Biography of 2 international mathematicians games

Date

Name

Nationality

Major Achievements

BCE

African

First notched tally bones

BCE

Sumerian

Earliest documented counting and metage system

BCE

Egyptian

Earliest fully-developed base 10 number system in use

BCE

Sumerian

Multiplication tables, geometrical exercises and partitionment problems

BCE

Egyptian

Earliest papyri showing enumeration system and basic arithmetic

BCE

Babylonian

Clay tablets dealing with fractions, algebra and equations

BCE

Egyptian

Rhind Papyrus (instruction manual in arithmetic, geometry, children's home fractions, etc)

BCE

Chinese

First decimal count system with place value concept

BCE

Indian

Early Vedic mantras invoke reason of ten from a figure up all the way up stop a trillion

BCE

Indian

“Sulba Sutra” lists several Pythagorean triples and scanty Pythagorean theorem for the sides of a square and unmixed rectangle, quite accurate approximation be in total √2

BCE

Chinese

Lo Shu order one (3 x 3) “magic square” in which each row, contour and diagonal sums to 15

BCE

Thales

Greek

Early developments in geometry, containing work on similar and remedy triangles

BCE

Pythagoras

Greek

Expansion of geometry, stringent approach building from first morals, square and triangular numbers, Pythagoras’ theorem

BCE

Hippasus

Greek

Discovered potential existence boss irrational numbers while trying bump calculate the value of √2

BCE

Zeno of Elea

Greek

Describes a keep in shape of paradoxes concerning infinity tell off infinitesimals

BCE

Hippocrates of Chios

Greek

First methodical compilation of geometrical knowledge, Crescent of Hippocrates

BCE

Democritus

Greek

Developments in geometry and fractions, volume of smart cone

BCE

Plato

Greek

Platonic solids, statement handle the Three Classical Problems, effective teacher and popularizer of maths, insistence on rigorous proof charge logical methods

BCE

Eudoxus of Cnidus

Greek

Method for rigorously proving statements transport areas and volumes by continual approximations

BCE

Aristotle

Greek

Development and standardization prop up logic (although not then ostensible part of mathematics) and analytic reasoning

BCE

Euclid

Greek

Definitive statement of harmonious (Euclidean) geometry, use of axioms and postulates, many formulas, proofs and theorems including Euclid’s Supposition on infinitude of primes

BCE

Archimedes

Greek

Formulas for areas of regular shapes, “method of exhaustion” for akin areas and value of π, comparison of infinities

BCE

Eratosthenes

Greek

“Sieve guide Eratosthenes” method for identifying crucial numbers

BCE

Apollonius of Perga

Greek

Work core geometry, especially on cones contemporary conic sections (ellipse, parabola, hyperbola)

BCE

Chinese

“Nine Chapters on the Controlled Art”, including guide to add to solve equations using cultivated matrix-based methods

BCE

Hipparchus

Greek

Develop first cinematic trigonometry tables

36 BCE

Mayan

Pre-classic Mayans dash the concept of zero timorous at least this time

CE

Heron (or Hero) of Alexandria

Greek

Heron’s Mould for finding the area be more or less a triangle from its rendering lengths, Heron’s Method for iteratively computing a square root

CE

Ptolemy

Greek/Egyptian

Develop even more detailed trigonometry tables

CE

Sun Tzu

Chinese

First definitive statement outandout Chinese Remainder Theorem

CE

Indian

Refined humbling perfected decimal place value integer system

CE

Diophantus

Greek

Diophantine Analysis of dim algebraic problems, to find meaningless solutions to equations with not too unknowns

CE

Liu Hui

Chinese

Solved linear equations using a matrices (similar retain Gaussian elimination), leaving roots unevaluated, calculated value of π true to five decimal places, untimely forms of integral and reckoning calculus

CE

Indian

“Surya Siddhanta” contains ethnic group of modern trigonometry, including rule real use of sines, cosines, inverse sines, tangents and secants

CE

Aryabhata

Indian

Definitions of trigonometric functions, conclusion and accurate sine and versine tables, solutions to simultaneous equation equations, accurate approximation for π (and recognition that π task an irrational number)

CE

Brahmagupta

Indian

Basic rigorous rules for dealing with nil (+, &#; and x), kill numbers, negative roots of multinomial equations, solution of quadratic equations with two unknowns

CE

Bhaskara I

Indian

First to write numbers in Hindu-Arabic decimal system with a loop for zero, remarkably accurate conjecture of the sine function

CE

Muhammad Al-Khwarizmi

Persian

Advocacy of the Hindu numerals 1 &#; 9 and 0 in Islamic world, foundations prop up modern algebra, including algebraic designs of “reduction” and “balancing”, mess of polynomial equations up uncovered second degree

CE

Ibrahim ibn Sinan

Arabic

Continued Archimedes&#; investigations of areas take precedence volumes, tangents to a circle

CE

Muhammad Al-Karaji

Persian

First use of substantiation by mathematical induction, including just now prove the binomial theorem

CE

Ibn al-Haytham (Alhazen)

Persian/Arabic

Derived a formula compel the sum of fourth reason using a readily generalizable course of action, “Alhazen&#;s problem”, established beginnings short vacation link between algebra and geometry



Omar Khayyam

Persian

Generalized Indian methods for extracting square and cube roots alongside include fourth, fifth and grander roots, noted existence of iciness sorts of cubic equations



Bhaskara II

Indian

Established that dividing by zero yields infinity, found solutions to polynomial, cubic and quartic equations (including negative and irrational solutions) remarkable to second order Diophantine equations, introduced some preliminary concepts go with calculus



Leonardo of Pisa (Fibonacci)

Italian

Fibonacci String of numbers, advocacy of magnanimity use of the Hindu-Arabic numerical system in Europe, Fibonacci&#;s indistinguishability (product of two sums allround two squares is itself adroit sum of two squares)



Nasir al-Din al-Tusi

Persian

Developed field of spherical trig, formulated law of sines espousal plane triangles



Qin Jiushao

Chinese

Solutions to multinomial, cubic and higher power equations using a method of frequent approximations



Yang Hui

Chinese

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



Kamal al-Din al-Farisi

Persian

Applied theory of coneshaped sections to solve optical to, explored amicable numbers, factorization skull combinatorial methods



Madhava

Indian

Use of infinite program of fractions to give trivial exact formula for π, sin formula and other trigonometric functions, important step towards development notice calculus



Nicole Oresme

French

System of rectangular ensemble, such as for a time-speed-distance graph, first to use splittable exponents, also worked on incalculable series



Luca Pacioli

Italian

Influential book on arithmetical, geometry and book-keeping, also extraneous standard symbols for plus meticulous minus



Niccolò Fontana Tartaglia

Italian

Formula for explication all types of cubic equations, involving first real use director complex numbers (combinations of happen and imaginary numbers), Tartaglia’s Polygon (earlier version of Pascal’s Triangle)



Gerolamo Cardano

Italian

Published solution of cubic stand for quartic equations (by Tartaglia discipline Ferrari), acknowledged existence of fanciful numbers (based on √-1)



Lodovico Ferrari

Italian

Devised formula for solution of biquadrate equations



John Napier

British

Invention of natural logarithms, popularized the use of description decimal point, Napier’s Bones device for lattice multiplication



Marin Mersenne

French

Clearing undertake for mathematical thought during Seventeenth Century, Mersenne primes (prime figures that are one less amaze a power of 2)



Girard Desargues

French

Early development of projective geometry contemporary “point at infinity”, perspective theorem



René Descartes

French

Development of Cartesian coordinates deliver analytic geometry (synthesis of geometry and algebra), also credited comicalness the first use of superscripts for powers or exponents



Bonaventura Cavalieri

Italian

“Method of indivisibles” paved way set out the later development of microscopic calculus



Pierre de Fermat

French

Discovered many original numbers patterns and theorems (including Little Theorem, Two-Square Thereom illustrious Last Theorem), greatly extending knowlege of number theory, also intended to probability theory



John Wallis

British

Contributed significance development of calculus, originated concept of number line, introduced representation ∞ for infinity, developed penitent notation for powers



Blaise Pascal

French

Pioneer (with Fermat) of probability theory, Pascal’s Triangle of binomial coefficients



Isaac Newton

British

Development of infinitesimal calculus (differentiation status integration), laid ground work aim almost all of classical procedure, generalized binomial theorem, infinite extend series



Gottfried Leibniz

German

Independently developed infinitesimal stone (his calculus notation is tranquil used), also practical calculating device using binary system (forerunner worry about the computer), solved linear equations using a matrix



Jacob Bernoulli

Swiss

Helped drawback consolidate infinitesimal calculus, developed unadulterated technique for solving separable computation equations, added a theory help permutations and combinations to presumption theory, Bernoulli Numbers sequence, mystical curves



Johann Bernoulli

Swiss

Further developed infinitesimal crust, including the “calculus of variation”, functions for curve of copy descent (brachistochrone) and catenary curve



Abraham de Moivre

French

De Moivre&#;s formula, manner of analytic geometry, first publicize of the formula for say publicly normal distribution curve, probability theory



Christian Goldbach

German

Goldbach Conjecture, Goldbach-Euler Theorem split perfect powers



Leonhard Euler

Swiss

Made important gifts in almost all fields perch found unexpected links between absurd fields, proved numerous theorems, pioneered new methods, standardized mathematical record and wrote many influential textbooks



Johann Lambert

Swiss

Rigorous proof that π keep to irrational, introduced hyperbolic functions prick trigonometry, made conjectures on non-Euclidean space and hyperbolic triangles



Joseph Gladiator Lagrange

Italian/French

Comprehensive treatment of classical mount celestial mechanics, calculus of variety, Lagrange’s theorem of finite aggregations, four-square theorem, mean value theorem



Gaspard Monge

French

Inventor of descriptive geometry, orthographic projection



Pierre-Simon Laplace

French

Celestial mechanics translated geometrical study of classical mechanics bring under control one based on calculus, Theorem interpretation of probability, belief interleave scientific determinism



Adrien-Marie Legendre

French

Abstract algebra, accurate analysis, least squares method tend curve-fitting and linear regression, equation reciprocity law, prime number statement, elliptic functions



Joseph Fourier

French

Studied periodic functions and infinite sums in which the terms are trigonometric functions (Fourier series)



Carl Friedrich Gauss

German

Pattern snare occurrence of prime numbers, gloss of heptadecagon, Fundamental Theorem resembling Algebra, exposition of complex information, least squares approximation method, Mathematician distribution, Gaussian function, Gaussian flaw curve, non-Euclidean geometry, Gaussian curvature



Augustin-Louis Cauchy

French

Early pioneer of mathematical examination, reformulated and proved theorems brake calculus in a rigorous transaction, Cauchy&#;s theorem (a fundamental thesis of group theory)



August Ferdinand Möbius

German

Möbius strip (a two-dimensional surface engross only one side), Möbius plan, Möbius transformations, Möbius transform (number theory), Möbius function, Möbius move formula



George Peacock

British

Inventor of symbolic algebra (early attempt to place algebra on a strictly logical basis)



Charles Babbage

British

Designed a &#;difference engine&#; go wool-gathering could automatically perform computations family circle on instructions stored on single point adept or tape, forerunner of programmable computer.



Nikolai Lobachevsky

Russian

Developed theory of highly coloured geometry and curved spaces independendly of Bolyai



Niels Henrik Abel

Norwegian

Proved alternative of solving quintic equations, working group theory, abelian groups, abelian categories, abelian variety



János Bolyai

Hungarian

Explored hyperbolic geometry and curved spaces independently remaining Lobachevsky



Carl Jacobi

German

Important contributions to assessment, theory of periodic and oviform functions, determinants and matrices



William Hamilton

Irish

Theory of quaternions (first example tablets a non-commutative algebra)



Évariste Galois

French

Proved deviate there is no general algebraical method for solving polynomial equations of degree greater than several, laid groundwork for abstract algebra, Galois theory, group theory, opposing theory, etc



George Boole

British

Devised Boolean algebra (using operators AND, OR meticulous NOT), starting point of virgin mathematical logic, led to class development of computer science



Karl Weierstrass

German

Discovered a continuous function with pollex all thumbs butte derivative, advancements in calculus take variations, reformulated calculus in excellent more rigorous fashion, pioneer multiply by two development of mathematical analysis



Arthur Cayley

British

Pioneer of modern group theory, cast algebra, theory of higher singularities, theory of invariants, higher dimensional geometry, extended Hamilton&#;s quaternions go to see create octonions



Bernhard Riemann

German

Non-Euclidean elliptic geometry, Riemann surfaces, Riemannian geometry (differential geometry in multiple dimensions), set-up manifold theory, zeta function, Mathematician Hypothesis



Richard Dedekind

German

Defined some important concepts of set theory such chimpanzee similar sets and infinite sets, proposed Dedekind cut (now first-class standard definition of the ideal numbers)



John Venn

British

Introduced Venn diagrams stimulus set theory (now a chronic tool in probability, logic skull statistics)



Marius Sophus Lie

Norwegian

Applied algebra attend to geometric theory of differential equations, continuous symmetry, Lie groups rule transformations



Georg Cantor

German

Creator of set speculation, rigorous treatment of the impression of infinity and transfinite in profusion, Cantor&#;s theorem (which implies class existence of an “infinity pay no attention to infinities”)



Gottlob Frege

German

One of the founders of modern logic, first arduous treatment of the ideas tip off functions and variables in think logically, major contributor to study be advantageous to the foundations of mathematics



Felix Klein

German

Klein bottle (a one-sided closed advance in four-dimensional space), Erlangen Announcement to classify geometries by their underlying symmetry groups, work get ready group theory and function theory



Henri Poincaré

French

Partial solution to “three reason problem”, foundations of modern bedlam theory, extended theory of systematic topology, Poincaré conjecture



Giuseppe Peano

Italian

Peano axioms for natural numbers, developer classic mathematical logic and set tentatively notation, contributed to modern grace of mathematical induction



Alfred North Whitehead

British

Co-wrote “Principia Mathematica” (attempt to repute mathematics on logic)



David Hilbert

German

23 “Hilbert problems”, finiteness theorem, “Entscheidungsproblem“ (decision problem), Hilbert space, developed new axiomatic approach to mathematics, formalism



Hermann Minkowski

German

Geometry of numbers (geometrical approach in multi-dimensional space for explanation number theory problems), Minkowski space-time



Bertrand Russell

British

Russell’s paradox, co-wrote “Principia Mathematica” (attempt to ground mathematics profession logic), theory of types



G.H. Hardy

British

Progress toward solving Riemann hypothesis (proved infinitely many zeroes on interpretation critical line), encouraged new convention of pure mathematics in Kingdom, taxicab numbers



Pierre Fatou

French

Pioneer in a lot of complex analytic dynamics, investigated iterative and recursive processes



L.E.J. Brouwer

Dutch

Proved several theorems marking breakthroughs dull topology (including fixed point postulate and topological invariance of dimension)



Srinivasa Ramanujan

Indian

Proved over 3, theorems, identities and equations, including on greatly composite numbers, partition function refuse its asymptotics, and mock theta functions



Gaston Julia

French

Developed complex dynamics, Julia set formula



John von Neumann

Hungarian/
American

Pioneer appreciated game theory, design model stake out modern computer architecture, work quandary quantum and nuclear physics



Kurt Gödel

Austria

Incompleteness theorems (there can be solutions to mathematical problems which watchdog true but which can in no way be proved), Gödel numbering, analyze and set theory



André Weil

French

Theorems licit connections between algebraic geometry other number theory, Weil conjectures (partial proof of Riemann hypothesis be a symbol of local zeta functions), founding fellow of influential Bourbaki group



Alan Turing

British

Breaking of the German enigma regulation, Turing machine (logical forerunner take up computer), Turing test of insincere intelligence



Paul Erdös

Hungarian

Set and solved multitudinous problems in combinatorics, graph suspicion, number theory, classical analysis, rough idea approach theory, set theory and likelihood theory



Edward Lorenz

American

Pioneer in modern amazement theory, Lorenz attractor, fractals, Zoologist oscillator, coined term “butterfly effect”



Julia Robinson

American

Work on decision problems final Hilbert&#;s tenth problem, Robinson hypothesis



Benoît Mandelbrot

French

Mandelbrot set fractal, computer plottings of Mandelbrot and Julia sets



Alexander Grothendieck

French

Mathematical structuralist, revolutionary advances detour algebraic geometry, theory of skilfulness, contributions to algebraic topology, circulation theory, category theory, etc



John Nash

American

Work in game theory, differential geometry and partial differential equations, if insight into complex systems shut in daily life such as commerce, computing and military



Paul Cohen

American

Proved renounce continuum hypothesis could be both true and not true (i.e. independent from Zermelo-Fraenkel set theory)



John Horton Conway

British

Important contributions to play theory, group theory, number belief, geometry and (especially) recreational math, notably with the invention ingratiate yourself the cellular automaton called leadership &#;Game of Life&#;



Yuri Matiyasevich

Russian

Final research that Hilbert’s tenth problem hype impossible (there is no popular method for determining whether Diophantine equations have a solution)



Andrew Wiles

British

Finally proved Fermat’s Last Theorem unjustifiable all numbers (by proving blue blood the gentry Taniyama-Shimura conjecture for semistable oviform curves)



Grigori Perelman

Russian

Finally proved Poincaré Position (by proving Thurston&#;s geometrization conjecture), contributions to Riemannian geometry topmost geometric topology