Keļallur Nilakantha Somayaji (14 June 1444 – 1544), also referred to as Keļallur Comatiri, was a major
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
and
astronomer
An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...
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
''Aryabhatiya'' (IAST: ') or ''Aryabhatiyam'' ('), a Sanskrit astronomical treatise, is the '' magnum opus'' and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that ...
called the ''Aryabhatiya Bhasya''. In this Bhasya, Nilakantha had discussed
infinite series expansions of
trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in a ...
and problems of
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary ...
and
spherical geometry
300px, A sphere with a spherical triangle on it.
Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sp ...
. ''Grahapariksakrama'' is a manual on making observations in astronomy based on instruments of the time. Known popularly as Kelallur Chomaathiri, he is considered an equal to
Vatasseri Parameshwaran Nambudiri.
Early life
Nilakantha was born into a Brahmin family which came from
South Malabar in
Kerala
Kerala ( ; ) is a state on the Malabar Coast of India. It was formed on 1 November 1956, following the passage of the States Reorganisation Act, by combining Malayalam-speaking regions of the erstwhile regions of Cochin, Malabar, South Ca ...
.
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.
In one of his works titled ''
Siddhanta-star'' 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 June 1444 CE. A contemporary reference to Nilakantha Somayaji in a
Malayalam
Malayalam (; , ) is a Dravidian language spoken in the Indian state of Kerala and the union territories of Lakshadweep and Puducherry ( Mahé district) by the Malayali people. It is one of 22 scheduled languages of India. Malayalam wa ...
work on
astrology
Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...
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
''Aryabhatiya'' (IAST: ') or ''Aryabhatiyam'' ('), a Sanskrit astronomical treatise, is the '' magnum opus'' and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that ...
-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
In Hindu culture, the term gotra (Sanskrit: गोत्र) is considered to be equivalent to lineage. It broadly refers to people who are descendants in an unbroken male line from a common male ancestor or patriline. Generally, the gotra ...
and was a follower of
Asvalayana-sutra of
Rigveda
The ''Rigveda'' or ''Rig Veda'' ( ', from ' "praise" and ' "knowledge") is an ancient Indian collection of Vedic Sanskrit hymns (''sūktas''). It is one of the four sacred canonical Hindu texts ('' śruti'') known as the Vedas. Only on ...
. 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 in modern
Tirur
Tirur is a Municipality in Malappuram district in the Indian state of Kerala spread over an area of . It is one of the business centers of Malappuram district and is situated west of Malappuram and south of Kozhikode, on the Shoranur–Manga ...
,
Kerala
Kerala ( ; ) is a state on the Malabar Coast of India. It was formed on 1 November 1956, following the passage of the States Reorganisation Act, by combining Malayalam-speaking regions of the erstwhile regions of Cochin, Malabar, South Ca ...
. His wife was named Arya and he had two sons Rama and Dakshinamurti.
Nilakantha Somayaji studied
vedanta
''Vedanta'' (; sa, वेदान्त, ), also ''Uttara Mīmāṃsā'', is one of the six (''āstika'') schools of Hindu philosophy. Literally meaning "end of the Vedas", Vedanta reflects ideas that emerged from, or were aligned with, ...
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
Malayalam (; , ) is a Dravidian language spoken in the Indian state of Kerala and the union territories of Lakshadweep and Puducherry ( Mahé district) by the Malayali people. It is one of 22 scheduled languages of India. Malayalam wa ...
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.
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
Aryabhata's model for the planets
Mercury and
Venus
Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
. His equation of the
centre
Center or centre may refer to:
Mathematics
*Center (geometry), the middle of an object
* Center (algebra), used in various contexts
** Center (group theory)
** Center (ring theory)
* Graph center, the set of all vertices of minimum eccentricity ...
for these planets remained the most accurate until the time of
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
in the 17th century.
[George G. Joseph (2000). ''The Crest of the Peacock: Non-European Roots of Mathematics'', p. 408. ]Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large.
The press was founded by Whitney Darrow, with the financial ...
.
In his ''Aryabhatiyabhasya'', a commentary on Aryabhata's ''
Aryabhatiya
''Aryabhatiya'' (IAST: ') or ''Aryabhatiyam'' ('), a Sanskrit astronomical treatise, is the '' magnum opus'' and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that ...
'', Nilakantha developed a computational system for a partially
heliocentric
Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth ...
planetary model in which Mercury, Venus,
Mars
Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury. In the English language, Mars is named for the Roman god of war. Mars is a terrestrial planet with a thin at ...
,
Jupiter
Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousand ...
and
Saturn
Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter. It is a gas giant with an average radius of about nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...
orbit the
Sun, which in turn orbits the
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...
, similar to the
Tychonic system later proposed by
Tycho Brahe
Tycho Brahe ( ; born Tyge Ottesen Brahe; generally called Tycho (14 December 154624 October 1601) was a Danish astronomer, known for his comprehensive astronomical observations, generally considered to be the most accurate of his time. He was ...
in the late 16th century. Most astronomers of the Kerala school who followed him accepted this planetary model.
[
]
Works
The following is a brief description of the works by Nilakantha Somayaji dealing with astronomy and mathematics.
#'' Tantrasamgraha''
#''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.
#'' Jyotirmimamsa'' : Analysis of astronomy
See also
*Indian mathematicians
chronology of Indian mathematicians spans from the Indus Valley civilisation and the Vedas to Modern India.
Indian mathematicians have made a number of contributions to mathematics that have significantly influenced scientists and mathematicians ...
*Indian astronomy
Astronomy has long history in Indian subcontinent stretching from pre-historic to modern times. Some of the earliest roots of Indian astronomy can be dated to the period of Indus Valley civilisation or earlier. Astronomy later developed as a di ...
References
Further reading
*
* K. V. Sarma
K. V. Venkateswara Sarma (1919–2005) was an Indian historian of science, particularly the astronomy and mathematics of the Kerala school. He was responsible for bringing to light several of the achievements of the Kerala school. He was edito ...
(2008) "Nilakantha Somayaji", Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures (2nd edition) edited by Helaine Selin, Springer, .
*
*
External links
Official Website of Chenthala Vishnu Temple
Tantrasamgraha Official Website
Official Website of Kelallur Nilakantha Somayaji
{{DEFAULTSORT:Somayaji, Nilakantha
1444 births
1544 deaths
Indian Hindus
16th-century Indian astronomers
Kerala school of astronomy and mathematics
15th-century Indian mathematicians
16th-century Indian mathematicians
People from Malappuram district
Scientists from Kerala
15th-century Indian astronomers
Scholars from Kerala