This is in continuation of my earlier article History of Mathematics Preface Bakshali Manuscript.We may now look some ancient Indian treatises on Mathematics.The names that come to one’ s mind are Aryabhatta and Varahamihira.
Aryabhata (Sanskrit: आर्यभट, ISO: Āryabhaṭa) or Aryabhata I (476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old) and the Arya-siddhanta.Aryabhata (Sanskrit: आर्यभट, ISO: Āryabhaṭa) or Aryabhata I(476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the Āryabhaṭīya (which mentions that in 3600 Kali Yuga, 499 CE, he was 23 years old) and the Arya-siddhanta.…
His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers , algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.
The Arya-siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata’s contemporary, Varahamihira, and later mathematicians and commentators, including Brahmagupta and Bhaskara.
Brahmagupta (c. 598 – c. 668 CE) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the Brāhmasphuṭasiddhānta (BSS, “correctly established doctrine of Brahma”, dated 628), a theoretical treatise, and the Khaṇḍakhādyaka (“edible bite”, dated 665), a more practical text.
- Brāhmasphuṭasiddhānta,composed in 628 CE.
- Khaṇḍakhādyaka,composed in 665 CE.
- Grahaṇārkajñāna,(ascribed in one manuscript.
Lalla (c. 720–790 CE) was an Indian mathematician, astronomer, and astrologer who belonged to a family of astronomers.
Śiṣyadhīvṛddhidatantra is his work.
Panini 5th Century BC
We know Panini to be the grammarian of Sanskrit Language . He was an illustrious Mathematician too. His notation was similar to modern mathematical notation, and used metarules, transformations, and recursion.Pingala (roughly 3rd–1st centuries BC) in his treatise of prosody uses a device corresponding to a binary numeral system. His discussion of the combinatorics of meters corresponds to an elementary version of the binomial theorem. Pingala’s work also contains the basic ideas of Fibonacci numbers. Read this Mathematical Structures of Ashtadyayi
Pingala 3- 2 Century BC
Another great mathematician of ancient India.ancient Indian poet and mathematician, the author of the Chandaḥśāstra (also called Pingala-sutras), the earliest known treatise on Metres.( Chandas,Vedic Metres).The Chandaḥśāstra presents the first known description of a binary numeral system in connection with the systematic enumeration of meters with fixed patterns of short and long syllables. The discussion of the combinatorics of meter corresponds to the binomial theorem. Halāyudha’s commentary includes a presentation of Pascal’s triangle (called meruprastāra). Pingala’s work also includes material related to the Fibonacci numbers, called mātrāmeru.
The Surya Siddhanta,
The Surya Siddhanta ‘The text is known from a 15th-century CE palm-leaf manuscript, and several newer manuscripts. It was composed or revised c. 800 CE from an earlier text also called the Surya Siddhanta.Now date is arbitrarily assigned as 4/5 Century BC!(According to al-Biruni, the 11th-century Persian scholar and polymath, a text named the Surya Siddhanta was written by one Lāta.The second verse of the first chapter of the Surya Siddhanta attributes the words to an emissary of the solar deity of Hindu mythology, Surya, as recounted to an asura (a mythical being) called Maya at the end of Satya Yuga, the first golden age of Hindu mythology, around two million years ago.Maya has Tamil connection. I shall detail this in another post.The Surya Siddhanta thus consists of cryptic rules in Sanskrit verse. It is a compendium of astronomy that is easier to remember, transmit and use as reference or aid for the experienced, but does not aim to offer commentary, explanation or proof. The text has 14 chapters and 500 shlokas. It is one of the eighteen astronomical siddhanta (treatises), but thirteen of the eighteen are believed to be lost to history. The Surya Siddhanta text has survived since the ancient times, has been the best known and the most referred astronomical text in the Indian tradition. Suryasiddhantha
Shall write on Vedic Mathematical Structures, to be followed by Tamil concepts on Mathematics.