Mahavira writes the Ganitasarasangraha
Around 850 the Jain mathematician Mahavira, who enjoyed the patronage of the Rashtrakuta king Amoghavarsha I, wrote the Ganitasarasangraha (‘Compendium of the Essence of Mathematics’), one of the earliest surviving Indian treatises devoted to mathematics alone rather than forming part of an astronomical work. Its nine chapters cover arithmetic and fractions, the rule of three, algebraic problems and the measurement of areas, excavations and shadows.
- Date
- c. 850year known, approximate
- Place
- Manyakheta (Malkhed), the Rashtrakuta capitalapproximate locationtoday: Malkhed, Kalaburagi district, Karnataka, India · South Asia
- Participants
- Mahavira (mathematician), Amoghavarsha I
- Threads
- South Asia (6th–10th c.)
- Also known as
- Ganitasarasangraha; Gaṇita-sāra-saṅgraha; Ganita Sara Samgraha; Mahaviracharya; Ганита-сара-санграха; Махавирачарья
After two verses of homage to the Jina Mahavira, the treatise praises in six verses a king who ‘propounds the logic of syadvada’ and is known as Amoghavarsha Nripatunga, and wishes his rule prosperity; since Amoghavarsha reigned from 814/815 to 877/878, the work is placed in the middle of the 9th century. Mahavira then extols the science of calculation as useful in worldly and religious affairs, in love, wealth, music and drama, cookery, medicine, architecture, prosody, poetics, logic and grammar, and in the movements of the sun and the other heavenly bodies.
The nine chapters deal with terminology, arithmetical operations, fractions, miscellaneous problems, the rule of three, mixed problems, the measurement of areas, calculations concerning excavations, and shadows. The work gives systematic rules for breaking fractions into sums of unit fractions, treats permutations and combinations — a favourite topic of Jain mathematics — and gives an approximate rule for the perimeter and area of an ellipse. M. Rangacarya, who translated it into English in 1912, thought that Mahavira knew the work of Brahmagupta and tried to improve on it, with a simpler classification of operations, fuller rules and many more examples. The book was widely known in South India and was rendered into Telugu verse by Pavuluri Mallana, probably in the 11th century.
Connections
Related events
- Brahmagupta writes the Brahmasphutasiddhanta628 · South AsiaM. Rangacarya thought that Mahavira knew Brahmagupta’s work and tried to improve on it
- The Kavirajamarga, the earliest Kannada work on poeticsc. 850 · South AsiaMahavira wrote his mathematical compendium in the reign of the same king
Adjacent events in the thread
- Vijayalaya takes Thanjavur: the rise of the Cholasc. 850 · South Asia
Meanwhile in the world
Other regions, within a year of this event
Western and Central Europe
- Aghlabid conquest of SicilyJune 827 – 1 August 902
Eastern Europe
- Saltovo-Mayaki culturec. 750 – between 900 and 950
- The Khazar rulers adopt Judaismbetween 740 and 861
Balkans and Anatolia
- Leo the Mathematician heads the school of the Magnaurabetween 843 and 866
Middle East and Egypt
- The House of Wisdom and the translation movement in Baghdadc. 800 – c. 900
- Accounts of China and India: merchants’ reports on the sea route to Guangzhoubetween 851 and 852
- The mihna: the Abbasid inquisition over the createdness of the Qur’an833 – between 848 and 852
Africa
- Ifriqiya under the Aghlabids800 – March 909
- Igbo-Ukwu: bronze casting in the West African forest800–899 – 1100–1199
Central and Northern Asia
North America
Latin America
- Classic Maya collapse in the southern lowlandsc. 800 – c. 950
- Rise of Chichén Itzá in northern Yucatánc. 800 – between 900 and 1000
- Wari culture and the Middle Horizon state in the Central Andesc. 600 – c. 1000
- Tiwanaku culture at its height by Lake Titicacac. 600 – c. 1000
- Cacaxtla and Xochicalco: the Epiclassic cities of central Mexicoc. 650 – c. 900
The same period
Sources
- Wikipedia (English): Gaṇita-sāra-saṅgraha
- Wikipedia (English): Mahāvīra (mathematician)
- Wikipedia (English): Amoghavarsha
- MacTutor History of Mathematics: Mahavira
- The Ganita-sara-sangraha of Mahaviracarya / With English translation and notes by M. Rangacarya. — Madras: Government Press, 1912
- Wikidata: Q12423185