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- Computer Science | Britannica.com

At the time of Bachman s birth his father was the head football coach at Kansas Backus John Warner American computer scientist and mathematician who led the team that designed FORTRAN formula translation the first important algorithmic language for computers Restless as a young man Backus found his niche in mathematics earning a B S 1949 Baran Paul American electrical engineer inventor of the distributed network and contemporaneously with British computer scientist Donald Davies of data packet switching across distributed networks These inventions were the foundation for the Internet In 1928 Berners Lee Sir Tim British computer scientist generally credited as the inventor of the World Wide Web In 2004 he was awarded a knighthood by Queen Elizabeth II of the United Kingdom and the inaugural Millennium Technology Prize 1 million by the Finnish Technology Blum Manuel Venezuelan born American mathematician and computer scientist and winner of the 1995 A M Turing Award the highest honour in computer science in recognition of his contributions to the foundations of computational complexity theory and its application Brin Sergey American computer scientist and entrepreneur who created along with Larry Page the online search engine Google one of the most successful sites on the Internet Brin s family moved from Moscow to the United States in 1979 After receiving degrees Brooks Frederick Phillips Jr American computer scientist and winner of the 1999 A M Turing Award the highest honour in computer science for his landmark contributions to computer architecture operating systems and software engineering Brooks received a bachelor s degree Brooks Rodney Allen computer scientist artificial intelligence scientist and designer of mobile autonomous robots While attending Flinders University in Adelaide South Australia where he received bachelor s 1975 and master s degrees 1978 in pure mathematics Brooks Cerf Vinton Gray American computer scientist who is considered one of the founders along with Robert Kahn of the Internet In 2004 both Cerf and Kahn won the A M Turing Award the highest honour in computer science for their pioneering work on internetworking including Church Alonzo U S mathematician He earned a Ph D from Princeton University His contributions to number theory and the theories of algorithms and computability laid the foundations of computer science The rule known as Church s theorem or Church s thesis proposed Clarke Edmund Melson Jr American computer scientist and cowinner of the 2007 A M Turing Award the highest honour in computer science Clarke earned a bachelor s degree in mathematics in 1967 from the University of Virginia a master s degree in mathematics in 1968 from Duke Cocke John American mathematician and computer scientist and winner of the 1984 A M Turing Award the highest honour in computer science for significant contributions in the design and theory of compilers the architecture of large systems and the development Codd Edgar Frank British born American computer scientist and mathematician who devised the relational data model which led to the creation of the relational database a standard method of retrieving and storing

Original URL path: http://www.britannica.com/topic-browse/Mathematics/Computer-Science (2016-02-13)

Open archived version from archive - Fields Medal | Britannica.com

work in analysis Bourgain received a Ph D from the Free University of Brussels 1977 He held appointments at the Free University 1981 85 jointly at the University of Illinois Cohen Paul Joseph American mathematician who was awarded the Fields Medal in 1966 for his proof of the independence of the continuum hypothesis from the other axioms of set theory Cohen attended the University of Chicago M S 1954 Ph D 1958 He held appointments Connes Alain French mathematician who won the Fields Medal in 1982 for his work in operator theory Connes received a bachelor s degree 1970 and a doctorate 1973 from the École Normale Supérieure now part of the University of Paris He held appointments at Deligne Pierre René Belgian mathematician who was awarded the Fields Medal 1978 the Crafoord Prize 1988 and the Abel Prize 2013 for his work in algebraic geometry Deligne received a bachelor s degree in mathematics 1966 and a doctorate 1968 from the Free University Donaldson Simon Kirwan British mathematician who was awarded the Fields Medal in 1986 for his work in topology Donaldson attended Pembroke College Cambridge B A 1979 and Worcester College Oxford Ph D 1983 From 1983 to 1985 he was a Junior Research Fellow at All Douglas Jesse American mathematician who was awarded one of the first two Fields Medals in 1936 for solving the Plateau problem Douglas attended City College of New York and Columbia University Ph D 1920 He remained at Columbia until 1926 when he was awarded Drinfeld Vladimir Gershonovich Soviet mathematician who was awarded the Fields Medal in 1990 for his work in algebraic geometry and mathematical physics Drinfeld attended Moscow State University and the V A Steklov Institute of Mathematics Moscow Ph D 1988 He joined the Institute Faltings Gerd German mathematician who was awarded the Fields Medal in 1986 for his work in algebraic geometry Faltings attended the Westphalian Wilhelm University of Münster Ph D 1978 Following a visiting research fellowship at Harvard University Cambridge Fefferman Charles Louis American mathematician who was awarded the Fields Medal in 1978 for his work in classical analysis Fefferman attended the University of Maryland B S 1966 and Princeton N J University After receiving his Ph D in 1969 he remained at Princeton Fields Medal award granted to between two and four mathematicians for outstanding or seminal research The Fields Medal is often referred to as the mathematical equivalent of the Nobel Prize but it is granted only every four years and is given by tradition to Freedman Michael Hartley American mathematician who was awarded the Fields Medal in 1986 for his solution of the Poincaré conjecture in four dimensions Freedman received his Ph D from Princeton N J University in 1973 Following appointments at the University of California Gowers William Timothy British mathematician who won the Fields Medal in 1998 for his work in the theory of Banach spaces Gowers studied undergraduate mathematics at the University of Cambridge and went on to finish his doctorate

Original URL path: http://www.britannica.com/topic-browse/Mathematics/Fields-Medal (2016-02-13)

Open archived version from archive - Geometry | Britannica.com

ancient world Most of his other treatises are now lost although their titles and a general indication of their Archytas of Tarentum Greek scientist philosopher and major Pythagorean mathematician Plato a close friend made use of his work in mathematics and there is evidence that Euclid borrowed from him for the treatment of number theory in Book VIII of his Elements Archytas Atiyah Sir Michael Francis British mathematician who was awarded the Fields Medal in 1966 primarily for his work in topology Atiyah received a knighthood in 1983 and the Order of Merit in 1992 He also served as president of the Royal Society 1990 95 Atiyah s father was Lebanese Barrow Isaac English classical scholar theologian and mathematician who was the teacher of Isaac Newton He developed a method of determining tangents that closely approached the methods of calculus and he first recognized that what became known as the processes Bertrand Joseph French mathematician and educator remembered for his elegant applications of differential equations to analytical mechanics particularly in thermodynamics and for his work on statistical probability and the theory of curves and surfaces The nephew Betti Enrico mathematician who wrote a pioneering memoir on topology the study of surfaces and higher dimensional spaces and wrote one of the first rigorous expositions of the theory of equations developed by the noted French mathematician Évariste Galois 1811 32 Blaschke Wilhelm Johann Eugen German mathematician whose major contributions to geometry concerned kinematics and differential and integral geometry Blaschke became extraordinary professor of mathematics at the Deutsche Technische Hochschule German Technical University Prague Bliss Nathaniel Britain s fourth Astronomer Royal Bliss graduated from Pembroke College Oxford B A 1720 M A 1723 and became rector of St Ebbe s Oxford in 1736 He succeeded Edmond Halley as Savilian professor of geometry at the University of Oxford in 1742 Bolyai János Hungarian mathematician and one of the founders of non Euclidean geometry a geometry that differs from Euclidean geometry in its definition of parallel lines The discovery of a consistent alternative geometry that might correspond to the structure Boscovich Ruggero Giuseppe astronomer and mathematician who gave the first geometric procedure for determining the equator of a rotating planet from three observations of a surface feature and for computing the orbit of a planet from three observations of its position Boscovich s Brouwer Luitzen Egbertus Jan Dutch mathematician who founded mathematical intuitionism a doctrine that views the nature of mathematics as mental constructions governed by self evident laws and whose work completely transformed topology the study of the most basic properties of catastrophe theory in mathematics a set of methods used to study and classify the ways in which a system can undergo sudden large changes in behaviour as one or more of the variables that control it are changed continuously Catastrophe theory is generally considered Cavalieri Bonaventura Italian mathematician who made developments in geometry that were precursors to integral calculus As a boy Cavalieri joined the Jesuati a religious order sometimes called Apostolic

Original URL path: http://www.britannica.com/topic-browse/Mathematics/Geometry (2016-02-13)

Open archived version from archive - Information Theory | Britannica.com

and processing of information Most closely associated with the work of the American electrical engineer Claude Shannon in the mid 20th century information theory Nyquist Harry American physicist and electrical and communications engineer a prolific inventor who made fundamental theoretical and practical contributions to telecommunications Nyquist moved to the United States in 1907 He earned a B S 1914 and an M S 1915 Shannon Claude American mathematician and electrical

Original URL path: http://www.britannica.com/topic-browse/Mathematics/Information-Theory (2016-02-13)

Open archived version from archive - Mathematical Physics | Britannica.com

theory of relativity Fock became progressively deaf at a young age because of injuries sustained during military service in World War I In 1922 he graduated Green George English mathematician who was first to attempt to devise a theory of electricity and magnetism This work heralded the beginning of modern mathematical physics in Great Britain The son of a prosperous miller and a miller by trade himself Green was Legendre Adrien Marie French mathematician whose distinguished work on elliptic integrals provided basic analytic tools for mathematical physics Little is known about Legendre s early life except that his family wealth allowed him to study physics and mathematics beginning mathematical physics Branch of mathematical analysis that emphasizes tools and techniques of particular use to physicists and engineers It focuses on vector spaces matrix algebra differential equations especially for boundary value problems integral equations integral Poincaré Henri French mathematician one of the greatest mathematicians and mathematical physicists at the end of 19th century He made a series of profound innovations in geometry the theory of differential equations electromagnetism topology and the philosophy Polkinghorne John English physicist and priest who publicly championed the reconciliation of science and religion Polkinghorne was raised in a quietly devout Church of England family His mathematical ability was evident as a youngster He earned a bachelor s degree Smirnov Stanislav Russian mathematician who was awarded the Fields Medal in 2010 for his work in mathematical physics Smirnov graduated with a degree in mathematics in 1992 from St Petersburg State University in St Petersburg Russia He received a doctorate in mathematics Villani Cédric French mathematician who was awarded the Fields Medal in 2010 for his work in mathematical physics Villani studied mathematics at the École Normale Supériere in Paris He received a master s degree in numerical analysis from

Original URL path: http://www.britannica.com/topic-browse/Mathematics/Mathematical-Physics (2016-02-13)

Open archived version from archive - Number Theory | Britannica.com

theorem or Church s thesis proposed Dedekind Richard German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts Although not fully recognized in his lifetime his treatment of the ideas of the infinite and of what constitutes a real number continues to Deligne Pierre René Belgian mathematician who was awarded the Fields Medal 1978 the Crafoord Prize 1988 and the Abel Prize 2013 for his work in algebraic geometry Deligne received a bachelor s degree in mathematics 1966 and a doctorate 1968 from the Free University Dickson Leonard Eugene American mathematician who made important contributions to the theory of numbers and the theory of groups Appointed associate professor of mathematics at the University of Texas at Austin in 1899 Dickson joined the staff of the University of Chicago Diophantine equation equation involving only sums products and powers in which all the constants are integers and the only solutions of interest are integers For example 3 x 7 y 1 or x 2 y 2 z 3 where x y and z are integers Named in honour of the 3rd century Diophantus of Alexandria Greek mathematician famous for his work in algebra What little is known of Diophantus s life is circumstantial From the appellation of Alexandria it seems that he worked in the main scientific centre of the ancient Greek world and because he is Dirichlet Peter Gustav Lejeune German mathematician who made valuable contributions to number theory analysis and mechanics He taught at the universities of Breslau 1827 and Berlin 1828 55 and in 1855 succeeded Carl Friedrich Gauss at the University of Göttingen Dirichlet Dirichlet s theorem statement that there are infinitely many prime numbers contained in the collection of all numbers of the form n a b in which the constants a and b are integers that have no common divisors except the number 1 in which case the pair are known as being Drinfeld Vladimir Gershonovich Soviet mathematician who was awarded the Fields Medal in 1990 for his work in algebraic geometry and mathematical physics Drinfeld attended Moscow State University and the V A Steklov Institute of Mathematics Moscow Ph D 1988 He joined the Institute Eratosthenes sieve of systematic procedure for finding prime numbers that begins by arranging all of the natural numbers 1 2 3 in numerical order After striking out the number 1 simply strike out every second number following the number 2 every third number following Erdős Paul Hungarian freelance mathematician known for his work in number theory and combinatorics and legendary eccentric who was arguably the most prolific mathematician of the 20th century in terms of both the number of problems he solved and the number Eudoxus of Cnidus Greek mathematician and astronomer who substantially advanced proportion theory contributed to the identification of constellations and thus to the development of observational astronomy in the Greek world and established the first sophisticated geometrical Euler Leonhard Swiss mathematician and physicist one of the founders of pure mathematics He

Original URL path: http://www.britannica.com/topic-browse/Mathematics/Number-Theory (2016-02-13)

Open archived version from archive - Numerical Analysis | Britannica.com

the highest honour in computer science for his fundamental contributions to numerical analysis Kahan earned a bachelor s degree 1954 a master s degree 1956 numerical analysis area of mathematics and computer science that creates analyzes and implements algorithms for obtaining numerical solutions to problems involving continuous variables Such problems arise throughout the natural sciences social sciences engineering Wilkinson James H English mathematician and winner of the 1970 A M

Original URL path: http://www.britannica.com/topic-browse/Mathematics/Numerical-Analysis (2016-02-13)

Open archived version from archive - Optimization | Britannica.com

should be happening and a controller adjusts the game theory branch of applied mathematics that provides tools for analyzing situations in which parties called players make decisions that are interdependent This interdependence causes each player to consider the other player s possible decisions or strategies Karp Richard Manning American mathematician and computer scientist and winner of the 1985 A M Turing Award the highest honour in computer science for his continuing contributions to the theory of algorithms including the development of efficient algorithms for network linear programming mathematical modeling technique useful for guiding quantitative decisions in business planning industrial engineering and to a lesser extent in the social and physical sciences Applications of the method of linear programming were first seriously mathematical programming theoretical tool of management science and economics in which management operations are described by mathematical equations that can be manipulated for a variety of purposes If the basic descriptions involved take the form of linear algebraic equations optimization collection of mathematical principles and methods used for solving quantitative problems in many disciplines including physics biology engineering economics and business The subject grew from a realization that quantitative problems in manifestly prisoner s dilemma Imaginary situation employed in

Original URL path: http://www.britannica.com/topic-browse/Mathematics/Optimization (2016-02-13)

Open archived version from archive