Renowned Mathematicians PDF

GREEK MATHEMATICIANS Father of Greek Mathematics First True Mathematician THALES A pupil of Egyptians of Chaldeans Earth is disk shaped and not round and it floats on an ocean Pythagorean Theorem...

GREEK MATHEMATICIANS Father of Greek Mathematics First True Mathematician THALES A pupil of Egyptians of Chaldeans Earth is disk shaped and not round and it floats on an ocean Pythagorean Theorem Motto: ‘Everything is number’ PYTHAGORAS Musical notes could be translated into mathematical equations “Philosophy” and “Mathematics” Maker of Mathematicians Founder of the Academy in Athens, the first institution of higher learning in the Western World. PLATO Proponent of “Platonic Solids” and “Idealism” Three Classical Problems Motto: ‘Let no one ignorant of geometry enter here’ student of Plato and teacher of Alexander the Great Proponent of “Realism” ARISTOTLE Worked on the development and standardization of logic and deductive reasoning. Father of Classical Geometry Great Chronicler of Ancient Mathematics EUCLID Author of ELEMENTS Number theory Father of Scientific Astronomy EUDOXUS Derived the ‘Method of Exhaustion’ Discovered Theory of Proportion Greatest Mathematician of Antiquity Father of Mathematics Father of Mathematical Physics ARCHIMEDES Formulas for areas of regular figures Developed ‘The Sand Reckoner’ system that can express huge numbers Discovered buoyancy Expression: ‘Eureka!’ (I have found it!) when he stepped into a bathtub Developed ‘Sieve of Eratosthenes’ method for identifying prime numbers ERATOSTHENES Devised the first system of latitude and longitude Teacher of Pericles was imprisoned in Athens for impiety in asserting that the sun was not a deity but a huge red-hot stone as big as the whole Peloponnesus, and that the moon was ANAXAGORAS as inhabited earth that borrowed its light from the sun. “The moon is not a god, but a great rock, and the sun a hot rock.” tried to solve the problem of “squaring a circle” while he was in prison. PROTAGORAS Founding Father of Sophists Proponent of a materialistic atomic doctrine DEMOCRITUS Often referred to as the laughing philosopher MENAECHMUS Discovered the curves that were later known as the conic sections Worked on geometry, especially on cones and conic sections APOLLONIUS Author of TREATISE ON CONICS Established a basis for spherical triangles MENELAUS Author of SPHAERICA Discovered the precision of equinoxes HIPPARCHUS Developed the first detailed trigonometry tables  Calculated the distance of the moon from the Earth by measuring different parts of the moon visible at different locations, and calculated the length of the year as approximately 365.25 days. Author of ALMAGEST Developed even more detailed trigonometry tables Accurate representations of planetary motions PTOLEMY mathematical theories related to the solar system Geocentric theory of the universe, believes the Earth is the center of the solar system Father of Algebra First to recognize fractions as numbers Author of ARITHMETICA DIOPHANTUS Developed Diophantine Analysis of complex algebraic problems, to find rational solutions to equations with several unknowns. Famous with this “Diophantus Riddle” PERSIAN/ARABIC MATHEMATICIANS Father of Algebra MUHAMMAD AL- Introduced concepts like the number zero (0) and Hindu-Arabic Numeral KHWARIZMI system Algebraic methods of ‘reduction’ and ‘balancing’ MUHAMMAD AL- Proof by induction KARAJI Prove the binomial theorem Author of TREATISE ON DEMONSTRATION OF PROBLEMS OF ALGEBRA OMAR KHAYYAM Theory of proportion Worked on Jalali calendar which is considered more accurate than Gregorian NASIR AL-DIN AL- Developed field of spherical trigonometry TUSI Formulated law of sines for plane triangles KAMAL AL-DIN Applied theory of conic sections to solve optical problems AL-FARISI Amicable numbers, factorization, combinatorial methods INDIAN MATHEMATICIANS Introduced zero (0) to the world Definition of trigonometric functions ARYABHATA Approximated pi (π) to four decimal places Author of ARYABHATIYA Referred negative number as debt BRAHMAGUPTA Solution of quadratic equations with two unknowns Asserts that 0/0=0 First to write circle as zero BHASKARA I Remarkably accurate approximation of the sine function Established that dividing by zero yields infinity BHASKARA II Explained previously misunderstood operation of division by zero Landau-Ramanujan Constant SRINIVASA Contributions in number theory, mathematical analysis, string theory, and RAMANUJAN crystallography CHINESE MATHEMATICIANS  SUN TZU First definitive statement of Chinese Remainder Theorem Solved linear equations using matrices LUI HUI Calculate value of pi to five decimal places YANG HUI Culmination of Chinese ‘magic’ squares, circles, and triangles ZHU SHIJIE Jade Mirror of the Four Unknowns ITALIAN MATHEMATICIANS Most Talented Western Mathematician of the Middle Ages LEONARDO Famous for Fibonacci sequence PISANO BIGOLLO First to introduce Hindi-Arabic system to Europe FIBONACCI Author of LIBER ABACI Father of Accounting LUCA PACIOLI invented the standard symbols for plus and minus (+ and –). Author of SUMMA ARITHMETICA Formula for solving all types of cubic equations, involving first real use of complex numbers – real and imaginary NICCOLÒ published the first Italian translations of Archimedes and Euclid found a FONTANA formula for solving any cubic equation (including the first real application of TARTAGLIA complex numbers), and used mathematics to investigate the projectile motion of cannonballs. renowned for his work “ARS MAGNA”, the first Latin treatise devoted entirely GIROLAMO to algebra CARDANO acknowledge existence of imaginary numbers made the first systematic use of negative numbers BONAVENTURA method of indivisibles for infinitesimal calculus CAVALIERI FRENCH MATHEMATICIANS MARIN Mersenne primes MERSENNE Prime numbers that are one less than a power of 2 GIRARD Projective geometry DESARGUES Perspective theorem Father of Analytical Geometry Father of Modern Philosophy allows us to describe geometric shapes using algebra. RENÉ DESCARTES He refused to accept the authority of previous philosophers, and one of his best-known quotes is “I think, therefore I am” He is credited with the first use of superscripts for powers or exponents, and the cartesian coordinate system is named after him. Prince of Amateurs in Mathematics PIERRE DE is known for finding ordinates in curved lines; differential calculus. FERMAT Finding minima and maxima Greatest Might Have Been Pascal’s Triangle, an infinite triangle of numbers with some amazing properties. BLAISE PASCAL He invented some of the first mechanical calculators, as well as working on projective geometry, probability and the physics of the vacuum. At 16 years old, authored ‘The Geometry of Conics’ Invented the first calculating machine  worked on formalizing calculus, aiming to eliminate infinitesimals by basing JOSEPH-LOUIS calculus on algebra and power series expansions. LAGRANGE His work also laid the foundations for the calculus of variations. Authored by MECHANIQUE ANALYTIQUE Father of Differential Geometry GASPARD MONGE Founder of Modern Synthetic Geometry Inventor of descriptive geometry Quadratic Reciprocity Law ADRIEN MARIE Prime Number Theorem LEGENDRE Elliptic Functions The Analytical Theory of Heat Fourier's work on heat flow led to the development of Fourier series and JOSEPH FOURIER Fourier transforms, which expanded the scope of calculus into the study of periodic functions and laid the groundwork for harmonic analysis and signal processing. AUGUSTIN LOUIS Invented calculus of residues CAUCHY Complex Theory functions GERMAN MATHEMATICIANS GOTTFRIED Leibniz developed calculus independently but focused more on formalism and WILHELM LEIBNIZ notation, which is closer to what is used today. He introduced the symbols Prince of Mathematicians Foremost of Mathematicians Study of electromagnetism CARL FRIEDRICH GAUSS Discovered non-Euclidean geometry contributed to the fundamental theorem of algebra (1799), which states that every non-constant polynomial equation has at least one complex root. This was crucial for the development of higher algebra. KARL Father of Modern Analysis WEIERSTRASS Analytic Continuation Immediate Predecessor of Einstein introduced the Riemann integral, formalizing the concept of integration. BERNHARD He also contributed to the understanding of Fourier series and laid the RIEMANN groundwork for what became known as Riemannian geometry, important in modern physics. Zeta function GEORGE CANTOR Discover Set Theory Hilbert’s Basis Theorem DAVID HILBERT Worked on Invariant Theory SOPHIE GERMAIN The Revolutionary Mathematician BRITISH MATHEMATICIANS Inventor of First Systems of Logarithm JOHN NAPIER Popularized use of decimal point Father of Calculus Development of Binomial Theorem Influence of his work on calculus and mechanics ISAAC NEWTON Newton’s laws as a foundation for understanding the physical world. Ex. law of inertia, law of acceleration, law of interaction and law of gravitation. Developed calculus and formulated the laws of motion and gravitation.  Originated idea of number line published the Mathesis Universalis (“Universal Mathematics”), on algebra, JOHN WALLIS arithmetic, and geometry, in which he further developed notation. He invented and introduced the symbol ∞ for infinity. This symbol found use in treating a series of squares of indivisibles. GEORGE Inventor of Symbolic Algebra PEACOCK CHARLES Difference engine BABBAGE Boolean algebra (and, or, not) GEORGE BOOLE Mathematical analysis of logic JOHN VENN Venn Diagram ANDREW WILES Proved Fermat’s Last Theorem Father of Computer Science ALAN TURING Breaking of the German enigma code Turing Machine THOMAS Discovered star polygons BRADWARDINE SWISS MATHEMATICIANS DANIEL Basic Principle of Fluid Behaviour BERNOULLI Bernoulli Principle Hydrodynamica Most Successful Notation Builder of All Times Popularized e (base of natural logarithm), i (imaginary), f(x), ∑ (sum), π (pi), xyz (triangle sides) LEONHARD Contributions to calculus, topology, and mechanics EULER Euler's role in applying mathematics to engineering and physical sciences played a crucial role in formalizing and expanding calculus. He applied calculus to solve problems in physics, astronomy, and engineering JOHANN proof that π is irrational LAMBERT REVITALIZATION OF EUROPEAN MATHEMATICS He helped in translating and preserving the works of Greek mathematicians. JOHANN MÜLLER A German physiologist and comparative anatomist, one of the great natural philosophers of the 19th century. the author of a TREATISE ON ALGEBRA and is a central figure in the RAFAEL understanding of imaginary numbers; BOMBELLI managed to address the problem with imaginary numbers. Father of Modern Algebraic Notation FRANÇOIS VIÈTE made significant advances in Algebra, and first introduced the use of letters to represent variables. Dutch Archimedes SIMON STEVIN He helped standardize the use of decimal fractions, and made many mother contributions to science and engineering. Father of Modern Science Pioneered use of telescoe He was able to show that the path of a projectile, disregarding air resistance, GALILEO GALILEI is a parabola In mathematics, Galileo, like Moses came within sight of the promise land, but he could not enter it.  Laws of planetary motions Developed principle of continuity for conics JOHANNES The idea that a parabola has two foci, one at infinity, is due to Kepler, as is KEPLER also the word “focus” (latin for “hearthside”) who discovered three major laws of planetary motion He also did important work in optics and geometry. known for his work on the theories of centrifugal force, the wave theory of CHRISTIAAN light, and the pendulum clock. HUYGENS Discovered rings of Saturn Theory of probability owes more to Laplace than to any other mathematician PIERRE-SIMON LAPLACE Wrote that, "At the bottom, the theory of probabilities is only common sense expressed in number.” AGE OF ENLIGHTENMENT The Age of Enlightenment was an intellectual and philosophical movement in the 18th century focused on reason, science, and the pursuit of knowledge. Mathematics played a critical role in shaping Enlightenment thought, providing a framework to understand the natural world in a precise, logical way. The mechanistic worldview emerged from the works of thinkers like Descartes and Newton. It viewed the universe as a vast machine governed by physical laws. Mathematics became the language used to describe and predict these laws, emphasizing determinism and rationality. The mechanistic worldview posits that the universe operates like a machine, where all components interact systematically and predictably Determinism: The belief that every event or action is determined by preceding events according to natural laws. Rationalism: The idea that reason and logic are the primary sources of knowledge, guiding our understanding of the universe. Predictability: The notion that, through understanding these laws, we can predict outcomes and behaviors in the natural world. Mathematics as the Language of the Mechanistic World Mathematics serves as the fundamental language that describes the workings of the mechanistic universe, allowing scientists to formulate theories and express natural laws clearly. Mathematics as a Tool for Uncovering Universal Laws Mathematics was viewed as essential for discovering and explaining universal laws of nature, helping to unlock the secrets of physics, astronomy, and other sciences. JEAN LE ROND Co-author of the Encyclopédie D'ALEMBERT d'Alembert's principle in mechanics PIERRE SIMON Probability theory developed during the 18th century, largely through the work of MARQUIS DE Laplace and Bayes. It became important for understanding uncertainty and was LAPLACE & applied to areas like gambling, insurance, and risk management. Early statistical REVEREND methods also began to emerge in fields like economics and demography. THOMAS BAYES EXPANSION OF CALCULUS The history of the expansion of calculus is deeply intertwined with the broader history of mathematics, as calculus evolved from its origins in ancient mathematics to its formalization in the 17th century and beyond. BROOK TAYLOR Both contributed to the theory of series expansions. Taylor series and Maclaurin AND COLIN series are named after them, crucial tools in approximating functions. MACLAURIN EXPANSION OF ALGEBRA Algebra and number theory HENRI POINCARÉ introduced group theory to physics, and was the first to study the group of Lorentz transformations. He also made major contributions to the theory of discrete groups and their representations. MAJOR GEOMETRIES Euclidean Geometry is the oldest and most fundamental form of geometry. It is EUCLIDEAN based on a set of simple axioms and is used to solve problems involving straight GEOMETRY lines, circles, and other shapes. It is the most widely studied and taught form of geometry. Several mathematicians, including Carl Friedrich Gauss, Nikolai Lobachevsky, and János Bolyai, independently developed non-Euclidean geometries in the 18th NON-EUCLIDEAN century. GEOMETRY Non-Euclidean geometries are a family of geometries that are based on different sets of axioms than Euclidean geometry. These geometries challenge the parallel postulate of Euclidean geometry. Rene Descartes ANALYTIC Analytic geometry uses coordinate geometry to solve geometric problems. It GEOMETRY combines algebra and geometry by representing points and lines using algebraic equations. Girard Desargues PROJECTIVE Projective geometry deals with points, lines, and shapes in a projective plane. In GEOMETRY a projective plane, any point can be projected onto any other point. Carl Friedrich Gauss, Gaspard Monge DIFFERENTIAL GEOMETRY Differential geometry studies curved surfaces and spaces using calculus. It focuses on the curvature of surfaces and how that curvature changes over time. Several mathematicians, including Henri Poincaré, Felix Hausdorff, and Bernhard Riemann, made significant contributions to topology in the late 19th and early 20th centuries. TOPOLOGY Topology studies the properties of shapes that remain unchanged under continuous deformations, such as stretching, bending, or twisting. It focuses on concepts like connectedness and compactness. MATHEMATICS IN THE MODERN WORLD an American Mathematician who used a technique called forcing to prove the PAUL COHEN independence in set theory of the axiom choice proved that continuum hypothesis could be both true and not true corecipient of the 1994 Nobel Prize for Economics JOHN FORBES formulated the “Nash Equilibrium” which involves a universal solution concept NASH for noncooperative games  best known for the “Nash embedding theorem” pioneer in modern chaos theory, Lorenz attractor, fractals, Lorenz oscillator EDWARD LORENZ coined the term “butterfly effect” pioneer of game theory, design model for computer architecture noted for his fundamental contributions to the theory of quantum mechanics JOHN VON particularly the concept of “rings of operators” NEUMAN He is also known for the design of the high speed electronic computers famous for Operator Theory an American mathematician, electrical engineer, computer scientist and CLAUDE cryptographer known as the "father of information theory" SHANNON noted for his development of the theory of communication now known as information theory NORBERT Founder of Cybernetics WEINER GEORGE Linear Programming DANTZIG a Hungarian mathematician who set and solved many problems in PAUL ERDOS combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory and probability theory a Russian mathematician and geometer who developed theory of hyperbolic NIKOLAI geometry and curved spaces independently of Bolyai LOBACHEVSKY his writings include: (1) Principles of Geometry, (2) Imaginary Geometry an Austrian mathematician best known for his formula on the area of a polygon in a lattice of points GEORGE PICK known for his Pick's Theorem which is a method in finding the area of polygons on a square - unit grid of points COMPUTER DEVICES first real manual calculating device ABACUS said to be the origin of present-day computer originated in China a computing device developed by John Napier in a form of a set of sticks with numbers printed on it NAPIER'S BONES perform both multiplication and division also know as Napier's Rods invented by William Oughtred SLIDE RULE comes up with a result on multiplication fastly functions by sliding one ruler over the other a mechanical calculator invented by Blaise Pascal PASCALINE it can add and subtract numbers by dialing a series of wheel up to 8 digits each wheel represents numbers 0-9 DIFFERENCE designed and partially built by Charles Babbage ENGINE a machine which can perform calculation of simple tables invented by Charles Babbage ANALYTICAL ENGINE a general-purpose, fully program-controlled, automatic mechanical digital computer BURROUGH'S the first commercial adding machine developed by William Seward Burroughs ADDING MACHINE capable of computing the sum and at the same time printing the result DIFFERENTIAL the first large-scale automatic general-purpose mechanical analog computer ANALYZER built by Vannevar Bush at the Massachusetts Institute of Technology (MIT) ATANASOFF - first machine to make use of vacuum tubes as the logic circuits BERY COMPUTER  built by John Atanasoff and Clifford Berry the first digital electronic computer in the U.S. the Electronic Numeric Integrator and Calculator (ENIAC) was built by John Mauchly and J. Eckert ENIAC the first programmable general-purpose electronic digital computer built during World War II by the United States developed in 1943 by engineer Tommy Flower COLOSSUS designed to decode the encrypted transmissions from the German teleprinter Lorenz cipher the Electronic Discrete Variable Automatic Computer (EDVAC) was built by Mauchly and Eckert EDVAC the first mainframe computer that represented binary systems rather than decimal systems