# Timeline of scientific discoveries

The timeline below shows the date of publication of possible major scientific breakthroughs, theories and discoveries, along with the discoverer. For the purposes of this article, we do not regard mere speculation as discovery, although imperfect reasoned arguments, arguments based on elegance/simplicity, and numerically/experimentally verified conjectures qualify (as otherwise no scientific discovery before the late 19th century would count). We begin our timeline at the Bronze Age, as it is difficult to estimate the timeline before this point, such as of the discovery of counting, natural numbers and arithmetic.

To avoid overlap with Timeline of historic inventions, we do not list examples of documentation for manufactured substances and devices unless they reveal a more fundamental leap in the theoretical ideas in a field.

## Bronze Age

Many early innovations of the Bronze Age were requirements resulting from the increase in trade, and this also applies to the scientific advances of this period. For context, the major civilizations of this period are Egypt, Mesopotamia, and the Indus Valley, with Greece rising in importance towards the end of the third millennium BC. It is to be noted that the Indus Valley script remains undeciphered and there are very little surviving fragments of its writing, thus any inference about scientific discoveries in the region must be made based only on archaeological digs.

### Mathematics

#### Numbers, measurement and arithmetic

• Around 3000 BC: Units of measurement are developed in the major Bronze Age civilisations: Egypt, Mesopotamia, Elam and the Indus Valley. The Indus Valley may have been the major innovator on this, as the first measurement devices (rulers, protractors, weighing scales) were invented in Lothal in Gujarat, India.
• 1800 BC: Fractions were first studied by the Egyptians in their study of Egyptian fractions.

#### Algebra

• 2100 BC: Quadratic equations, in the form of problems relating the areas and sides of rectangles, are solved by Babylonians..

#### Number theory and discrete mathematics

• 2000 BC: Pythagorean triples are first discussed in Babylon and Egypt, and appear on later manuscripts such as the Berlin Papyrus 6619.

#### Numerical mathematics and algorithms

• 2000 BC: Multiplication tables in Babylon.
• 1800 BC – 1600 BC: A numerical approximation for the square root of two, accurate to 6 decimal places, is recorded on YBC 7289, a Babylonian clay tablet believed to belong to a student.
• 19th to 17th century BCE: A Babylonian tablet uses ​258 as an approximation for π, which has an error of 0.5%.
• Early 2nd millennium BCE: The Rhind Mathematical Papyrus (a copy of an older Middle Kingdom text) contains the first documented instance of inscribing a polygon (in this case, an octagon) into a circle to estimate the value of π.

#### Notation and conventions

• 3000 BC: The first deciphered numeral system is that of the Egyptian numerals, a sign-value system (as opposed to a place-value system).
• 2000 BC: Primitive positional notation for numerals is seen in the Babylonian cuneiform numerals. However, the lack of clarity around the notion of zero made their system highly ambiguous (e.g. 13200 would be written the same as 132).

### Astronomy

• Early 2nd millennium BC: The periodicity of planetary phenomenon is recognised by Babylonian astronomers.

### Biology and anatomy

• Early 2nd millennium BC: Ancient Egyptians study anatomy, as recorded in the Edwin Smith Papyrus. They identified the heart and its vessels, liver, spleen, kidneys, hypothalamus, uterus, and bladder, and correctly identified that blood vessels emanated from the heart (however, they also believed that tears, urine, and semen, but not saliva and sweat, originated in the heart, see Cardiocentric hypothesis).

## Iron Age

### Mathematics

#### Geometry and trigonometry

• c. 700 BC: The Pythagoras theorem is discovered by Baudhayana in the Hindu Shulba Sutras in Upanishadic India. However, Indian mathematics, especially North Indian mathematics, generally did not have a tradition of communicating proofs, and it is not fully certain that Baudhayana or Apastamba knew of a proof.

#### Number theory and discrete mathematics

• c. 700 BC: Pell's equations are first studied by Baudhayana in India, the first diophantine equations known to be studied.

### Biology and anatomy

• 600 BC – 200 BC: The Sushruta Samhita (3.V) shows an understanding of musculoskeletal structure (including joints, ligaments and muscles and their functions).
• 600 BC – 200 BC: The Sushruta Samhita refers to the cardiovascular system as a closed circuit.
• 600 BC – 200 BC: The Sushruta Samhita (3.IX) identifies the existence of nerves.

## 500 BC – 0 AD

The Greeks make numerous advances in mathematics and astronomy through the Archaic, Classical and Hellenistic periods.

### Mathematics

#### Logic and proof

• 4th century BC: Greek philosophers study the properties of logical negation.
• 4th century BC: The first true formal system is constructed by Pāṇini in his Sanskrit grammar.
• c. 300 BC: Greek mathematician Euclid in the Elements describes a primitive form of formal proof and axiomatic systems. However, modern mathematicians generally believe that his axioms were highly incomplete, and that his definitions were not really used in his proofs.

#### Algebra

• 5th century BC: Possible date of the discovery of the triangular numbers (i.e. the sum of consecutive integers), by the Pythagoreans.
• c. 300 BC: Finite geometric progressions are studied by Euclid in Ptolemaic Egypt.
• 3rd century BC: Archimedes relates problems in geometric series to those in arithmetic series, foreshadowing the logarithm.
• 190 BC: Magic squares appear in China. The theory of magic squares can be considered the first example of a vector space.
• 165-142 BC: Zhang Cang in Northern China is credited with the development of Gaussian elimination.

#### Number theory and discrete mathematics

• c. 500 BC: Hippasus, a Pythagorean, discovers irrational numbers.
• 4th century BC: Thaetetus shows that square roots are either integer or irrational.
• 4th century BC: Thaetetus enumerates the Platonic solids, an early work in graph theory.
• 3rd century BC: Pingala in Mauryan India describes the Fibonacci sequence.
• c. 300 BC: Euclid proves the infinitude of primes.
• c. 300 BC: Euclid proves the Fundamental Theorem of Arithmetic.
• c. 300 BC: Euclid discovers the Euclidean algorithm.
• 3rd century BC: Pingala in Mauryan India discovers the binomial coefficients in a combinatorial context and the additive formula for generating them ${\tbinom {n}{r}}={\tbinom {n-1}{r}}+{\tbinom {n-1}{r-1}}$ , i.e. a prose description of Pascal's triangle, and derived formulae relating to the sums and alternating sums of binomial coefficients. It has been suggested that he may have also discovered the binomial theorem in this context.
• 3rd century BC: Eratosthenes discovers the Sieve of Eratosthenes.

#### Geometry and trigonometry

• 5th century BC: The Greeks start experimenting with straightedge-and-compass constructions.
• 4th century BC: Menaechmus discovers conic sections.
• 4th century BC: Menaechmus develops co-ordinate geometry.
• c. 300 BC: Euclid publishes the Elements, a compendium on classical Euclidean geometry, including: elementary theorems on circles, definitions of the centers of a triangle, the tangent-secant theorem, the law of sines and the law of cosines.
• 3rd century BC: Archimedes derives a formula for the volume of a sphere in The Method of Mechanical Theorems.
• 3rd century BC: Archimedes calculates areas and volumes relating to conic sections, such as the area bounded between a parabola and a chord, and various volumes of revolution.
• 3rd century BC: Archimedes discovers the sum/difference identity for trigonometric functions in the form of the "Theorem of Broken Chords".
• c. 200 BC: Apollonius of Perga discovers Apollonius's theorem.
• c. 200 BC: Apollonius of Perga assigns equations to curves.

#### Numerical mathematics and algorithms

• 3rd century BC: Archimedes uses the method of exhaustion to construct a strict inequality bounding the value of π within an interval of 0.002.

### Physics

#### Astronomy

• 5th century BC: The earliest documented mention of a spherical Earth comes from the Greeks in the 5th century BC. It is known that the Indians modeled the Earth as spherical by 300 BC
• 500 BC: Anaxagoras identifies moonlight as reflected sunlight.
• 260 BC: Aristarchus of Samos proposes a basic heliocentric model of the universe.
• c. 200 BC: Apollonius of Perga develops epicycles. While an incorrect model, it was a precursor to the development of Fourier series.
• 2nd century BC: Hipparchos discovers the apsidal precession of the Moon's orbit.
• 2nd century BC: Hipparchos discovers Axial precession.

#### Mechanics

• 3rd century BC: Archimedes develops the field of statics, introducing notions such as the center of gravity, mechanical equilibrium, the study of levers, and hydrostatics.
• 350-50 BC: Clay tablets from (possibly Hellenistic-era) Babylon describe the mean speed theorem.

#### Optics

• 4th century BC: Mozi in China gives a description of the camera obscura phenomenon.
• c. 300 BC: Euclid's Optics introduces the field of geometric optics, making basic considerations on the sizes of images.

#### Thermal physics

• 460 BC: Empedocles describes thermal expansion.

### Biology and anatomy

• 4th century BC: Around the time of Aristotle, a more empirically founded system of anatomy is established, based on animal dissection. In particular, Praxagoras makes the distinction between arteries and veins.
• 4th century BC: Aristotle differentiates between near-sighted and far-sightedness. Graeco-Roman physician Galen would later use the term "myopia" for near-sightedness.

### Social science

#### Economics

• Late 4th century BC: Kautilya establishes the field of economics with the Arthashastra (literally "Science of wealth"), a prescriptive treatise on economics and statecraft for Mauryan India.

#### Linguistics

• 4th century BC: Pāṇini develops a full-fledged formal grammar (for Sanskrit).

### Astronomical and geospatial measurements

• 3rd century BC: Eratosthenes measures the circumference of the Earth.
• 2nd century BC: Hipparchos measures the sizes of and distances to the moon and sun.

Mathematics and astronomy flourish during the Golden Age of India (4th to 6th centuries AD) under the Gupta Empire. Meanwhile, Greece and its colonies have entered the Roman period in the last few decades of the preceding millennium, and Greek science is negatively impacted by the Fall of the Western Roman Empire and the economic decline that follows.

### Mathematics

#### Algebra

• 499 AD: Aryabhata discovers the formula for the square-pyramidal numbers (the sums of consecutive square numbers).
• 499 AD: Aryabhata discovers the formula for the simplicial numbers (the sums of consecutive cube numbers).

#### Geometry and trigonometry

• c. 60 AD: Heron's formula is discovered by Hero of Alexandria.
• c. 100 AD: Menelaus of Alexandria describes spherical triangles, a precursor to non-Euclidean geometry.
• 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.

#### Numerical mathematics and algorithms

• By the 4th century AD: a square root finding algorithm with quartic convergence, known as the Bakhshali method (after the Bakhshali manuscript which records it), is discovered in India.
• 499 AD: Aryabhata describes a numerical algorithm for finding cube roots.
• 499 AD: Aryabhata develops an algorithm to solve the Chinese remainder theorem.
• 1st to 4th century AD: 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.

#### Notation and conventions Diophantus' Arithmetica (pictured: a Latin translation from 1621) contained the first known use of symbolic mathematical notation. Despite the relative decline in the importance of the sciences during the Roman era, several Greek mathematicians continued to flourish in Alexandria.
• c. 150 AD: 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.
• 3rd century AD: Diophantus uses a primitive form of algebraic symbolism, which is quickly forgotten.
• By the 4th century AD: 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.
• By the 5th century AD: The decimal separator is developed in India, as recorded in al-Uqlidisi's later commentary on Indian mathematics.
• By 499 AD: Aryabhata's work shows the use of the modern fraction notation, known as bhinnarasi.

### Physics

#### Astronomy

• c. 150 AD: Ptolemy's Almagest contains practical formulae to calculate latitudes and day lengths.
• 2nd century AD: Ptolemy formalises the epicycles of Apollonius.
• By the 5th century AD: 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.
• 499 AD: 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.

#### Optics

• 2nd century - Ptolemy publishes his Optics, discussing colour, reflection, and refraction of light, and Including the first known table of refractive angles.

### Biology and anatomy

• 2nd century AD: Galen studies the anatomy of pigs.

### Astronomical and geospatial measurements

• 499 AD: 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.

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.

### Mathematics

#### Numbers, measurement and arithmetic

• 628 AD: Brahmagupta writes down rules for arithmetic involving zero, as well as for negative numbers, extending the basic rules for the latter introduced earlier by Liu Hui.

#### Number theory and discrete mathematics

• 628 AD: Brahmagupta writes down Brahmagupta's identity, an important lemma in the theory of Pell's equation.
• 628 AD: Brahmagupta produces an infinite (but not exhaustive) number of solutions to Pell's equation.
• c. 850 AD: Mahāvīra derives the expression for the binomial coefficient in terms of factorials, ${\tbinom {n}{r}}={\tfrac {n!}{r!(n-r)!}}$ .
• c. 975 AD: Halayudha organizes the binomial coefficients into a triangle, i.e. Pascal's triangle.

#### Analysis

• 10th century AD: Manjula in India discovers the derivative, deducing that the derivative of the sine function is the cosine.

#### Probability and statistics

• 9th century AD: Al-Kindi's Manuscript on Deciphering Cryptographic Messages contains the first use of statistical inference.

#### Numerical mathematics and algorithms

• 628 AD: Brahmagupta discovers second-order interpolation, in the form of Brahmagupta's interpolation formula.
• 629 AD: Bhāskara I produces the first approximation of a transcendental function with a rational function, in the sine approximation formula that bears his name.
• 816 AD: Jain mathematician Virasena describes the integer logarithm.
• 9th century AD: 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 AD: 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.

#### Notation and conventions

• 628 AD: Brahmagupta invents a symbolic mathematical notation, which is then adopted by mathematicians through India and the Near East, and eventually Europe.

### Physics

#### Astronomy

• 6th century AD: Varahamira in the Gupta empire is the first to describe comets as astronomical phenomena, and as periodic in nature.

#### Mechanics

• c. 525 AD: 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.

### Mathematics

#### Algebra

• 11th century: Alhazen discovers the formula for the simplicial numbers defined as the sums of consecutive quartic powers.

#### Geometry and trigonometry

• 15th century: Parameshvara discovers a formula for the circumradius of a quadrilateral.

#### Numerical mathematics and algorithms

• 12th century AD: al-Tusi develops a numerical algorithm to solve cubic equations.
• 1380 AD: 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.

### Physics

#### Astronomy

• 1058 AD: al-Zarqālī in Islamic Spain discovers the apsidal precession of the sun.
• c. 1500 AD: 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.

#### Mechanics

• 12th century AD: Jewish polymath Baruch ben Malka in Iraq formulates a qualitative form of Newton's second law for constant forces.

#### Optics

• 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
• c1290 - Eye Glasses are invented in Northern Italy, possibly Pisa, demonstrating knowledge of human biology[citation needed] and optics, to offer bespoke works that compensate for an individual human disability.

### Social science

#### Economics

• 14th century AD: French priest Jean Buridan provides a basic explanation of the price system.

### Philosophy of science

• 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.

## 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.

### Mathematics

#### Algebra

• c. 1500: Scipione del Ferro solves the special cubic equation $x^{3}=px+q$ .
• 16th century: Gerolamo Cardano solves the general cubic equation (by reducing them to the case with zero quadratic term).
• 16th century: Lodovico Ferrari solves the general quartic equation (by reducing it to the case with zero quartic term).
• 16th century: François Viète discovers Vieta's formulas.

#### Probability and statistics

• 1564: Gerolamo Cardano is the first to produce a systematic treatment of probability.

#### Notation and conventions

Various pieces of modern symbolic notation were introduced in this period, notably:

### Physics

#### Astronomy

• 1543: Nicolaus Copernicus develops a heliocentric model, which assuming Aryabhata did not use a heliocentric model, would be the first quantitative heliocentric model in history.
• Late 16th century: Tycho Brahe proves that comets are astronomical (and not atmospheric) phenomena.

### Biology and anatomy

• 1543 – Vesalius: pioneering research into human anatomy

### Social science

#### Economics

• 1517: Nicolaus Copernicus develops the quantity theory of money and states the earliest known form of Gresham's law: ("Bad money drowns out good").

## 21st century

• 2020 – NASA and SOFIA (Stratospheric Observatory of Infrared Astronomy) discovered about 12oz of surface water in one of the moon's largest visible crater. This has sparked new motivation to venture into space. We continue to discover water is more common than we originally thought.