---
title: "History of science"
chunk: 4/19
source: "https://en.wikipedia.org/wiki/History_of_science"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:38:18.549055+00:00"
instance: "kb-cron"
---

The earliest traces of mathematical knowledge in the Indian subcontinent appear with the Indus Valley Civilisation (c. 3300 – c. 1300 BCE). The people of this civilization made bricks whose dimensions were in the proportion 4:2:1, which is favorable for the stability of a brick structure. They also tried to standardize measurement of length to a high degree of accuracy. They designed a ruler—the Mohenjo-daro ruler—whose length of approximately 1.32 in (34 mm) was divided into ten equal parts. Bricks manufactured in ancient Mohenjo-daro often had dimensions that were integral multiples of this unit of length.
The Bakhshali manuscript contains problems involving arithmetic, algebra and geometry, including mensuration. The topics covered include fractions, square roots, arithmetic and geometric progressions, solutions of simple equations, simultaneous linear equations, quadratic equations and indeterminate equations of the second degree. In the 3rd century BCE, Pingala presents the Pingala-sutras,  the earliest known treatise on Sanskrit prosody. He also presents a numerical system by adding one to the sum of place values. Pingala's work also includes material related to the Fibonacci numbers, called mātrāmeru.
Indian astronomer and mathematician Aryabhata (476–550), in his Aryabhatiya (499) introduced the sine function in trigonometry and the number 0. In 628, Brahmagupta suggested that gravity was a force of attraction. He also lucidly explained the use of zero as both a placeholder and a decimal digit, along with the Hindu–Arabic numeral system now used universally throughout the world. Arabic translations of the two astronomers' texts were soon available in the Islamic world, introducing what would become Arabic numerals to the Islamic world by the 9th century.
Narayana Pandita (1340–1400) was an Indian mathematician. Plofker writes that his texts were the most significant Sanskrit mathematics treatises after those of Bhaskara II, other than the Kerala school. He wrote the Ganita Kaumudi (lit. "Moonlight of mathematics") in 1356 about mathematical operations. The work anticipated many developments in combinatorics.
Between the 14th and 16th centuries, the Kerala school of astronomy and mathematics made significant advances in astronomy and especially mathematics, including fields such as trigonometry and analysis. In particular, Madhava of Sangamagrama led advancement in analysis by providing the infinite and taylor series expansion of some trigonometric functions and pi approximation.  Parameshvara (1380–1460), presents a case of the Mean Value theorem in his commentaries on Govindasvāmi and Bhāskara II. The Yuktibhāṣā  was written by Jyeshtadeva in 1530.

==== Astronomy ====

The first textual mention of astronomical concepts comes from the Vedas, religious literature of India. According to Sarma (2008): "One finds in the Rigveda intelligent speculations about the genesis of the universe from nonexistence, the configuration of the universe, the spherical self-supporting earth, and the year of 360 days divided into 12 equal parts of 30 days each with a periodical intercalary month.".
The first 12 chapters of the Siddhanta Shiromani, written by Bhāskara in the 12th century, cover topics such as: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; syzygies; lunar eclipses; solar eclipses; latitudes of the planets; risings and settings; the moon's crescent; conjunctions of the planets with each other; conjunctions of the planets with the fixed stars; and the patas of the sun and moon. The 13 chapters of the second part cover the nature of the sphere, as well as significant astronomical and trigonometric calculations based on it.
In the Tantrasangraha treatise, Nilakantha Somayaji's updated the Aryabhatan model for the interior planets, Mercury, and Venus and the equation that he specified for the center of these planets was more accurate than the ones in European or Islamic astronomy until the time of Johannes Kepler in the 17th century. Jai Singh II of Jaipur constructed five observatories called Jantar Mantars in total, in New Delhi, Jaipur, Ujjain, Mathura and Varanasi; they were completed between 1724 and 1735.

==== Grammar ====
Some of the earliest linguistic activities can be found in Iron Age India (1st millennium BCE) with the analysis of Sanskrit for the purpose of the correct recitation and interpretation of Vedic texts. The most notable grammarian of Sanskrit was Pāṇini (c. 520–460 BCE), whose grammar formulates close to 4,000 rules for Sanskrit. Inherent in his analytic approach are the concepts of the phoneme, the morpheme and the root. The Tolkāppiyam text, composed in the early centuries of the common era, is a comprehensive text on Tamil grammar, which includes sutras on orthography, phonology, etymology, morphology, semantics, prosody, sentence structure and the significance of context in language.

==== Medicine ====

Findings from Neolithic graveyards in what is now Pakistan show evidence of proto-dentistry among an early farming culture. The ancient text Suśrutasamhitā of Suśruta describes procedures on various forms of surgery, including rhinoplasty, the repair of torn ear lobes, perineal lithotomy, cataract surgery, and several other excisions and other surgical procedures. The Charaka Samhita of Charaka describes ancient theories on human body, etiology, symptomology and therapeutics for a wide range of diseases. It also includes sections on the importance of diet, hygiene, prevention, medical education, and the teamwork of a physician, nurse and patient necessary for recovery to health.

==== Politics and state ====
An ancient Indian treatise on statecraft, economic policy and military strategy by Kautilya and Viṣhṇugupta, who are traditionally identified with Chāṇakya (c. 350–283 BCE). In this treatise, the behaviors and relationships of the people, the King, the State, the Government Superintendents, Courtiers, Enemies, Invaders, and Corporations are analyzed and documented. Roger Boesche describes the Arthaśāstra as "a book of political realism, a book analyzing how the political world does work and not very often stating how it ought to work, a book that frequently discloses to a king what calculating and sometimes brutal measures he must carry out to preserve the state and the common good."