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Mathematics

Mathematics (0190-)

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The study of mathematics that underpins all science.
Timeline
c.    0190  CEHsu Yo, Chinese mathematician, wrote, Shu Shu Chi I
c.    0200  CE(Between 200-300) Diophantus, a 3rd century Greek mathematician, wrote the first text on Algebra.
c.    0250  CELiu Hui, Chinese mathematician, wrote 'Hai Tao Suan Ching'.
c.    0250  CEDiophantus of Alexandria wrote the first book on algebra, 'Arithmetica'.
    0370  CEHypatia (370-415), female mathematician born in Alexandria, Egypt. She was a professor of mathematics and philosophy at the University of Alexandria.
    0520  CEGuptas invent the decimal system in India.
    0595  CEFirst authenticated record of decimal number system (0-9) appears in India
    0625  CEBrahmagupta, the Indian mathematician, taught at Ujjain.
c.    0800  CE(Between 800-900) Muhammed ibn-Musa al-Khwarizmi, Arab mathematician and astronomer, wrote his 'ab al-jabr w' al muqabalah' (the science of reduction and comparison). The work dealt with solving equations. It was the first time that algebra was discussed as a separate branch of mathematics. In the 12th century it was translated into Latin as 'Ludus algebrae et almucgrabalaeque.'
    1091  CEThe Norman conquest of Saracen-held Sicily provided access to Arabic manuscripts that showed a place-notated decimal system that forms the basis of modern mathematics.
    1123  CEOmar Khayyam, Persian poet and mathematician, died.
c.    1170  CELeonardo Fibonacci, Italian mathematician, was born. It is believed Fibonacci discovered the relationship of what are now referred to as Fibonacci numbers while studying the Great Pyramid of Giza in Egypt and by investigating how fast rabbits could breed in ideal circumstances.
    1340  CEDouble-entry bookkeeping was invented in Italy about this time.
    1458  CEBenedetto Cotrugli published the first known work on double-entry bookkeeping. It was invented in Italy around 1340.
    1494  CELuca Pacioli, considered the father of accounting, published a book on bookkeeping.
    1500  CEArithmetic add and subtract symbols are used in Europe
    1512  CEGerard Mercator was born (1512-1592) (Gerhard Kremer) who becme a cartographer and mathematician
    1520  CEScipione Ferro develops a method for solving cubic equations.
    1520  CEScipione del Ferro, Italian mathematician, solved cubic equations for the first time.
    1524  CEPeter Bennewitz, German professor of mathematics, produced the first textbook on theoretical geography, 'Cosmographia'.
    1525  CEAlbrecht Durer, German engraver, compiled the first German manual on geometry.
    1535  CENiccolo Tartaglia develops a method for solving cubic equations.
    1540  CELodovico Ferrari solves the quartic equation
    1550  CERhaticus, German mathematician, published a set of trigonometric tables.
    1556  CERobert Recorde, English mathematician, wrote a navigational guide to China, 'The Castle of Knowledge'. He was the first person to use the '=' sign.
    1557  CERobert Recorde published the first English treatise on algebra, 'Whetstone of Witte'.
    1558  CEJohn Dee, English mathematician, invented two compasses for master pilots.
  5 Mar 1574  CEWilliam Oughtred, mathematician and inventor of the slide rule, was born.
    1576  CEFrancois Viete, French mathematician, introduced the use of letters for quantities in algebra.
    1576  CEThe basilica of San Petronio was erected by Egnatio Danti, a mathematician and Dominican friar who worked for Cosimo I dei Medici, the Grand Duke of Tuscany. The structure included a solar observatory. Danti also advised Pope Gregory on calendar reform.
    1580  CEJohn Dee, mathematician and warden of Manchester College in England, invented the crystal ball.
    1583  CEGalileo discovered the parabolic nature of trajectories.
    1585  CESimon Stevin, Dutch mathematician and military and civil engineer, introduces decimals into the mathematical calculations of his physics in Die Thiende.
    1588  CEMarin Mersenne (1588-1648), French monk and mathematician, was born. Mersenne numbers, which come from multiplying 2 over and over and subtracting one, are named after him. A small percentage of mersenne numbers are also prime numbers.
    1596  CELudolf van Ceulen computes Pi to twenty decimal places using inscribed and cirumscribed polygons.
    1601  CEPierre de Fermat (1601-1665), French mathematician, was born. His equation xn + yn = zn is called Fermat's Last Theorem and remained unproven for many years.
    1614  CEJohn Napier invents Napierian logarithms in 'Mirifici Logarithmorum Canonis Descriptio'
    1617  CEHenry Briggs discusses decimal logarithms in 'Logarithmorum Chilias Prima'
    1617  CEJohn Napier discusses the Napier's bones calculating method in 'Rabdologia'
    1619  CEReneactue Descartes discovers analytical geometry.
 24 Apr 1620  CEJohn Graunt, statistician, founder of science of demography, was born.
    1622  CEEnglish mathematician William Oughtred invents the slide rule.
    1629  CEPierre de Fermat develops a rudimentary differential calculus
    1634  CEG. Pers de Roberval shows that the area under a cycloid is three times the area of its generating circle
    1637  CEPierre de Fermat claims to have proven Fermat's Last Theorem in his copy of 'Diophantus Arithmetica'.
    1637  CEFrench mathematician and philosopher Rene Descartes introduced co-ordinate geometry.
    1637  CERene Descartes, French mathematician, began using the final letters of the alphabet to represent unknowns. He published his 6 tome 'Discours de la Methode' in Leyden.
    1642  CEFrench mathamatician Blaise Pascal develops a mechanical calculator at the age of 21. He did so to ease the drudgery of his tax-collector father, but it was considered too complicated.
    1645  CEFrench mathematician Blaise Pascal (1623-1662) completes his 5-digit 'Pascaline' that can add, after three years work.
    1654  CEBlaise Pascal and Pierre de Fermat create the theory of probability
    1655  CEJohn Wallis writes 'Arithmetica Infinitorum'.
  8 Nov 1656  CEEdmond Halley, mathematician and astronomer who predicted the return of the comet which is named for him, was born.
    1657  CEPierre de Fermat introduces Fermat's principle of least time into optics.
    1658  CEChristian Huygens experimentally discovers that balls placed anywhere inside an inverted cycloid reach the lowest point of the cycloid in the same time and hence shows that the cycloid is the isochrone.
    1658  CEChristopher Wren shows that the length of a cycloid is four times the diameter of its generating circle
    1665  CEIsaac Newton invents his calculus.
 26 May 1667  CEAbraham De Moivre, mathematician, was born.
    1667  CEJohan Bernouilli (1667-1748), Swiss mathematician and brother of Jacob, was born.
    1668  CENicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment
    1671  CEJames Gregory discovers the series expansion for the inverse-tangent function
    1673  CEGottfried Leibniz invents his calculus
    1675  CEIsaac Newton invents an algorithm for the computation of functional roots
 16 Apr 1682  CEJohn Hadley (1682-1744), was born, in in Enfield Chase (near East Barnet, now in London), Hertfordshire, in England.
    1684  CEGottfreid Leibniz creates differential calculus
  6 Jul 1687  CEEnglish mathematician and physicist Isaac Newton (1642-1727) publishes his 'Principia Mathematica' proving the theory that the Sun is at the center of the Solar System
    1690  CEJohann Bernoulli (1667-1748) shows that the cycloid is the solution to the isochrone problem
    1691  CEGottfried Leibniz discovers the technique of separation of variables for ordinary differential equations.
    1691  CEJohann (James) Bernoulli shows that a chain freely suspended from two points will form a catenary curve which has the lowest possible center of gravity.
    1696  CEJohann Bernoulli shows that the cycloid is the solution to the brachistochrone problem.
    1706  CEJohn Machin develops a quickly converging inverse-tangent series for Pi and computes Pi to 100 decimal places.
    1710  CEIrish philosopher, George Berkeley (1685-1753) describes an idealist philosophy against materialism.
    1712  CEBrook Taylor develops Taylor series'
    1714  CEBrook Taylor derives the fundamental frequency of a stretched vibrating string in terms of its tension and mass per unit length by solving an ordinary differential equation.
    1716  CEJohn Hadley (1682-1744), became a Fellow of the Royal Society.
    1721  CEJohn Hadley (1682-1744), built the first Newtonian reflecting telescope.
    1730  CEJohn Hadley (1682-1744), invents a quadrant which measured the altitude of the Sun or of a star. This design later became the sextant.
    1733  CEGeralamo Saccheri studies what geometry would be like if Euclid's fifth postulate were false.
    1734  CEDaniel Bernoulli solves the ordinary differental equation for the vibrations of an elastic bar clamped at one end.
    1734  CELeonhard Euler introduces the integrating factor technique for solving first order ordinary differential equations.
    1736  CELeonhard Euler solves the Koenigsberg bridge problem.
 
  1739  CELeonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients
 
 
  1739  CELeonhard Euler solves differential equation for a forced harmonic oscillator and notices the resonance phenomenon.
 
 
  1742  CEChristian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes.
 
 
  1744  CEJean d'Alembert develops a theory of fluid dynamics.
 
 
  1744  CEJean-Phillipe de Cheseaux puts forth an early form of Olbers' paradox.
 
 
  1744  CELeonhard Euler develops the Euler-Lagrange equations.
 
 
  1744  CELeonhard Euler shows the existence of transcendental numbers.
 
 
  1746  CELeonhard Euler develops the wave theory of light refraction and dispersion.
 
 
  1747  CEd'Alembert and Euler develop a solution of equations for vibrating strings.
 
 
  1759  CELeonhard Euler solves the partial differential equation for the vibration of a rectangular drum.
 
 
  1761  CEThomas Bayes proves Bayes' theorem.
 
 
  1764  CELeonhard Euler examines the partial differential equation for the vibration of a circular drum and finds one of the Bessel function solutions.
 
 
  1772  CEJoseph Lagrange develops the theory of Lagrange points.
 
 
  1788  CEJoseph Lagrange presents Lagrange's equations of motion in 'Mecanique Analytique'. This is now known as 'Lagrangian Mechanics'.
 
 
  1796  CEKarl Gauss presents a method for constructing a heptadecagon using only a compass and straightedge. he also shows that only polygons with certain numbers of sides can be constructed.
 
 
  1797  CECaspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms
 
 
  1799  CEKarl Gauss proves that every polynomial equation has a solution among the complex numbers
 
 
  1806  CEJean-Robert Argand associates vectors with complex numbers and studies complex number operations in geometrical terms.
 
 
  1807  CEFrench matematician Joseph Fourier showed that matematical functions can be represented by trigonometric series.
 
 
  1811  CEJean-Baptiste Fourier develops harmonic analysis.
 
 
  1811  CEKarl Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration
 
 
  1812  CEFrench astronomer and mathematician Pierre Simon Laplace published the first complete account of probability theory.
 
 
  1815  CESimeon Poisson carries out integrations along paths in the complex plane
 
 
  1817  CEBernard Bolzano presents Bolzano's theorem. This shows that a continuous function which is negative at one point and positive at another point must be zero for at least one point in between.
 
 
  1820  CEBichat, using the new mathematics of probability discovered by Laplace, begins the first application of statistics (compiled from the French Revolution) to medicine.
 
 
  1821  CEWilliam Hamilton begins his analysis of Hamilton's characteristic function.
 
 
  1822  CEAugustin-Louis Cauchy presents the Cauchy integral theorem for integration around the boundary of a rectangle.
 
 
  1822  CEJoseph Fourier formally introduces the use of dimensions for physical quantities in his 'Theorie Analytique de la Chaleur'.
 
 
  1824  CENiels Abel partially proves that the general quintic or higher equations do not have algebraic solutions.
 
 
  1825  CEAugustin-Louis Cauchy introduces the theory of residues.
 
 
  1825  CEAugustin-Louis Cauchy presents the Cauchy integral theorem for general integration paths when he assumed that the function being integrated has a continuous derivative
 
 
  1825  CEPeter Dirichlet and Adrien Legendre prove Fermat's Last Theorem for n=5.
 
 
  1825  CEPierre Laplace completes his study of gravitation, the stability of the solar system, tides, the precession of the equinoxes, the libration of the Moon and Saturn's rings in 'Mécanique Céleste' (Celestial Mechanics).
 
 
  1828  CEGeorge Green proves Green's theorem.
 
 
  1829  CEFrench matematician Evarise Galois introduced the theory of groups.
 
 
  1829  CERussian Nikolai Lobachevski publishes his work on hyperbolic non-Euclidean geometry.
 
 
  1832  CEEvariste Galois presents a general condition for the solvability of algebraic equations.
 
 
  1832  CEPeter Dirichlet proves Fermat's Last Theorem for n=14.
 
 
  1834  CEWilliam Hamilton states the Principle of least action and develops Hamiltonian Mechanics.
 
 
  1835  CEWilliam Hamilton states Hamilton's canonical equations of motion.
 
 
  1837  CEPierre Wantsel proves that doubling the cube and trisecting the angle are impossible with only a compass and a straightedge (ruler).
 
 
  1843  CEWilliam Hamilton discovers the calculus of quaternions and deduces that they are non-commutative.
 
 
  1844  CEFrench mathematician Joseph Liouville found the first trancendental number which cannot be expressed as an agebraic equation with rational coeficients.
 
 
  1844  CEIn Germany, Hermann Grassmann studied vectors with more than three dimensions.
 
 
  1849  CEGeorge Stokes shows that solitary waves can arise from a combination of periodic waves.
 
 
  1850  CEGeorge Stokes proves Stokes' theorem.
 
 
  1852  CEGeorge Stokes defines the Stokes parameters of polarization.
 
 
  1854  CEIn the UK George Boole published his systesm of symbolic logic now called boolean algebra.
 
 
  1854  CEArthur Cayley shows that quaternions can be used to represent rotations in four-dimensional space.
 
 
  1854  CEBernhard Riemann introoduces the possibility of space curvature on small or large scales using Riemannian geometry.
 
 
  1854  CEHermann von Helmholtz predicts the 'heat death' of the universe.
 
 
  1858  CEEnglish mathematician Arthur Cayley developed calculations using ordered tables called matrices.
 
 
  1858  CEAugust Mobius invents the Möbius strip
 
 
  1860  CEMaxwell and Waterston develop the equipartition theorem of statistical mechanics.
 
 
  1870  CEFelix Klein constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate.
 
 
  1870  CERudolph Clausius proves the scalar virial theorem.
 
 
  1873  CECharles Hermite proves that 'e' is transcendental.
 
 
  1873  CEGeorg Frobenius presents his method for finding series solutions to linear differential equations with regular singular points.
 
 
  1878  CECharles Hermite solves the general quintic equation by means of elliptic and modular functions.
 
 
  1881  CEJosiah Willard Gibbs (1839-1903) develops vector algebra.
 
 
  1882  CEFerdinand Lindeman proves that Pi is transcendental and that the circle cannot be squared with a compass and a ruler.
 
 
  1895  CEHendrick Lorentz develops the first form of Lorentz transformation.
 
 
  1896  CEJacques Hadamard and Charles de La Vallée-Poussin independently prove the prime number theorem.
 
 
  1898  CEJoseph Larmor develops the complete form of the Lorentz transformation.
 
 
  1899  CEDavid Hilbert presents a set of self-consistent geometric axioms in Foundations of Geometry.
 
 
  1900  CEDavid Hilbert states his list of 23 problems which show where further mathematical work is needed.
 
 
  1901  CEElie Cartan develops the exterior derivative.
 
 
  1903  CEC. Runge presents a fast Fourier transform algorithm.
 
 
  1904  CEHendrik Lorentz documents the completed Lorentz transformations.
 
 
  1908  CEErnst Zermelo axiomatizes set theory.
 
 
  1914  CESrinivasa Ramanujan publishes Modular Equations and Approximations to Pi.
 
 
  1960  CEEugene Wigner postulates the unreasonable effectiveness of mathematics in natural science
 
 
  1961  CEEdward Lorenz develops chaos theory.
 
 
  1962  CEBenoit Mandelbrot develops fractal images.
 
 
  1962  CEDonald Marquardt proposes the Levenberg-Marquardt nonlinear least squares fitting algorithm.
 
 
  1973  CELargest known prime, 2^132049-1, is discovered.
 
 
  1978  CELaura Nickel and Curt Noll find the 25th Mersenne prime, 2^21701-1.
 
 
  1980  CEShakuntala Devi, mentally multiplies two 13-digit numbers in 28 seconds.
 
 
  1981  CEWillem Klein mentally extracts 13th root of a 100-digit number in 29 seconds.
 
 
  1992  CEBritish scientists find new largest perfect number, 2^756839-1.
 
 
  1993  CEAndrew Wiles proves part of the Taniyama-Shimura Conjecture and thereby proves Fermat's Last Theorem.
 
 
  1998  CERoland Clarkson discovers the 37th known Mersenne prime, 2^3021377-1.
 
 
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