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Bhāskara II, also known as Bhāskarāchārya, was an Indian polymath, mathematician, astronomer and engineer. From verses in his main work, Siddhāṁta Śiromaṇī, it can be inferred that he was born in 1114 in Vijjadavida (Vijjalavida) and living in the Satpuda mountain ranges of Western Ghats, believed to be the town of Patana in Chalisgaon, located in present-day Khandesh region of Maharashtra by scholars. In a temple in Maharashtra, an inscription supposedly created by his grandson Changadeva, lists Bhaskaracharya's ancestral lineage for several generations before him as well as two generations after him. Henry Colebrooke who was the first European to translate (1817) Bhaskaracharya II's mathematical classics refers to the family as Maharashtrian Brahmins residing on the banks of the Godavari.
Keļallur Nīlakaṇṭha Somayāji, also referred to as Keļallur Comatiri, was a major mathematician and astronomer 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 called the Aryabhatiya Bhasya. In this Bhasya, Nilakantha had discussed infinite series expansions of trigonometric functions and problems of algebra and spherical geometry. Grahapariksakrama is a manual on making observations in astronomy based on instruments of the time.
Acharya Pingala was an ancient Indian poet and mathematician, and the author of the Chhandaḥśāstra, also called the Pingala-sutras, the earliest known treatise on Sanskrit prosody.
The Baudhāyana sūtras are a group of Vedic Sanskrit texts which cover dharma, daily ritual, mathematics and is one of the oldest Dharma-related texts of Hinduism that have survived into the modern age from the 1st-millennium BCE. They belong to the Taittiriya branch of the Krishna Yajurveda school and are among the earliest texts of the genre.
A. A. Krishnaswami Ayyangar (1892–1953) was an Indian mathematician. He received his M.A. in Mathematics at the age of 18 from Pachaiyappa's College, and subsequently taught mathematics there. In 1918, he joined the mathematics department of the University of Mysore and retired from there in 1947. He was born in a Tamil Brahmin family. He died in June 1953. He was the father of the Kannada poet and scholar A. K. Ramanujan.
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics, important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II,Varāhamihira, and Madhava. The decimal number system in use today was first recorded in Indian mathematics. Indian mathematicians made early contributions to the study of the concept of zero as a number, negative numbers, arithmetic, and algebra. In addition, trigonometry was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there. These mathematical concepts were transmitted to the Middle East, China, and Europe and led to further developments that now form the foundations of many areas of mathematics.
Mādhava of Sangamagrāma (Mādhavan) was an Indian mathematician and astronomer who is considered to be the founder of the Kerala school of astronomy and mathematics in the Late Middle Ages. Madhava made pioneering contributions to the study of infinite series, calculus, trigonometry, geometry and algebra. He was the first to use infinite series approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their limit-passage to infinity".
Jyeṣṭhadeva was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama. He is best known as the author of Yuktibhāṣā, a commentary in Malayalam of Tantrasamgraha by Nilakantha Somayaji (1444–1544). In Yuktibhāṣā, Jyeṣṭhadeva had given complete proofs and rationale of the statements in Tantrasamgraha. This was unusual for traditional Indian mathematicians of the time. The Yuktibhāṣā is now believed to contain the essential elements of calculus like Taylor and infinity series. Jyeṣṭhadeva also authored Drk-karana, a treatise on astronomical observations.
The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and its original discoveries seem to have ended with Narayana Bhattathiri (1559–1632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa, written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha.
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built upon syntheses of Greek mathematics and Indian mathematics. Important developments of the period include extension of the place-value system to include decimal fractions, the systematised study of algebra and advances in geometry and trigonometry.
The Ishango bone, discovered at the "Fisherman Settlement" of Ishango in the Democratic Republic of the Congo, is a bone tool and possible mathematical device that dates to the Upper Paleolithic era. The curved bone is dark brown in color, about 10 centimeters in length, and features a sharp piece of quartz affixed to one end, perhaps for engraving. Because the bone has been narrowed, scraped, polished, and engraved to a certain extent, it is no longer possible to determine what animal the bone belonged to, although it is assumed to have been a mammal.
Yuktibhāṣā, also known as Gaṇita-yukti-bhāṣā and Gaṇitanyāyasaṅgraha, is a major treatise on mathematics and astronomy, written by the Indian astronomer Jyesthadeva of the Kerala school of mathematics around 1530. The treatise, written in Malayalam, is a consolidation of the discoveries by Madhava of Sangamagrama, Nilakantha Somayaji, Parameshvara, Jyeshtadeva, Achyuta Pisharati, and other astronomer-mathematicians of the Kerala school. It also exists in a Sanskrit version, with unclear author and date, composed as a rough translation of the Malayalam original.
Chitrabhanu was a mathematician of the Kerala school and a student of Nilakantha Somayaji. He was a Nambudiri brahmin from the town of Covvaram near present day Trissur. He is noted for a karaṇa, a concise astronomical manual, dated to 1530, an algebraic treatise, and a commentary on a poetic text. Nilakantha and he were both teachers of Shankara Variyar.
Tantrasamgraha, or Tantrasangraha, is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics. The treatise was completed in 1501 CE. It consists of 432 verses in Sanskrit divided into eight chapters. Tantrasamgraha had spawned a few commentaries: Tantrasamgraha-vyakhya of anonymous authorship and Yuktibhāṣā authored by Jyeshtadeva in about 1550 CE. Tantrasangraha, together with its commentaries, bring forth the depths of the mathematical accomplishments the Kerala school of astronomy and mathematics, in particular the achievements of the remarkable mathematician of the school Sangamagrama Madhava. In his Tantrasangraha, Nilakantha revised Aryabhata's model for the planets Mercury and Venus. According to George G Joseph his equation of the centre for these planets remained the most accurate until the time of Johannes Kepler in the 17th century.
Sankara Variyar was an astronomer-mathematician of the Kerala school of astronomy and mathematics. His family were employed as temple-assistants in the temple at Tṛkkuṭaveli near modern Ottapalam.
Govinda Bhaṭṭathiri was an Indian astrologer and astronomer who flourished in Kerala during the thirteenth century CE.
A Passage to Infinity: Medieval Indian Mathematics from Kerala and Its Impact is a 2009 book by George Gheverghese Joseph chronicling the social and mathematical origins of the Kerala school of astronomy and mathematics. The book discusses the highlights of the achievements of Kerala school and also analyses the hypotheses and conjectures on the possible transmission of Kerala mathematics to Europe.
Burjor Avari (1938–2019) was a teacher of South Asian history at the Manchester Metropolitan University. He received an MBE in recognition of his work in multicultural education.
The Crest of the Peacock: Non-European Roots of Mathematicsis a book authored by George Gheverghese Joseph, and was first published by Princeton University Press in 1991. The book was brought out as a response to view of the history of mathematics epitomized by Morris Kline's statement that, comparing to what the Greeks achieved, "the mathematics of Egyptians and Babylonians is the scrawling of children just learning to write, as opposed to great literature", criticised by Joseph as "Eurocentric". The third edition of the book was released in 2011.
Thrikkandiyoor is a village in Tirur Block in Malappuram district of Kerala state in India. The village is known for a Shiva Temple located at the heart of the village. Devotees of Shiva believe that the idol in the temple was installed by Parashurama, the
References
- "An Interview with George Gherverghese Joseph | Mathematical Association of America".
- A Passage to Infinity
- The Crest of the Peacock
- Joseph, George Gheverghese (24 October 2010). The Crest of the Peacock. ISBN 9780691135267.
- "Indians predated Newton 'discovery' by 250 years". The University of Manchester News. 13 August 2007. Retrieved 2020-07-04.
- Krishnamachari, Suganthy (29 October 2015). "A passage to Europe?". The Hindu. ISSN 0971-751X . Retrieved 2020-07-04– via www.thehindu.com.