A siddhanta (Sanskrit: सिद्धान्त, “established conclusion” or “doctrine”) is a systematic astronomical or mathematical treatise in the classical Indian tradition. The term denotes a work that presents a coherent, self-contained system - typically covering the computation of planetary positions, the structure of time, calendrical reckoning, and cosmological framework. Siddhantas formed the backbone of Indian mathematical astronomy from roughly the 4th century CE onward and shaped astronomical practice across South and Southeast Asia for more than a millennium.

A canonical siddhanta typically addresses several domains: the structure of cosmic time (kalpas, yugas, and their subdivisions), mean and true planetary longitudes, the geometry of eclipses, rising and setting times, and the construction of instruments. The mathematical tools employed include trigonometry (particularly the use of sine tables, called jya), arithmetic progressions, and techniques for iterative approximation. Some siddhantas also incorporate chapters on gnomonic shadow reckoning and questions of mathematical pedagogy.

The genre is distinguished from the karana literature - shorter, computational handbooks derived from siddhantas and designed for practical use - and from the samhita literature, which deals with omens and divination rather than mathematical astronomy.

The recognized classical siddhantas include:

• Paitamaha Siddhanta - among the oldest surviving siddhanta texts, preserved partially in the Vishnu Dharmottara Purana.
• Surya Siddhanta - one of the most widely used; the text circulating today is likely a revised version of an earlier work. It remains foundational to the Hindu calendar in use today.
• Aryabhatiya (499 CE) - composed by Aryabhata; technically a ganita (mathematical) treatise rather than a full siddhanta, but enormously influential on subsequent siddhanta authors. See the Aryabhata page.
• Brahmasphutasiddhanta (628 CE) - composed by Brahmagupta; introduced systematic treatment of zero and negative numbers as algebraic quantities.
• Sisyadhivrddhida Tantra (c. 748 CE) - by Lalla.
• Siddhanta Shiromani (c. 1150 CE) - by Bhaskaracharya (Bhaskara II); considered the culminating classical synthesis.

The five siddhantas summarized in Varahamihira's Panchasiddhantika (c. 550 CE) - the Saura, Romaka, Paulisa, Vasishtha, and Paitamaha - represent an earlier stratum, most now lost except through Varahamihira's redaction.

Scholars debate the degree to which early siddhantas were influenced by Babylonian and Hellenistic astronomy transmitted through intermediary sources, and the degree to which they represent independent development. The presence of Greco-Roman terms (kendra from Greek kentron) and of parameters resembling those in Ptolemaic sources has fueled ongoing discussion. The Sanskrit jya (bowstring), the standard term for the sine-like quantity in siddhanta mathematics, passed into Arabic as jiba, was subsequently misread as jaib (bosom), and was rendered into Latin as sinus - the path by which the Indian sine function entered European mathematics. The indigenous development viewpoint and the transmission viewpoint each have scholarly proponents. See Siddhanta - Debate for a fuller treatment.

Siddhanta astronomy also traveled outward: Sanskrit astronomical texts influenced Tibetan, Javanese, Khmer, and Thai calendrical systems, and - through Arabic translation during the Abbasid period - entered the Islamic and ultimately European astronomical traditions.

There is broad scholarly consensus that the siddhanta genre represents a mathematically sophisticated and internally coherent tradition. Disagreement persists on questions of external influence versus indigenous origin and on the dating and textual history of specific works. See Siddhanta - Historical Scholarship Consensus for an overview of areas of agreement.

• Indigenous Development - The siddhanta tradition developed its core methods independently, with external borrowing limited to terminology and a few parameters.
• Hellenistic Transmission - Key structural and parametric features of early siddhantas derive from Babylonian or Greco-Roman astronomy, transmitted through now-lost intermediary texts.
• Continuous Revision - Siddhanta texts were not fixed compositions but living documents revised by successive astronomers, complicating authorship and dating claims.

• Siddhanta - History
• Siddhanta - Debate
• Siddhanta - Historical Scholarship Consensus
• Aryabhata
• Brahmagupta
• Bhaskaracharya
• Varahamihira
• Surya Siddhanta
• Indian Mathematics
• Hindu Calendar
• Panchasiddhantika

1. David Pingree, Census of the Exact Sciences in Sanskrit, American Philosophical Society, 1970-1994. The standard reference catalogue for siddhanta literature.
2. Kim Plofker, Mathematics in India, Princeton University Press, 2009. Comprehensive treatment of the mathematical content of siddhantas.
3. David Pingree, “History of Mathematical Astronomy in India,” Dictionary of Scientific Biography, vol. 15, 1978, pp. 533-633.
4. Varahamihira, Panchasiddhantika, ed. and trans. T.S. Kuppanna Sastry and K.V. Sarma, P.P.S.T. Foundation, 1993.
5. George Abraham, “The Gnomon in Early Indian Astronomy,” Indian Journal of History of Science, 16(2), 1981.
6. Takao Hayashi, “Indian Mathematics,” in The Mathematics of Egypt, Mesopotamia, China, India, and Islam, ed. Victor Katz, Princeton University Press, 2007.