Mathematics (0190-) The study of mathematics that underpins all science.

Size: px

Start display at page:

Download "Mathematics (0190-) The study of mathematics that underpins all science."

Edwin King
5 years ago
Views:

1 c Hsu Yo, Chinese mathematician, wrote, Shu Shu Chi I c (Between ) Diophantus, a 3rd century Greek mathematician, wrote the first text on Algebra. c Liu Hui, Chinese mathematician, wrote 'Hai Tao Suan Ching'. c Diophantus of Alexandria wrote the first book on algebra, 'Arithmetica' Hypatia ( ), female mathematician born in Alexandria, Egypt. She was a professor of mathematics and philosophy at the University of Alexandria Guptas invent the decimal system in India First authenticated record of decimal number system (0-9) appears in India 0625 Brahmagupta, the Indian mathematician, taught at Ujjain. c (Between ) 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 The 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. Copyright (c) , HistoryMole.com, All rights reserved. Page 1

2 1123 Omar Khayyam, Persian poet and mathematician, died. c Leonardo 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 Double-entry bookkeeping was invented in Italy about this time Benedetto Cotrugli published the first known work on double-entry bookkeeping. It was invented in Italy around Luca Pacioli, considered the father of accounting, published a book on bookkeeping Arithmetic add and subtract symbols are used in Europe 1512 Gerard Mercator was born ( ) (Gerhard Kremer) who becme a cartographer and mathematician 1520 Scipione Ferro develops a method for solving cubic equations Scipione del Ferro, Italian mathematician, solved cubic equations for the first time Peter Bennewitz, German professor of mathematics, produced the first textbook on theoretical geography, 'Cosmographia' Albrecht Durer, German engraver, compiled the first German manual on geometry. Copyright (c) , HistoryMole.com, All rights reserved. Page 2

3 1535 Niccolo Tartaglia develops a method for solving cubic equations Lodovico Ferrari solves the quartic equation 1550 Rhaticus, German mathematician, published a set of trigonometric tables Robert Recorde, English mathematician, wrote a navigational guide to China, 'The Castle of Knowledge'. He was the first person to use the '=' sign Robert Recorde published the first English treatise on algebra, 'Whetstone of Witte' John Dee, English mathematician, invented two compasses for master pilots. 5 Mar 1574 William Oughtred, mathematician and inventor of the slide rule, was born Francois Viete, French mathematician, introduced the use of letters for quantities in algebra The 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 John Dee, mathematician and warden of Manchester College in England, invented the crystal ball Galileo discovered the parabolic nature of trajectories. Copyright (c) , HistoryMole.com, All rights reserved. Page 3

4 1585 Simon Stevin, Dutch mathematician and military and civil engineer, introduces decimals into the mathematical calculations of his physics in Die Thiende Marin Mersenne ( ), 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 Ludolf van Ceulen computes Pi to twenty decimal places using inscribed and cirumscribed polygons Pierre de Fermat ( ), French mathematician, was born. His equation xn + yn = zn is called Fermat's Last Theorem and remained unproven for many years John Napier invents Napierian logarithms in 'Mirifici Logarithmorum Canonis Descriptio' 1617 Henry Briggs discusses decimal logarithms in 'Logarithmorum Chilias Prima' 1617 John Napier discusses the Napier's bones calculating method in 'Rabdologia' 1619 Reneactue Descartes discovers analytical geometry. 24 Apr 1620 John Graunt, statistician, founder of science of demography, was born English mathematician William Oughtred invents the slide rule Pierre de Fermat develops a rudimentary differential calculus Copyright (c) , HistoryMole.com, All rights reserved. Page 4

5 1634 G. Pers de Roberval shows that the area under a cycloid is three times the area of its generating circle 1637 Pierre de Fermat claims to have proven Fermat's Last Theorem in his copy of 'Diophantus Arithmetica' French mathematician and philosopher Rene Descartes introduced co-ordinate geometry Rene 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 French 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 French mathematician Blaise Pascal ( ) completes his 5-digit 'Pascaline' that can add, after three years work Blaise Pascal and Pierre de Fermat create the theory of probability 1655 John Wallis writes 'Arithmetica Infinitorum'. 8 Nov 1656 Edmond Halley, mathematician and astronomer who predicted the return of the comet which is named for him, was born Pierre de Fermat introduces Fermat's principle of least time into optics. Copyright (c) , HistoryMole.com, All rights reserved. Page 5

6 1658 Christian 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 Christopher Wren shows that the length of a cycloid is four times the diameter of its generating circle 1665 Isaac Newton invents his calculus. 26 May 1667 Abraham De Moivre, mathematician, was born Johan Bernouilli ( ), Swiss mathematician and brother of Jacob, was born Nicholas Mercator and William Brouncker discover an infinite series for the logarithm while attempting to calculate the area under a hyperbolic segment 1671 James Gregory discovers the series expansion for the inverse-tangent function 1673 Gottfried Leibniz invents his calculus 1675 Isaac Newton invents an algorithm for the computation of functional roots 16 Apr 1682 John Hadley ( ), was born, in in Enfield Chase (near East Barnet, now in London), Hertfordshire, in England Gottfreid Leibniz creates differential calculus Copyright (c) , HistoryMole.com, All rights reserved. Page 6

7 6 Jul 1687 English mathematician and physicist Isaac Newton ( ) publishes his 'Principia Mathematica' proving the theory that the Sun is at the center of the Solar System 1690 Johann Bernoulli ( ) shows that the cycloid is the solution to the isochrone problem 1691 Gottfried Leibniz discovers the technique of separation of variables for ordinary differential equations Johann (James) Bernoulli shows that a chain freely suspended from two points will form a catenary curve which has the lowest possible center of gravity Johann Bernoulli shows that the cycloid is the solution to the brachistochrone problem John Machin develops a quickly converging inverse-tangent series for Pi and computes Pi to 100 decimal places Irish philosopher, George Berkeley ( ) describes an idealist philosophy against materialism Brook Taylor develops Taylor series' 1714 Brook 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 John Hadley ( ), became a Fellow of the Royal Society. Copyright (c) , HistoryMole.com, All rights reserved. Page 7

8 1721 John Hadley ( ), built the first Newtonian reflecting telescope John Hadley ( ), invents a quadrant which measured the altitude of the Sun or of a star. This design later became the sextant Geralamo Saccheri studies what geometry would be like if Euclid's fifth postulate were false Daniel Bernoulli solves the ordinary differental equation for the vibrations of an elastic bar clamped at one end Leonhard Euler introduces the integrating factor technique for solving first order ordinary differential equations Leonhard Euler solves the Koenigsberg bridge problem Leonhard Euler solves the general homogeneous linear ordinary differential equation with constant coefficients 1739 Leonhard Euler solves differential equation for a forced harmonic oscillator and notices the resonance phenomenon Christian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes Jean d'alembert develops a theory of fluid dynamics. Copyright (c) , HistoryMole.com, All rights reserved. Page 8

9 1744 Jean-Phillipe de Cheseaux puts forth an early form of Olbers' paradox Leonhard Euler develops the Euler-Lagrange equations Leonhard Euler shows the existence of transcendental numbers Leonhard Euler develops the wave theory of light refraction and dispersion d'alembert and Euler develop a solution of equations for vibrating strings Leonhard Euler solves the partial differential equation for the vibration of a rectangular drum Thomas Bayes proves Bayes' theorem Leonhard Euler examines the partial differential equation for the vibration of a circular drum and finds one of the Bessel function solutions Joseph Lagrange develops the theory of Lagrange points Joseph Lagrange presents Lagrange's equations of motion in 'Mecanique Analytique'. This is now known as 'Lagrangian Mechanics' Karl 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. Copyright (c) , HistoryMole.com, All rights reserved. Page 9

10 1797 Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms 1799 Karl Gauss proves that every polynomial equation has a solution among the complex numbers 1806 Jean-Robert Argand associates vectors with complex numbers and studies complex number operations in geometrical terms French matematician Joseph Fourier showed that matematical functions can be represented by trigonometric series Jean-Baptiste Fourier develops harmonic analysis Karl Gauss discusses the meaning of integrals with complex limits and briefly examines the dependence of such integrals on the chosen path of integration 1812 French astronomer and mathematician Pierre Simon Laplace published the first complete account of probability theory Simeon Poisson carries out integrations along paths in the complex plane 1817 Bernard 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 Bichat, using the new mathematics of probability discovered by Laplace, begins the first application of statistics (compiled from the French Revolution) to medicine. Copyright (c) , HistoryMole.com, All rights reserved. Page 10

11 1821 William Hamilton begins his analysis of Hamilton's characteristic function Augustin-Louis Cauchy presents the Cauchy integral theorem for integration around the boundary of a rectangle Joseph Fourier formally introduces the use of dimensions for physical quantities in his 'Theorie Analytique de la Chaleur' Niels Abel partially proves that the general quintic or higher equations do not have algebraic solutions Augustin-Louis Cauchy introduces the theory of residues Augustin-Louis Cauchy presents the Cauchy integral theorem for general integration paths when he assumed that the function being integrated has a continuous derivative 1825 Peter Dirichlet and Adrien Legendre prove Fermat's Last Theorem for n= Pierre 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) George Green proves Green's theorem French matematician Evarise Galois introduced the theory of groups Russian Nikolai Lobachevski publishes his work on hyperbolic non-euclidean geometry. Copyright (c) , HistoryMole.com, All rights reserved. Page 11

12 1832 Evariste Galois presents a general condition for the solvability of algebraic equations Peter Dirichlet proves Fermat's Last Theorem for n= William Hamilton states the Principle of least action and develops Hamiltonian Mechanics William Hamilton states Hamilton's canonical equations of motion Pierre Wantsel proves that doubling the cube and trisecting the angle are impossible with only a compass and a straightedge (ruler) William Hamilton discovers the calculus of quaternions and deduces that they are non-commutative French mathematician Joseph Liouville found the first trancendental number which cannot be expressed as an agebraic equation with rational coeficients In Germany, Hermann Grassmann studied vectors with more than three dimensions George Stokes shows that solitary waves can arise from a combination of periodic waves George Stokes proves Stokes' theorem George Stokes defines the Stokes parameters of polarization In the UK George Boole published his systesm of symbolic logic now called boolean algebra. Copyright (c) , HistoryMole.com, All rights reserved. Page 12

13 1854 Arthur Cayley shows that quaternions can be used to represent rotations in four-dimensional space Bernhard Riemann introoduces the possibility of space curvature on small or large scales using Riemannian geometry Hermann von Helmholtz predicts the 'heat death' of the universe English mathematician Arthur Cayley developed calculations using ordered tables called matrices August Mobius invents the Möbius strip 1860 Maxwell and Waterston develop the equipartition theorem of statistical mechanics Felix Klein constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate Rudolph Clausius proves the scalar virial theorem Charles Hermite proves that 'e' is transcendental Georg Frobenius presents his method for finding series solutions to linear differential equations with regular singular points Charles Hermite solves the general quintic equation by means of elliptic and modular functions. Copyright (c) , HistoryMole.com, All rights reserved. Page 13

14 1881 Josiah Willard Gibbs ( ) develops vector algebra Ferdinand Lindeman proves that Pi is transcendental and that the circle cannot be squared with a compass and a ruler Hendrick Lorentz develops the first form of Lorentz transformation Jacques Hadamard and Charles de La Vallée-Poussin independently prove the prime number theorem Joseph Larmor develops the complete form of the Lorentz transformation David Hilbert presents a set of self-consistent geometric axioms in Foundations of Geometry David Hilbert states his list of 23 problems which show where further mathematical work is needed Elie Cartan develops the exterior derivative C. Runge presents a fast Fourier transform algorithm Hendrik Lorentz documents the completed Lorentz transformations Ernst Zermelo axiomatizes set theory. Copyright (c) , HistoryMole.com, All rights reserved. Page 14

15 1914 Srinivasa Ramanujan publishes Modular Equations and Approximations to Pi Eugene Wigner postulates the unreasonable effectiveness of mathematics in natural science 1961 Edward Lorenz develops chaos theory Benoit Mandelbrot develops fractal images Donald Marquardt proposes the Levenberg-Marquardt nonlinear least squares fitting algorithm Largest known prime, 2^ , is discovered Laura Nickel and Curt Noll find the 25th Mersenne prime, 2^ Shakuntala Devi, mentally multiplies two 13-digit numbers in 28 seconds Willem Klein mentally extracts 13th root of a 100-digit number in 29 seconds British scientists find new largest perfect number, 2^ Andrew Wiles proves part of the Taniyama-Shimura Conjecture and thereby proves Fermat's Last Theorem Roland Clarkson discovers the 37th known Mersenne prime, 2^ Copyright (c) , HistoryMole.com, All rights reserved. Page 15

Complex Analysis: A Round-Up

Complex Analysis: A Round-Up October 1, 2009 Sergey Lototsky, USC, Dept. of Math. *** 1 Prelude: Arnold s Principle Valdimir Igorevich Arnold (b. 1937): Russian The Arnold Principle. If a notion bears