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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| History of mathematics | 7/13 | https://en.wikipedia.org/wiki/History_of_mathematics | reference | science, encyclopedia | 2026-05-05T03:59:56.476741+00:00 | kb-cron |
Around 500 AD, Aryabhata wrote the Aryabhatiya, a slim volume, written in verse, intended to supplement the rules of calculation used in astronomy and mathematical mensuration, though with no feeling for logic or deductive methodology. It is in the Aryabhatiya that the decimal place-value system first appears. Several centuries later, the Muslim mathematician Abu Rayhan Biruni described the Aryabhatiya as a "mix of common pebbles and costly crystals". In the 7th century, Brahmagupta identified the Brahmagupta theorem, Brahmagupta's identity and Brahmagupta's formula, and for the first time, in Brahma-sphuta-siddhanta, he lucidly explained the use of zero as both a placeholder and decimal digit, and explained the Hindu–Arabic numeral system. It was from a translation of this Indian text on mathematics (c. 770) that Islamic mathematicians were introduced to this numeral system, which they adapted as Arabic numerals. Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, all of which evolved from the Brahmi numerals. Each of the roughly dozen major scripts of India has its own numeral glyphs. In the 10th century, Halayudha's commentary on Pingala's work contains a study of the Fibonacci sequence and Pascal's triangle. In the 12th century, Bhāskara II, who lived in southern India, wrote extensively on the mathematical knowledge of his time. In his astronomical work, he described results that have been interpreted by later scholars as resembling early infinitesimal methods. His writings include ideas approximately equivalent to infinitesimals and a special case of the mean value theorem in inverse interpolation of sine.He also made significant contributions to algebra, including methods for solving indeterminate equations of the type later known as Pell equations, which he treated using cyclic procedures such as the chakravāla method. In the 14th century, Narayana Pandita completed his Ganita Kaumudi. Also in the 14th century, Madhava of Sangamagrama, the founder of the Kerala School of Mathematics, found the Madhava–Leibniz series and obtained from it a transformed series, whose first 21 terms he used to compute the value of π as 3.14159265359. Madhava also found the Madhava-Gregory series to determine the arctangent, the Madhava-Newton power series to determine sine and cosine and the Taylor approximation for sine and cosine functions. In the 16th century, Jyesthadeva consolidated many of the Kerala School's developments and theorems in the Yukti-bhāṣā. has been argued that certain ideas of calculus like infinite series and taylor series of some trigonometry functions, were transmitted to Europe in the 16th century via Jesuit missionaries and traders who were active around the ancient port of Muziris at the time and, as a result, directly influenced later European developments in analysis and calculus. However, other scholars argue that the Kerala School did not formulate a systematic theory of differentiation and integration, and that there is not any direct evidence of their results being transmitted outside Kerala.
== Islamic empires ==