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## #1 2015-09-27 15:39:53

ganesh
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Registered: 2005-06-28
Posts: 22,686

### Greatest Mathematicians from 1 CE ...

Greatest Mathematicians  from 1 CE (also called AD) :

10-70 AD    Heron (or Hero) of Alexandria    : Greek : Heron’s Formula for finding the area of a triangle from its side lengths, Heron’s Method for iteratively computing a square root

90-168 AD:  Ptolemy : Greek/Egyptian : Develop even more detailed trigonometry tables

200 AD : Sun Tzu : Chinese : First definitive statement of Chinese Remainder Theorem

200 AD :     Indian : Refined and perfected decimal place value number system

200-284 AD : Diophantus : Greek :    Diophantine Analysis of complex algebraic problems, to find rational solutions to equations with several unknowns

220-280 AD : Liu Hui : Chinese : Solved linear equations using a matrices (similar to Gaussian elimination), leaving roots unevaluated, calculated value of π correct to five decimal places, early forms of integral and differential calculus

400 AD :     Indian : “Surya Siddhanta” contains roots of modern trigonometry, including first real use of sines, cosines, inverse sines, tangents and secants

476-550 AD : Aryabhata     Indian : Definitions of trigonometric functions, complete and accurate sine and versine tables, solutions to simultaneous quadratic equations, accurate approximation for π (and recognition that π is an irrational number)

598-668 AD : Brahmagupta : Indian : Basic mathematical rules for dealing with zero (+, - and x), negative numbers, negative roots of quadratic equations, solution of quadratic equations with two unknowns

600-680 AD : Bhaskara I : Indian    First to write numbers in Hindu-Arabic decimal system with a circle for zero, remarkably accurate approximation of the sine function

780-850 AD : Muhammad Al-Khwarizmi :Persian : Advocacy of the Hindu numerals 1 - 9 and 0 in Islamic world, foundations of modern algebra, including algebraic methods of “reduction” and “balancing”, solution of polynomial equations up to second degree

908-946 AD : Ibrahim ibn Sinan : Arabic    Continued Archimedes' investigations of areas and volumes, tangents to a circle

953-1029 AD : Muhammad Al-Karaji : Persian    First use of proof by mathematical induction, including to p
prove the binomial theorem

966-1059 AD :    Ibn al-Haytham (Alhazen) : Persian/Arabic    Derived a formula for the sum of fourth powers using a readily generalizable method, “Alhazen's problem”, established beginnings of link between algebra and geometry

1048-1131 AD :  Omar Khayyam :    Persian    Generalized Indian methods for extracting square and cube roots to include fourth, fifth and higher roots, noted existence of different sorts of cubic equations

1114-1185 AD :Bhaskara II : Indian    Established that dividing by zero yields infinity, found solutions to quadratic, cubic and quartic equations (including negative and irrational solutions) and to second order Diophantine equations, introduced some preliminary concepts of calculus

1170-1250 AD :Leonardo of Pisa  (Fibonacci) : Italian :     Fibonacci Sequence of numbers, advocacy of the use of the Hindu-Arabic numeral system in Europe, Fibonacci's identity (product of two sums of two squares is itself a sum of two squares)

1201-1274 AD: Nasir al-Din al-Tusi : Persian :
Developed field of spherical trigonometry, formulated law of sines for plane triangles

1202-1261 AD : Qin Jiushao :     Chinese    : Solutions to quadratic, cubic and higher power equations using a method of repeated approximations

1238-1298 AD : Yang Hui :     Chinese    Culmination of Chinese “magic” squares, circles and triangles, Yang Hui’s Triangle (earlier version of Pascal’s Triangle of binomial co-efficients)

1267-1319 AD : Kamal al-Din al-Farisi    Persian    Applied theory of conic sections to solve optical problems, explored amicable numbers, factorization and combinatorial methods

1350-1425 AD : Madhava : Indian :    Use of infinite series of fractions to give an exact formula for π, sine formula and other trigonometric functions, important step towards development of calculus

1323-1382 AD : Nicole Oresme : French : System of rectangular coordinates, such as for a time-speed-distance graph, first to use fractional exponents, also worked on infinite series
1446-1517 AD : Luca Pacioli :    Italian : Influential book on arithmetic, geometry and book-keeping, also introduced standard symbols for plus and minus

1499-1557 AD : Niccolò Fontana Tartaglia : Italian    Formula for solving all types of cubic equations, involving first real use of complex numbers (combinations of real and imaginary numbers), Tartaglia’s Triangle (earlier version of Pascal’s Triangle)

1501-1576 AD : Gerolamo Cardano : Italian :    Published solution of cubic and quartic equations (by Tartaglia and Ferrari), acknowledged existence of imaginary numbers (based on √-1)

1522-1565 AD : Lodovico Ferrari :    Italian : Devised formula for solution of quartic equations

1550-1617 AD : John Napier :    British : Invention of natural logarithms, popularized the use of the decimal point, Napier’s Bones tool for lattice multiplication

1588-1648 AD : Marin Mersenne :    French : Clearing house for mathematical thought during 17th Century, Mersenne primes (prime numbers that are one less than a power of 2)
1591-1661 AD : Girard Desargues : French :    Early development of projective geometry and “point at infinity”, perspective theorem

1596-1650 AD : René Descartes :    French :    Development of Cartesian coordinates and analytic geometry (synthesis of geometry and algebra), also credited with the first use of superscripts for powers or exponents

1598-1647 AD : Bonaventura Cavalieri :    Italian : “Method of indivisibles” paved way for the later development of infinitesimal calculus

1601-1665 AD : Pierre de Fermat    : French :    Discovered many new numbers patterns and theorems (including Little Theorem, Two-Square Theorem  and Last Theorem), greatly extending knowlege of number theory, also contributed to probability theory

1616-1703 AD : John Wallis :    British :    Contributed towards development of calculus, originated idea of number line, introduced symbol ∞ for infinity, developed standard notation for powers

1623-1662 AD : Blaise Pascal : French    Pioneer (with Fermat) of probability theory, Pascal’s Triangle of binomial coefficients

1643-1727 AD : Isaac Newton : British :    Development of infinitesimal calculus (differentiation and integration), laid ground work for almost all of classical mechanics, generalized binomial theorem, infinite power series

1646-1716 AD :Gottfried Leibniz :    German    Independently developed infinitesimal calculus (his calculus notation is still used), also practical calculating machine using binary system (forerunner of the computer), solved linear equations using a matrix

1654-1705 AD : Jacob Bernoulli    Swiss    Helped to consolidate infinitesimal calculus, developed a technique for solving separable differential equations, added a theory of permutations and combinations to probability theory, Bernoulli Numbers sequence, transcendental curves

1667-1748 AD : Johann Bernoulli :    Swiss : Further developed infinitesimal calculus, including the “calculus of variation”, functions for curve of fastest descent (brachistochrone) and catenary curve

1667-1754 AD : Abraham de Moivre : French    De Moivre's formula, development of analytic geometry, first statement of the formula for the normal distribution curve, probability theory

1690-1764 AD : Christian Goldbach : German : Goldbach Conjecture, Goldbach-Euler Theorem on perfect powers

1707-1783 AD : Leonhard Euler : Swiss : Made important contributions in almost all fields and found unexpected links between different fields, proved numerous theorems, pioneered new methods, standardized mathematical notation and wrote many influential textbooks

1728-1777 AD : Johann Lambert :     Swiss : Rigorous proof that π is irrational, introduced hyperbolic functions into trigonometry, made conjectures on non-Euclidean space and hyperbolic triangles

1736-1813 AD : Joseph Louis Lagrange : Italian/French : Comprehensive treatment of classical and celestial mechanics, calculus of variations, Lagrange’s theorem of finite groups, four-square theorem, mean value theorem

1746-1818 AD : Gaspard Monge :     French    Inventor of descriptive geometry, orthographic projection

1749-1827 AD : Pierre-Simon Laplace :    French : Celestial mechanics translated geometric study of classical mechanics to one based on calculus, Bayesian interpretation of probability, belief in scientific determinism

1752-1833 AD : Adrien-Marie Legendre : French    Abstract algebra, mathematical analysis, least squares method for curve-fitting and linear regression, quadratic reciprocity law, prime number theorem, elliptic functions

1768-1830 AD : Joseph Fourier :    French : Studied periodic functions and infinite sums in which the terms are trigonometric functions (Fourier series)

1777-1825 AD : Carl Friedrich Gauss :    German : Pattern in occurrence of prime numbers, construction of heptadecagon, Fundamental Theorem of Algebra, exposition of complex numbers, least squares approximation method, Gaussian distribution, Gaussian function, Gaussian error curve, non-Euclidean geometry, Gaussian curvature

1789-1857 AD : Augustin-Louis Cauchy    French    Early pioneer of mathematical analysis, reformulated and proved theorems of calculus in a rigorous manner, Cauchy's theorem (a fundamental theorem of group theory)

1790-1868 AD : August Ferdinand Möbius :    German    Möbius strip (a two-dimensional surface with only one side), Möbius configuration, Möbius transformations, Möbius transform (number theory), Möbius function, Möbius inversion formula

1791-1858 AD : George Peacock :    British : Inventor of symbolic algebra (early attempt to place algebra on a strictly logical basis)

1791-1871 AD : Charles Babbage :British : Designed a "difference engine" that could automatically perform computations based on instructions stored on cards or tape, forerunner of programmable computer.

1792-1856 AD : Nikolai Lobachevsky :    Russian :    Developed theory of hyperbolic geometry and curved spaces independendly of Bolyai

1802-1829 AD :  Niels Henrik Abel     :Norwegian :    Proved impossibility of solving quintic equations, group theory, abelian groups, abelian categories, abelian variety

1802-1860 AD : János Bolyai : Hungarian :    Explored hyperbolic geometry and curved spaces independently of Lobachevsky

1804-1851 AD : Carl Jacobi :    German :    Important contributions to analysis, theory of periodic and elliptic functions, determinants and matrices

1805-1865 AD : William Hamilton :    Irish : Theory of quaternions (first example of a non-commutative algebra)

1811-1832 AD : Évariste Galois    French    Proved that there is no general algebraic method for solving polynomial equations of degree greater than four, laid groundwork for abstract algebra, Galois theory, group theory, ring theory, etc

1815-1864  AD :  George Boole : British :  Devised Boolean algebra (using operators AND, OR and NOT), starting point of modern mathematical logic, led to the development of computer science

1815-1897 AD : Karl Weierstrass :    German :    Discovered a continuous function with no derivative, advancements in calculus of variations, reformulated calculus in a more rigorous fashion, pioneer in development of mathematical analysis

1821-1895 AD :    Arthur Cayley :    British : Pioneer of modern group theory, matrix algebra, theory of higher singularities, theory of invariants, higher dimensional geometry, extended Hamilton's quaternions to create octonions

1826-1866 AD :  Bernhard Riemann : German : Non-Euclidean elliptic geometry, Riemann surfaces, Riemannian geometry (differential geometry in multiple dimensions), complex manifold theory, zeta function, Riemann Hypothesis

1831-1916 AD : Richard Dedekind :  German :  Defined some important concepts of set theory such as similar sets and infinite sets, proposed Dedekind cut (now a standard definition of the real numbers)

1834-1923 AD : John Venn :    British : Introduced Venn diagrams into set theory (now a ubiquitous tool in probability, logic and statistics)

1842-1899 AD :  Marius Sophus Lie : Norwegian :    Applied algebra to geometric theory of differential equations, continuous symmetry, Lie groups of transformations

1845-1918 AD :  Georg Cantor : German : Creator of set theory, rigorous treatment of the notion of infinity and transfinite numbers, Cantor's theorem (which implies the existence of an “infinity of infinities”)

1848-1925 AD : Gottlob Frege : German : One of the founders of modern logic, first rigorous treatment of the ideas of functions and variables in logic, major contributor to study of the foundations of mathematics

1849-1925 AD : Felix Klein :     German    : Klein bottle (a one-sided closed surface in four-dimensional space), Erlangen Program to classify geometries by their underlying symmetry groups, work on group theory and function theory

1854-1912 AD :  Henri Poincaré :     French :     Partial solution to “three body problem”, foundations of modern chaos theory, extended theory of mathematical topology, Poincaré conjecture

1858-1932 AD :  Giuseppe Peano : Italian :    Peano axioms for natural numbers, developer of mathematical logic and set theory notation, contributed to modern method of mathematical induction

1861-1947 AD : Alfred North Whitehead :  British    : Co-wrote “Principia Mathematica” (attempt to ground mathematics on logic)

1862-1943 AD : David Hilbert : German : 23 “Hilbert problems”, finiteness theorem, “Entscheidungsproblem“ (decision problem), Hilbert space, developed modern axiomatic approach to mathematics, formalism

1864-1909 AD :  Hermann Minkowski :    German :    Geometry of numbers (geometrical method in multi-dimensional space for solving number theory problems), Minkowski space-time

1872-1970 AD : Bertrand Russell :British    Russell’s paradox, co-wrote “Principia Mathematica” (attempt to ground mathematics on logic), theory of types

1877-1947 AD :    G.H. Hardy :    British :    Progress toward solving Riemann hypothesis (proved infinitely many zeroes on the critical line), encouraged new tradition of pure mathematics in Britain, taxicab numbers

1878-1929 AD : Pierre Fatou :    French :    Pioneer in field of complex analytic dynamics, investigated iterative and recursive processes

1881-1966 AD :  L.E.J. Brouwer :    Dutch :    Proved several theorems marking breakthroughs in topology (including fixed point theorem and topological invariance of dimension)

1887-1920 AD : Srinivasa Ramanujan    : Indian :    Proved over 3,000 theorems, identities and equations, including on highly composite numbers, partition function and its asymptotics, and mock theta functions

1893-1978 AD :Gaston Julia :    French :    Developed complex dynamics, Julia set formula

1903-1957 AD : John von Neumann :    Hungarian/ American :    Pioneer of game theory, design model for modern computer architecture, work in quantum and nuclear physics

1906-1978 AD :Kurt Gödel :    Austria :    Incompleteness theorems (there can be solutions to mathematical problems which are true but which can never be proved), Gödel numbering, logic and set theory

1906-1998 AD : André Weil :    French :    Theorems allowed connections between algebraic geometry and number theory, Weil conjectures (partial proof of Riemann hypothesis for local zeta functions), founding member of influential Bourbaki group

1912-1954 AD :Alan Turing    :British :    Breaking of the German enigma code, Turing machine (logical forerunner of computer), Turing test of artificial intelligence

1913-1996 AD : Paul Erdös :    Hungarian : Set and solved many problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory

1917-2008 AD :  Edward Lorenz :    American    Pioneer in modern chaos theory, Lorenz attractor, fractals, Lorenz oscillator, coined term “butterfly effect”

1919-1985 AD : Julia Robinson :    American : Work on decision problems and Hilbert's tenth problem, Robinson hypothesis

1924-2010 AD : Benoît Mandelbrot  :    French :    Mandelbrot set fractal, computer plottings of Mandelbrot and Julia sets

Born 1928 AD -     Alexander Grothendieck    : French :    Mathematical structuralist, revolutionary advances in algebraic geometry, theory of schemes, contributions to algebraic topology, number theory, category theory, etc.

1928 - 2015 AD : John Forbes Nash, Jr.   :  American : Mathematician with fundamental contributions in game theory, differential geometry, and partial differential equations. Has provided insight into the factors that govern chance and decision making inside complex systems found in daily life.

1934-2007 AD : Paul Cohen :    American :    Proved that continuum hypothesis could be both true and not true (i.e. independent from Zermelo-Fraenkel set theory)

Born 1937-    John Horton Conway :    British : Important contributions to game theory, group theory, number theory, geometry and (especially) recreational mathematics, notably with the invention of the cellular automaton called the "Game of Life"

Born 1947- Yuri Matiyasevich : Russian : Final proof that Hilbert’s tenth problem is impossible (there is no general method for determining whether Diophantine equations have a solution)

Born 1953 - Andrew Wiles :    British :    Finally proved Fermat’s Last Theorem for all numbers (by proving the Taniyama-Shimura conjecture for semistable elliptic curves)

Born 1966-    Grigori Perelman :    Russian :    Finally proved Poincaré Conjecture (by proving Thurston's geometrization conjecture), contributions to Riemannian geometry and geometric topology

Last edited by ganesh (2015-09-27 17:52:20)

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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## #2 2015-09-27 15:46:32

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 108,752

### Re: Greatest Mathematicians from 1 CE ...

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2015-09-27 17:54:59

ganesh
Moderator
Registered: 2005-06-28
Posts: 22,686

### Re: Greatest Mathematicians from 1 CE ...

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline