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Timeline of scientific discoveries

Article Discussion

Template:Short description Template:See also

Template:More citations needed Template:Use dmy dates The timeline below shows the date of publication of possible major scientific breakthroughs, theories and discoveries, along with the discoverer. This article discounts 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). The timeline begins at the Bronze Age, as it is difficult to give even estimates for the timing of events prior to this, such as of the discovery of counting, natural numbers and arithmetic.

To avoid overlap with timeline of historic inventions, the timeline does 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 AgeEdit

Many early innovations of the Bronze Age were prompted by 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. The Indus Valley script remains undeciphered and there are very little surviving fragments of its writing, thus any inference about scientific discoveries in that region must be made based only on archaeological digs. The following dates are approximations.

File:Nippur cubit.JPG
The Nippur cubit-rod, c. 2650 BCE, in the Archeological Museum of Istanbul, Turkey

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  • 2650 BC: The oldest extant record of a unit of length, the cubit-rod ruler, is from Nippur.
  • 2600 BC: The oldest attested evidence for the existence of units of weight, and weighing scales date to the Fourth Dynasty of Egypt, with Deben (unit) balance weights, excavated from the reign of Sneferu, though earlier usage has been proposed.<ref>Template:Citation</ref>
  • 2100 BC: The concept of area is first recognized in Babylonian clay tablets,<ref name="Friberg2009">Template:Cite journal</ref> and 3-dimensional volume is discussed in an Egyptian papyrus. This begins the study of geometry.
  • 2100 BC: Quadratic equations, in the form of problems relating the areas and sides of rectangles, are solved by Babylonians.<ref name="Friberg2009" />
  • 2000 BC: Pythagorean triples are first discussed in Babylon and Egypt, and appear on later manuscripts such as the Berlin Papyrus 6619.<ref>Richard J. Gillings, Mathematics in the Time of the Pharaohs, Dover, New York, 1982, 161.</ref>
  • 2000 BC: Multiplication tables in a base-60, rather than base-10 (decimal), system from Babylon.<ref name="Qiu">Template:Cite journal</ref>
  • 2000 BC: Primitive positional notation for numerals is seen in the Babylonian cuneiform numerals.<ref name="Chrisomalis2">Template:Cite book</ref> However, the lack of clarity around the notion of zero made their system highly ambiguous (e.g. Template:Val would be written the same as Template:Val).<ref name="lmnz">Template:Citation</ref>
  • Early 2nd millennium BC: Similar triangles and side-ratios are studied in Egypt for the construction of pyramids, paving the way for the field of trigonometry.<ref name="Maor-20">Template:Cite book</ref>
  • 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).<ref name="Porter1999">Template:Cite book</ref>
  • 1800 BC: The Middle Kingdom of Egypt develops Egyptian fraction notation.
  • 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.<ref name="bs">Template:Citation</ref>
  • 1800 BC - 1600 BC: A Babylonian tablet uses Template:Frac = 3.125 as an approximation for Template:Pi, which has an error of 0.5%.<ref>Template:Cite book</ref><ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref><ref>Template:Cite book</ref>

Iron AgeEdit

The following dates are approximations.

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  • 600 BC: Maharshi Kanada gives the ideal of the smallest units of matter. According to him, matter consisted of indestructible minutes particles called paramanus, which are now called as atoms.<ref>{{#invoke:citation/CS1|citation

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  • 600 BC - 200 BC: The Sushruta Samhita shows an understanding of musculoskeletal structure (including joints, ligaments and muscles and their functions) (3.V).<ref name="bhisha">Template:Cite book Alt URL</ref> It refers to the cardiovascular system as a closed circuit.<ref>Template:Cite journal</ref> In (3.IX) it identifies the existence of nerves.<ref name="bhisha" />

500 BC – 1 BCEdit

The following dates are approximations.

  • 500 BC: Hippasus, a Pythagorean, discovers irrational numbers.<ref>Template:Cite journal</ref><ref>Template:Cite journal.</ref>
  • 500 BC: Anaxagoras identifies moonlight as reflected sunlight.<ref>Template:Cite magazine</ref>
  • 5th century BC: The Greeks start experimenting with straightedge-and-compass constructions.<ref name="Bold">Bold, Benjamin. Famous Problems of Geometry and How to Solve Them, Dover Publications, 1982 (orig. 1969).</ref>
  • 5th century BC: The earliest documented mention of a spherical Earth comes from the Greeks in the 5th century BC.<ref name="dicks1">Template:Cite book</ref> It is known that the Indians modeled the Earth as spherical by 300 BC<ref>

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  • 460 BC: Empedocles describes thermal expansion.<ref name="valleriani">Template:Cite book</ref>
  • Late 5th century BC: Antiphon discovers the method of exhaustion, foreshadowing the concept of a limit.
  • 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.<ref>Bhate, S. and Kak, S. (1993) Panini and Computer Science. Annals of the Bhandarkar Oriental Research Institute, vol. 72, pp. 79-94.</ref><ref>Template:Citation</ref>
  • 4th century BC: Eudoxus of Cnidus states the Archimedean property.<ref name="Knopp1951">Template:Cite book</ref>
  • 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.
  • 4th century BC: Menaechmus discovers conic sections.<ref>Template:Harvnb. "It was consequently a signal achievement on the part of Menaechmus when he disclosed that curves having the desired property were near at hand. In fact, there was a family of appropriate curves obtained from a single source – the cutting of a right circular cone by a plane perpendicular to an element of the cone. That is, Menaechmus is reputed to have discovered the curves that were later known as the ellipse, the parabola, and the hyperbola. [...] Yet the first discovery of the ellipse seems to have been made by Menaechmus as a mere by-product in a search in which it was the parabola and hyperbola that proffered the properties needed in the solution of the Delian problem."</ref>
  • 4th century BC: Menaechmus develops co-ordinate geometry.<ref>Template:Harvnb. "Menaechmus apparently derived these properties of the conic sections and others as well. Since this material has a strong resemblance to the use of coordinates, as illustrated above, it has sometimes been maintained that Menaechmus had analytic geometry. Such a judgment is warranted only in part, for certainly Menaechmus was unaware that any equation in two unknown quantities determines a curve. In fact, the general concept of an equation in unknown quantities was alien to Greek thought. It was shortcomings in algebraic notations that, more than anything else, operated against the Greek achievement of a full-fledged coordinate geometry."</ref>
  • 4th century BC: Mozi in China gives a description of the camera obscura phenomenon.
  • 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.<ref name="myopia">Template:Cite book</ref> Graeco-Roman physician Galen would later use the term "myopia" for near-sightedness.
    File:Birch bark MS from Kashmir of the Rupavatra Wellcome L0032691.jpg
    Pāṇini's Aṣṭādhyāyī, an early Indian grammatical treatise that constructs a formal system for the purpose of describing Sanskrit grammar.
  • 4th century BC: Pāṇini develops a full-fledged formal grammar (for Sanskrit).
  • Late 4th century BC: Chanakya (also known as Kautilya) establishes the field of economics with the Arthashastra (literally "Science of wealth"), a prescriptive treatise on economics and statecraft for Mauryan India.<ref name="Mabbett">Template:Cite journal</ref>
  • 4th - 3rd century BC: In Mauryan India, The Jain mathematical text Surya Prajnapati draws a distinction between countable and uncountable infinities.<ref>Template:Cite book</ref>
  • 350 BC - 50 BC: Clay tablets from (possibly Hellenistic-era) Babylon describe the mean speed theorem.<ref>Template:Cite journal</ref>
  • 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.
  • 300 BC: Finite geometric progressions are studied by Euclid in Ptolemaic Egypt.<ref>Template:Cite book</ref>
  • 300 BC: Euclid proves the infinitude of primes.<ref>Template:Citation</ref>
  • 300 BC: Euclid proves the Fundamental Theorem of Arithmetic.
  • 300 BC: Euclid discovers the Euclidean algorithm.
  • 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.<ref name="Boyer Early Trigonometry">Template:Harvnb. "Trigonometry, like other branches of mathematics, was not the work of any one man, or nation. Theorems on ratios of the sides of similar triangles had been known to, and used by, the ancient Egyptians and Babylonians. In view of the pre-Hellenic lack of the concept of angle measure, such a study might better be called "trilaterometry", or the measure of three sided polygons (trilaterals), than "trigonometry", the measure of parts of a triangle. With the Greeks we first find a systematic study of relationships between angles (or arcs) in a circle and the lengths of chords subtending these. Properties of chords, as measures of central and inscribed angles in circles, were familiar to the Greeks of Hippocrates' day, and it is likely that Eudoxus had used ratios and angle measures in determining the size of the earth and the relative distances of the sun and the moon. In the works of Euclid there is no trigonometry in the strict sense of the word, but there are theorems equivalent to specific trigonometric laws or formulas. Propositions II.12 and 13 of the Elements, for example, are the laws of cosines for obtuse and acute angles respectively, stated in geometric rather than trigonometric language and proved by a method similar to that used by Euclid in connection with the Pythagorean theorem. Theorems on the lengths of chords are essentially applications of the modern law of sines. We have seen that Archimedes' theorem on the broken chord can readily be translated into trigonometric language analogous to formulas for sines of sums and differences of angles."</ref>
  • 300 BC: Euclid's Optics introduces the field of geometric optics, making basic considerations on the sizes of images.
  • 3rd century BC: Archimedes relates problems in geometric series to those in arithmetic series, foreshadowing the logarithm.<ref>Ian Bruce (2000) "Napier’s Logarithms", American Journal of Physics 68(2):148</ref>
  • 3rd century BC: Pingala in Mauryan India studies binary numbers, making him the first to study the radix (numerical base) in history.<ref>Template:Cite journal</ref>
  • 3rd century BC: Pingala in Mauryan India describes the Fibonacci sequence.<ref name="HistoriaMathematica">Template:Citation</ref><ref name="knuth-v1">Template:Citation</ref>
  • 3rd century BC: Pingala in Mauryan India discovers the binomial coefficients in a combinatorial context and the additive formula for generating them <math>\tbinom{n}{r}=\tbinom{n-1}{r}+\tbinom{n-1}{r-1}</math>,<ref name="edwards">A. W. F. Edwards. Pascal's arithmetical triangle: the story of a mathematical idea. JHU Press, 2002. Pages 30–31.</ref><ref name="ed-cam">Template:Citation</ref> 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.<ref>Template:Cite journal</ref>
  • 3rd century BC: Eratosthenes discovers the Sieve of Eratosthenes.<ref name="nicomachus">Template:Citation</ref>
  • 3rd century BC: Archimedes derives a formula for the volume of a sphere in The Method of Mechanical Theorems.<ref>Template:Citation</ref>
  • 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.<ref>Template:Citation</ref>
  • 3rd century BC: Archimedes discovers the sum/difference identity for trigonometric functions in the form of the "Theorem of Broken Chords".<ref name="Boyer Early Trigonometry" />
  • 3rd century BC: Archimedes makes use of infinitesimals.<ref>Archimedes, The Method of Mechanical Theorems; see Archimedes Palimpsest</ref>
  • 3rd century BC: Archimedes further develops the method of exhaustion into an early description of integration.<ref>{{#invoke:citation/CS1|citation

|CitationClass=web }}</ref><ref>Template:Cite journal</ref>

  • 3rd century BC: Archimedes calculates tangents to non-trigonometric curves.<ref>Template:Harvnb. "Greek mathematics sometimes has been described as essentially static, with little regard for the notion of variability; but Archimedes, in his study of the spiral, seems to have found the tangent to a curve through kinematic considerations akin to differential calculus. Thinking of a point on the spiral 1=r = aθ as subjected to a double motion — a uniform radial motion away from the origin of coordinates and a circular motion about the origin — he seems to have found (through the parallelogram of velocities) the direction of motion (hence of the tangent to the curve) by noting the resultant of the two component motions. This appears to be the first instance in which a tangent was found to a curve other than a circle.
    Archimedes' study of the spiral, a curve that he ascribed to his friend Conon of Alexandria, was part of the Greek search for the solution of the three famous problems."</ref>
  • 3rd century BC: Archimedes uses the method of exhaustion to construct a strict inequality bounding the value of Template:Pi within an interval of 0.002.
  • 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.
  • 3rd century BC: Eratosthenes measures the circumference of the Earth.<ref>D. Rawlins: "Methods for Measuring the Earth's Size by Determining the Curvature of the Sea" and "Racking the Stade for Eratosthenes", appendices to "The Eratosthenes–Strabo Nile Map. Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Eratosthenes' Experiment?", Archive for History of Exact Sciences, v.26, 211–219, 1982</ref>
  • 260 BC: Aristarchus of Samos proposes a basic heliocentric model of the universe.<ref>Template:Cite book</ref>
  • 200 BC: Apollonius of Perga discovers Apollonius's theorem.
  • 200 BC: Apollonius of Perga assigns equations to curves.
  • 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.<ref>Template:Cite journal</ref>
  • 2nd century BC: Hipparchos discovers Axial precession.
  • 2nd century BC: Hipparchos measures the sizes of and distances to the Moon and Sun.<ref>Bowen A.C., Goldstein B.R. (1991). "Hipparchus' Treatment of Early Greek Astronomy: The Case of Eudoxus and the Length of Daytime Author(s)". Proceedings of the American Philosophical Society 135(2): 233–254.</ref>
  • 190 BC: Magic squares appear in China. The theory of magic squares can be considered the first example of a vector space.
  • 165 BC - 142 BC: Zhang Cang in Northern China is credited with the development of Gaussian elimination.<ref>Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth (Vol. 3), p 24. Taipei: Caves Books, Ltd.</ref>

1 AD – 500 ADEdit

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.

  • 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,<ref>Template:Cite book</ref> 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.<ref>Template:Cite journal</ref>
  • 60 AD: Heron's formula is discovered by Hero of Alexandria.<ref>Template:Cite book</ref>
  • 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.<ref>Template:Cite journal</ref>
  • 100: Menelaus of Alexandria describes spherical triangles, a precursor to non-Euclidean geometry.<ref name="Boyer Menelaus of Alexandria">Template:Harvnb. "In Book I of this treatise Menelaus establishes a basis for spherical triangles analogous to that of Euclid I for plane triangles. Included is a theorem without Euclidean analogue – that two spherical triangles are congruent if corresponding angles are equal (Menelaus did not distinguish between congruent and symmetric spherical triangles); and the theorem A + B + C > 180° is established. The second book of the Sphaerica describes the application of spherical geometry to astronomical phenomena and is of little mathematical interest. Book III, the last, contains the well known "theorem of Menelaus" as part of what is essentially spherical trigonometry in the typical Greek form – a geometry or trigonometry of chords in a circle. In the circle in Fig. 10.4 we should write that chord AB is twice the sine of half the central angle AOB (multiplied by the radius of the circle). Menelaus and his Greek successors instead referred to AB simply as the chord corresponding to the arc AB. If BOB' is a diameter of the circle, then chord A' is twice the cosine of half the angle AOB (multiplied by the radius of the circle)."</ref>
  • 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.
    File:Diophantus-cover.png
    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.
  • 3rd century: Diophantus discusses linear diophantine equations.
  • 3rd century: Diophantus uses a primitive form of algebraic symbolism, which is quickly forgotten.<ref>Kurt Vogel, "Diophantus of Alexandria." in Complete Dictionary of Scientific Biography, Encyclopedia.com, 2008. Quote: The symbolism that Diophantus introduced for the first time, and undoubtedly devised himself, provided a short and readily comprehensible means of expressing an equation... Since an abbreviation is also employed for the word ‘equals’, Diophantus took a fundamental step from verbal algebra towards symbolic algebra.</ref>
  • 210: Negative numbers are accepted as numeric by the late Han-era Chinese text The Nine Chapters on the Mathematical Art.<ref>* Struik, Dirk J. (1987). A Concise History of Mathematics. New York: Dover Publications. pp. 32–33. "In these matrices we find negative numbers, which appear here for the first time in history."</ref> Later, Liu Hui of Cao Wei (during the Three Kingdoms period) writes down laws regarding the arithmetic of negative numbers.<ref name="Hodgkin">Template:Cite book</ref>
  • 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.<ref>Template:Cite news</ref>
  • 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.<ref>

{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> 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.Template:Sfn 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,<ref>Reimer, L., and Reimer, W. Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians, Vol. 2. 1995. pp. 22-22. Parsippany, NJ: Pearson Education, Inc. as Dale Seymor Publications. Template:ISBN.</ref> as recorded in al-Uqlidisi's later commentary on Indian mathematics.<ref name="Berggren">Template:Cite book</ref>
  • 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.<ref>Hayashi (2008), Aryabhata I.Template:Full citation needed</ref>
  • By 499: Aryabhata's work shows the use of the modern fraction notation, known as bhinnarasi.<ref name="jeff">{{#invoke:citation/CS1|citation

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File:P. Lund, Inv. 35a.jpg
Example of the early Greek symbol for zero (lower right corner) from a 2nd-century papyrus
  • 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).<ref name="arbhsimp">Template:Harvnb. "He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes."</ref>
  • 499: Aryabhata discovers the formula for the simplicial numbers (the sums of consecutive cube numbers).<ref name="arbhsimp" />
  • 499: Aryabhata discovers Bezout's identity, a foundational result to the theory of principal ideal domains.<ref name="Datta">Template:Cite book</ref>
  • 499: Aryabhata develops Kuṭṭaka, an algorithm very similar to the Extended Euclidean algorithm.<ref name="Datta" />
  • 499: Aryabhata describes a numerical algorithm for finding cube roots.<ref>Template:Britannica</ref><ref>Template:Cite arXiv</ref>
  • 499: Aryabhata develops an algorithm to solve the Chinese remainder theorem.<ref>Template:Citation</ref>
  • 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).<ref>The concept of Indian heliocentrism has been advocated by B. L. van der Waerden, Das heliozentrische System in der griechischen, persischen und indischen Astronomie. Naturforschenden Gesellschaft in Zürich. Zürich:Kommissionsverlag Leeman AG, 1970.</ref><ref>B.L. van der Waerden, "The Heliocentric System in Greek, Persian and Hindu Astronomy", in David A. King and George Saliba, ed., From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. S. Kennedy, Annals of the New York Academy of Science, 500 (1987), pp. 529–534.</ref><ref>Template:Cite book</ref> This claim is based on his description of the planetary period about the Sun (śīghrocca), but has been met with criticism.<ref>Noel Swerdlow, "Review: A Lost Monument of Indian Astronomy," Isis, 64 (1973): 239–243.</ref>
  • 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.<ref name="Ansari">

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500 AD – 1000 ADEdit

File:Indian Rashtrakuta Empire map.svg
The age of Imperial Karnataka was a period of significant advancement in Indian mathematics.

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.

  • 6th century: Varahamira in the Gupta empire is the first to describe comets as astronomical phenomena, and as periodic in nature.<ref name="comets">Template:Cite book</ref>
  • 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.<ref>Morris R. Cohen and I. E. Drabkin (eds. 1958), A Source Book in Greek Science (p. 220), with several changes. Cambridge, MA: Harvard University Press, as referenced by David C. Lindberg (1992), The Beginnings of Western Science: The European Scientific Tradition in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450, University of Chicago Press, p. 305, Template:ISBN
  • Note the influence of Philoponus' statement on Galileo's Two New Sciences (1638)</ref> 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.<ref>Henry Thomas Colebrooke. Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara, London 1817, p. 339 (online)</ref>
  • 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.<ref>Template:Citation</ref>
  • 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.<ref>Template:Citation</ref>
  • 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).Template:Citation needed
  • 9th century: Mahāvīra discovers the first algorithm for writing fractions as Egyptian fractions,<ref>Template:Citation</ref> which is in fact a slightly more general form of the Greedy algorithm for Egyptian fractions.
  • 816: Jain mathematician Virasena describes the integer logarithm.<ref>Template:Citation</ref>
  • 850: Mahāvīra derives the expression for the binomial coefficient in terms of factorials, <math>\tbinom{n}{r}=\tfrac{n!}{r!(n-r)!}</math>.<ref name="ed-cam" />
  • 10th century AD: Manjula in India discovers the derivative, deducing that the derivative of the sine function is the cosine.<ref name="pcock">Template:Citation</ref>
  • 10th century AD: Kashmiri<ref>Bina Chatterjee (introduction by), The Khandakhadyaka of Brahmagupta, Motilal Banarsidass (1970), p. 13</ref><ref>Lallanji Gopal, History of Agriculture in India, Up to C. 1200 A.D., Concept Publishing Company (2008), p. 603</ref><ref>Kosla Vepa, Astronomical Dating of Events & Select Vignettes from Indian History, Indic Studies Foundation (2008), p. 372</ref><ref>Dwijendra Narayan Jha (edited by), The feudal order: state, society, and ideology in early medieval India, Manohar Publishers & Distributors (2000), p. 276</ref> astronomer Bhaṭṭotpala lists names and estimates periods of certain comets.<ref name="comets" />
  • 975: Halayudha organizes the binomial coefficients into a triangle, i.e. Pascal's triangle.<ref name="ed-cam" />
  • 984: Ibn Sahl discovers Snell's law.<ref>http://spie.org/etop/2007/etop07fundamentalsII.pdf," R. Rashed credited Ibn Sahl with discovering the law of refraction [23], usually called Snell’s law and also Snell and Descartes’ law."</ref><ref>Template:Cite book</ref>

1000 AD – 1500 ADEdit


(cf. Abel B. Franco (October 2003). "Avempace, Projectile Motion, and Impetus Theory", Journal of the History of Ideas 64 (4), p. 521-546 [528].)</ref>

  • 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.<ref name="RG">{{#invoke:citation/CS1|citation

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  • 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,<ref>{{#invoke:citation/CS1|citation

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16th centuryEdit

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

  • 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.
  • 16th century: François Viète discovers Viète's formula for Template:Pi.<ref name="beckmann">Template:Cite book</ref>1500: Scipione del Ferro solves the special cubic equation <math>x^3 = px + q</math>.<ref>Template:Cite book</ref><ref name=":0">Template:Cite book</ref>
  • Late 16th century: Tycho Brahe proves that comets are astronomical (and not atmospheric) phenomena.
  • 1517: Nicolaus Copernicus develops the quantity theory of money and states the earliest known form of Gresham's law: ("Bad money drowns out good").<ref name="Volckart 1997">Template:Cite journal</ref>
  • 1543: Nicolaus Copernicus develops a heliocentric model, rejecting Aristotle's Earth-centric view, would be the first quantitative heliocentric model in history.
  • 1543: Vesalius: pioneering research into human anatomy.
  • 1545: Gerolamo Cardano discovers complex numbers.<ref>Template:Cite book</ref>
  • 1556: Niccolò Tartaglia introduces parenthesis.
  • 1557: Robert Recorde introduces the equal sign.<ref>Template:Cite book</ref><ref>Robert Recorde, The Whetstone of Witte (London, England: John Kyngstone, 1557), p. 236 (although the pages of this book are not numbered). From the chapter titled "The rule of equation, commonly called Algebers Rule" (p. 236): "Howbeit, for easie alteration of equations. I will propounde a fewe examples, bicause the extraction of their rootes, maie the more aptly bee wroughte. And to avoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in worke use, a paire of paralleles, or Gemowe [twin, from gemew, from the French gemeau (twin / twins), from the Latin gemellus (little twin)] lines of one lengthe, thus: = , bicause noe .2. thynges, can be moare equalle." (However, for easy manipulation of equations, I will present a few examples in order that the extraction of roots may be more readily done. And to avoid the tedious repetition of these words "is equal to", I will substitute, as I often do when working, a pair of parallels or twin lines of the same length, thus: = , because no two things can be more equal.)</ref>
  • 1564: Gerolamo Cardano is the first to produce a systematic treatment of probability.<ref name="Westfall">{{#invoke:citation/CS1|citation

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17th centuryEdit

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18th centuryEdit

1800–1849Edit

1850–1899Edit

1900–1949Edit

1950–1999Edit

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21st centuryEdit

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  • 2003: Grigori Perelman presents proof of the Poincaré Conjecture.
  • 2003: The Human Genome Project sequences the human genome with a 92% accuracy.<ref>{{#invoke:citation/CS1|citation

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  • 2019: The first image of a black hole is captured, using eight different telescopes taking simultaneous pictures, timed with extremely precise atomic clocks. [1]
  • 2020: NASA and SOFIA (Stratospheric Observatory for Infrared Astronomy) discover about Template:Convert of surface water in one of the Moon's largest visible craters.<ref>{{#invoke:citation/CS1|citation

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  • 2022: The standard reference gene, GRCh38.p14, of the human genome, is fully sequenced and contains 3.1 billion base pairs.<ref>{{#invoke:citation/CS1|citation

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ReferencesEdit

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External linksEdit

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