---
title: "Timeline of scientific discoveries"
chunk: 3/7
source: "https://en.wikipedia.org/wiki/Timeline_of_scientific_discoveries"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:28:31.534973+00:00"
instance: "kb-cron"
---

1st to 4th century: A precursor to long division, known as "galley division" is developed at some point. Its discovery is generally believed to have originated in India around the 4th century AD, although Singaporean mathematician Lam Lay Yong claims that the method is found in the Chinese text The Nine Chapters on the Mathematical Art, from the 1st century AD.
60 AD: Heron's formula is discovered by Hero of Alexandria.
2nd century: Ptolemy formalises the epicycles of Apollonius.
2nd century: Ptolemy publishes his Optics, discussing colour, reflection, and refraction of light, and including the first known table of refractive angles.
2nd century: Galen studies the anatomy of pigs.
100: Menelaus of Alexandria describes spherical triangles, a precursor to non-Euclidean geometry.
150: The Almagest of Ptolemy contains evidence of the Hellenistic zero. Unlike the earlier Babylonian zero, the Hellenistic zero could be used alone, or at the end of a number. However, it was usually used in the fractional part of a numeral, and was not regarded as a true arithmetical number itself.
150: Ptolemy's Almagest contains practical formulae to calculate latitudes and day lengths.
3rd century: Diophantus discusses linear diophantine equations.
3rd century: Diophantus uses a primitive form of algebraic symbolism, which is quickly forgotten.
210: Negative numbers are accepted as numeric by the late Han-era Chinese text The Nine Chapters on the Mathematical Art. Later, Liu Hui of Cao Wei (during the Three Kingdoms period) writes down laws regarding the arithmetic of negative numbers.
By the 4th century: A square root finding algorithm with quartic convergence, known as the Bakhshali method (after the Bakhshali manuscript which records it), is discovered in India.
By the 4th century: The present Hindu–Arabic numeral system with place-value numerals develops in Gupta-era India, and is attested in the Bakhshali Manuscript of Gandhara. The superiority of the system over existing place-value and sign-value systems arises from its treatment of zero as an ordinary numeral.
4th to 5th centuries: The modern fundamental trigonometric functions, sine and cosine, are described in the Siddhantas of India. This formulation of trigonometry is an improvement over the earlier Greek functions, in that it lends itself more seamlessly to polar co-ordinates and the later complex interpretation of the trigonometric functions.
By the 5th century: The decimal separator is developed in India, as recorded in al-Uqlidisi's later commentary on Indian mathematics.
By the 5th century: The elliptical orbits of planets are discovered in India by at least the time of Aryabhata, and are used for the calculations of orbital periods and eclipse timings.
By 499: Aryabhata's work shows the use of the modern fraction notation, known as bhinnarasi.
499: Aryabhata gives a new symbol for zero and uses it for the decimal system.
499: Aryabhata discovers the formula for the square-pyramidal numbers (the sums of consecutive square numbers).
499: Aryabhata discovers the formula for the simplicial numbers (the sums of consecutive cube numbers).
499: Aryabhata discovers Bezout's identity, a foundational result to the theory of principal ideal domains.
499: Aryabhata develops Kuṭṭaka, an algorithm very similar to the Extended Euclidean algorithm.
499: Aryabhata describes a numerical algorithm for finding cube roots.
499: Aryabhata develops an algorithm to solve the Chinese remainder theorem.
499: Historians speculate that Aryabhata may have used an underlying heliocentric model for his astronomical calculations, which would make it the first computational heliocentric model in history (as opposed to Aristarchus's model in form). This claim is based on his description of the planetary period about the Sun (śīghrocca), but has been met with criticism.
499: Aryabhata creates a particularly accurate eclipse chart. As an example of its accuracy, 18th century scientist Guillaume Le Gentil, during a visit to Pondicherry, India, found the Indian computations (based on Aryabhata's computational paradigm) of the duration of the lunar eclipse of 30 August 1765 to be short by 41 seconds, whereas his charts (by Tobias Mayer, 1752) were long by 68 seconds.

== 500 AD – 1000 AD ==

The Golden Age of Indian mathematics and astronomy continues after the end of the Gupta empire, especially in Southern India during the era of the Rashtrakuta, Western Chalukya and Vijayanagara empires of Karnataka, which variously patronised Hindu and Jain mathematicians. In addition, the Middle East enters the Islamic Golden Age through contact with other civilisations, and China enters a golden period during the Tang and Song dynasties.