---
title: "Timeline of scientific discoveries"
chunk: 4/7
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"
---

6th century: Varahamira in the Gupta empire is the first to describe comets as astronomical phenomena, and as periodic in nature.
525: John Philoponus in Byzantine Egypt describes the notion of inertia, and states that the motion of a falling object does not depend on its weight. His radical rejection of Aristotlean orthodoxy lead him to be ignored in his time
628: Brahmagupta states the arithmetic rules for addition, subtraction, and multiplication with zero, as well as the multiplication of negative numbers, extending the basic rules for the latter found in the earlier The Nine Chapters on the Mathematical Art.
628: Brahmagupta writes down Brahmagupta's identity, an important lemma in the theory of Pell's equation.
628: Brahmagupta produces an infinite (but not exhaustive) number of solutions to Pell's equation.
628: Brahmagupta provides an explicit solution to the quadratic equation.
628: Brahmagupta discovers Brahmagupta's formula, a generalization of Heron's formula to cyclic quadrilaterals.
628: Brahmagupta discovers second-order interpolation, in the form of Brahmagupta's interpolation formula.
628: Brahmagupta invents a symbolic mathematical notation, which is then adopted by mathematicians through India and the Near East, and eventually Europe.
629: Bhāskara I produces the first approximation of a transcendental function with a rational function, in the sine approximation formula that bears his name.
9th century: Jain mathematician Mahāvīra writes down a factorisation for the difference of cubes.
9th century: Algorisms (arithmetical algorithms on numbers written in place-value system) are described by al-Khwarizmi in his kitāb al-ḥisāb al-hindī (Book of Indian computation) and kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī (Addition and subtraction in Indian arithmetic).
9th century: Mahāvīra discovers the first algorithm for writing fractions as Egyptian fractions, which is in fact a slightly more general form of the Greedy algorithm for Egyptian fractions.
816: Jain mathematician Virasena describes the integer logarithm.
850: Mahāvīra derives the expression for the binomial coefficient in terms of factorials, 
  
    
      
        
          
            
              
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10th century AD: Manjula in India discovers the derivative, deducing that the derivative of the sine function is the cosine.
10th century AD: Kashmiri astronomer Bhaṭṭotpala lists names and estimates periods of certain comets.
975: Halayudha organizes the binomial coefficients into a triangle, i.e. Pascal's triangle.
984: Ibn Sahl discovers Snell's law.

== 1000 AD – 1500 AD ==
11th century: Alhazen discovers the formula for the simplicial numbers defined as the sums of consecutive quartic powers.
11th century: Alhazen systematically studies optics and refraction, which would later be important in making the connection between geometric (ray) optics and wave theory.
11th century: Shen Kuo discovers atmospheric refraction and provides the correct explanation of rainbow phenomenon
11th century: Shen Kuo discovers the concepts of true north and magnetic declination.
11th century: Shen Kuo develops the field of geomorphology and natural climate change.
1000: Al-Karaji uses mathematical induction.
1058: al-Zarqālī in Islamic Spain discovers the apsidal precession of the Sun.
12th century: Bhāskara II develops the Chakravala method, solving Pell's equation.
12th century: Al-Tusi develops a numerical algorithm to solve cubic equations.
12th century: Jewish polymath Baruch ben Malka in Iraq formulates a qualitative form of Newton's second law for constant forces.
1220s: Robert Grosseteste writes on optics, and the production of lenses, while asserting models should be developed from observations, and predictions of those models verified through observation, in a precursor to the scientific method.
1267: Roger Bacon publishes his Opus Majus, compiling translated Classical Greek, and Arabic works on mathematics, optics, and alchemy into a volume, and details his methods for evaluating the theories, particularly those of Ptolemy's 2nd century Optics, and his findings on the production of lenses, asserting  “theories supplied by reason should be verified by sensory data, aided by instruments, and corroborated by trustworthy witnesses", in a precursor to the peer reviewed scientific method.
1290: Eyeglasses are invented in Northern Italy, possibly Pisa, demonstrating knowledge of human biology and optics, to offer bespoke works that compensate for an individual human disability.
1295: Scottish priest Duns Scotus writes about the mutual beneficence of trade.
14th century: French priest Jean Buridan provides a basic explanation of the price system.
1380: Madhava of Sangamagrama develops the Taylor series, and derives the Taylor series representation for the sine, cosine and arctangent functions, and uses it to produce the Leibniz series for π.
1380: Madhava of Sangamagrama discusses error terms in infinite series in the context of his infinite series for π.
1380: Madhava of Sangamagrama discovers continued fractions and uses them to solve transcendental equations.
1380: The Kerala school develops convergence tests for infinite series.
1380: Madhava of Sangamagrama solves transcendental equations by iteration.
1380: Madhava of Sangamagrama discovers the most precise estimate of π in the medieval world through his infinite series, a strict inequality with uncertainty 3e-13.
15th century: Parameshvara discovers a formula for the circumradius of a quadrilateral.
1480: Madhava of Sangamagrama found pi and that it was infinite.
1500: Nilakantha Somayaji discovers an infinite series for π.
1500: Nilakantha Somayaji develops a model similar to the Tychonic system. His model has been described as mathematically more efficient than the Tychonic system due to correctly considering the equation of the centre and latitudinal motion of Mercury and Venus.

== 16th century ==
The Scientific Revolution occurs in Europe around this period, greatly accelerating the progress of science and contributing to the rationalization of the natural sciences. 