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Line 103: − + − 1. Bhashya of Bhāskara I (c.629) on Āryabhañīya of Āryabhaña (c.499) 2. Bhāùya of Govindasvāmin (c.800) on Mahābhāskarīya of Bhāskara I (c.629) 3. Vāsanābhāùya of Caturveda Pçthūdakasvāmin (c.860) on Brāhmasphuñasiddhānta of Brahmagupta (c.628) 4. Vivaraõa of Bhāskarācārya II (c.1150) on Śiùyadhīvçddhidatantra of Lalla (c.748), 5. Vāsanā of Bhāskarācārya II (c.1150) on his own Līlāvatī, Bījagaõita and Siddhāntaśiromaõi 6. Siddhāntadīpikā of Parameśvara (c.1431) on the Bhāùya of Govindasvāmin (c.800) on Mahābhāskarīya of Bhāskara I (c.629) 7. Āryabhañīyabhāùya of Nīlakaõñha Somayājī (c.1501) on Āryabhañīya of Āryabhaña (c.499), K. Sambasiva Sastri (ed.), 3 Vols., Trivandrum 1931, 1932, 1957 8. Gaõita-Yuktibhāùā (in Malayalam) of Jyeùñhadeva (c.1530) 9. Yuktidīpikā of Śaïkara Vāriyār (c.1530) on Tantrasaïgraha of Nīlakaõñha Somayājī (c.1500) 10.Kriyākramakarī of Śaïkara Vāriyār (c.1535) on Līlāvatī of Bhāskarācārya II (c.1150) 11.Sūryaprakāśa of Sūryadāsa (c.1538) on Bījagaõita of Bhāskarācārya II (c.1150) 12.Buddhivilāsinī of Gaõeśa Daivajña (c.1545) on Līlāvatī of Bhāskarācārya II (c.1150)+ + + + + + + + + +
Ganita Shastra (गणितशास्त्रम्) (view source)
Revision as of 22:32, 24 March 2020
, 22:32, 24 March 2020added information about modern mathematicians
=== Siddhanta Works ===
=== Siddhanta Works ===
Eighteen siddhantas were composed during this period.
Eighteen siddhantas were composed by and named after their authors. However five of them primarily, Surya, Paulisa, Romaka, Vashishta, Paitamaha siddhantas and a few others have survived, while the remaining are lost. Scholars also opine that these works have undergone various changes over time.
{{columns-list|colwidth=15em|style=width: 600px; font-style: italic;|
* [[Surya Siddhanta]]
* [[Paitamaha Siddhanta]]
* [[Vyasa Siddhanta]]
* [[Vashishta Siddhanta]]
* [[Atri Siddhanta]]
* [[Parasara Siddhanta]]
* [[Kashyapa Siddhanta]]
* [[Narada Siddhanta]]
* [[Garga Siddhanta]]
* [[Marichi Siddhanta]]
* [[Manu Siddhanta]]
* [[Angira Siddhanta]]
* [[Lomasa Siddhanta]]
* [[Paulisa Siddhanta]]
* [[Chyavana Siddhanta]]
* [[Yavana Siddhanta]]
* [[Bhrugu Siddhanta]]
* [[Saunaka Siddhanta]]
}}
Astronomy which had been a branch of Mathematics, separated out and began to be regarded by the name Jyotisha. Geometry which belonged to the Kalpasutras came to be regarded as an integral part of the ganita. Thus the readjusted science of the ganita consisted mainly of arithmetic, algebra, and geometry. Among the Jainas and Buddhists the ganita was known by the name Samkyana (science of numbers).
=== Modern Indian Mathematicians ===
Three schools - Ujjain, Mysore and Kusumpura have been referred to as important schools of mathematics in the early christian era. Here we discuss the important mathematicians of the modern era.
# '''Aryabhata I (476 A.D.)''' - Aryabhatiya or Aryasiddhanta consists of four chapters namely Dasagitika (the ten Gitikas), Ganitapada (mathematics), Kalakriya (reckoning of time) and Gola (sphere) deals with astronomy and arithmetic.
# '''Varahamihira (505 A.D.)''' - Panchasiddhantika among other works is considered important in the history of astronomy. In the history of mathematics this work has a high place for its amount of trigonometrical information.
# '''Bhaskara I (600 A.D.)''' - Mahabhaskariya, an astronomical work, Aryabhatiyabhashya, a commentary on the Aryabhatiya of Aryabhata and Laghubhaskariya, an abridged and simplified version of Mahabhaskariya. He was mainly an astronomer but he propounded mathematical solutions for astronomical problems. He gave the solution of the indeterminate equation of the first degree in his Mahabhaskariya.
# '''Brahmagupta (628 A.D.)''' - Brahmasphutasiddanta and Khandakhadyaka are astronomical works which include his greatest contributions to the field of mathematics. He belonged to the Ujjain school. Brahmasphutasiddhanta, has two chapters Ganitadhyaya and Kuttakadhyaya. Ganitadhyaya deals with cyclic triange and quadrilateral, rules for arithmetical operations involving zero, negative numbers and quadratic equations. Kuttakadhyaya contains solutions of the indeterminate equations of both first and second degree. The Spastadhikara chapter however contains trigonometrical notations including the sine table. He has a significant place in the history of Indian Civilization.
# '''Lalla (768 A.D.)''' - Shishyadhivrddhida based on the Aryabhatiya of Aryabhata I, is devoted to astronomy. Associated with the school of Kusumpura his work contains important information on trigonometry.
# '''Govindasvamin (800-850 A.D.)''' - Bhashya on Mahabhaskariya of Bhaskara I and Govindakrti. He belonged to the Kerala school of mathematics.
# '''Mahavira (850 A.D.)''' - Ganitasarasamgraha deals with arithmetic, geometry and algebra. A Jaina mathematician he is associated with the school of Mysore.
# '''Sridhara (850-950 A.D.)''' - Patiganita is a work on arithmetic and mensuration.
The Kerala school of mathematics in the more recent centuries has been the seat of learning and has produced great mathematical works.
== Commentaries in Indian Mathematics ==
== Commentaries in Indian Mathematics ==
In his Vāsanābhāshya on his own treatise on Algebra, Bījaganita, Bhāskarācārya II (c.1150) explains that the tradition of upapatti has been for long a part of the oral instruction (pāñha-nibaddhā).3 The following are some of the important commentaries which are available in print and contain some discussion of upapattis for various results and procedures of Indian mathematics and astronomy:
In his Vāsanābhāshya on his own treatise on Algebra, Bījaganita, Bhāskarācārya II (c.1150) explains that the tradition of upapatti has been for long a part of the oral instruction (pāñha-nibaddhā).3 The following are some of the important commentaries which are available in print and contain some discussion of upapattis for various results and procedures of Indian mathematics and astronomy:
* Bhashya of Bhāskara I (c.629) on Āryabhañīya of Āryabhaña (c.499)
* Bhāùya of Govindasvāmin (c.800) on Mahābhāskarīya of Bhāskara I (c.629) Vāsanābhāùya of Caturveda Pçthūdakasvāmin (c.860) on Brāhmasphuñasiddhānta of Brahmagupta (c.628)
* Vivaraõa of Bhāskarācārya II (c.1150) on Śiùyadhīvçddhidatantra of Lalla (c.748),
* Vāsanā of Bhāskarācārya II (c.1150) on his own Līlāvatī, Bījagaõita and Siddhāntaśiromaõi
* Siddhāntadīpikā of Parameśvara (c.1431) on the Bhāùya of Govindasvāmin (c.800) on Mahābhāskarīya of Bhāskara I (c.629)
* Āryabhañīyabhāùya of Nīlakaõñha Somayājī (c.1501) on Āryabhañīya of Āryabhaña (c.499), K. Sambasiva Sastri (ed.), 3 Vols., Trivandrum 1931, 1932, 1957
* Gaõita-Yuktibhāùā (in Malayalam) of Jyeùñhadeva (c.1530)
* Yuktidīpikā of Śaïkara Vāriyār (c.1530) on Tantrasaïgraha of Nīlakaõñha Somayājī (c.1500)
* Kriyākramakarī of Śaïkara Vāriyār (c.1535) on Līlāvatī of Bhāskarācārya II (c.1150)
* Sūryaprakāśa of Sūryadāsa (c.1538) on Bījagaõita of Bhāskarācārya II (c.1150)
* Buddhivilāsinī of Gaõeśa Daivajña (c.1545) on Līlāvatī of Bhāskarācārya II (c.1150)
== References ==
== References ==
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[[Category:Shastras]]
[[Category:Shastras]]