical and "physical" benefits of the Ptolemaic system...
later proposed by Tycho Brahe
Tycho Brahe
Tycho Brahe , born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations...
in the late 16th century. Most astronomers of the Kerala school who followed him accepted this planetary model.
Works of Nilakantha Somayaji
The following is a brief description of the works by Nilakantha Somayaji dealing with astronomy and mathematics.- TantrasamgrahaTantrasamgrahaTantrasamgraha is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics....
- Golasara : Description of basic astronomical elements and procedures
- Sidhhantadarpana : A short work in 32 slokas enunciating the astronomical constants with reference to the Kalpa and specifying his views on astronomical concepts and topics.
- Candrachayaganita : A work in 32 verses on the methods for the calculation of time from the measurement of the shadow of the gnomon cast by the moon and vice versa.
- Aryabhatiya-bhashya : Elaborate commentary on Aryabhatiya.
- Sidhhantadarpana-vyakhya : Commentary on his own Siddhantadarapana.
- Chandrachhayaganita-vyakhya : Commentary on his own Chandrachhayaganita.
- Sundaraja-prasnottara : Nilakantha's answers to questions posed by Sundaraja, a Tamil Nadu based astronomer.
- Grahanadi-grantha : Rationale of the necessity of correcting old astronomical constants by observations.
- Grahapariksakrama : Description of the principles and methods for verifying astronomical computations by regular observations.
- JyotirmimamsaJyotirmimamsaJyotirmimamsa is a treatise on the methodology of astronomical studies authored by Nilakantha Somayaji in around 1504 CE. Nilakantha somayaji was an important astronomer-mathematician of the Kerala school of astronomy and mathematics and was the author of the much celebrated astronomical work...
: Analysis of astronomy