Documents for "Mathematics: Biographies":

• Abel, Niels Henrik 1802-29, Norwegian mathematician. While a student at the Univ. of Christiania (Oslo) he did fundamental work on the integration of functional expressions and proved the impossiblity of...

• Acarya see Bhaskara.

• Alembert, Jean le Rond d' 1717-83, French mathematician and philosopher. The illegitimate son of the chevalier Destouches, he was named for the St. Jean le Rond church, on whose steps he was found. His father had him...

• Alhazen see Ibn al-Haytham.

• Al-Khowarizmi fl. 820, Arab mathematician of the court of Mamun in Baghdad. His treatises on Hindu arithmetic and on algebra made him famous. He is said to have given algebra its name, and the word algorithm is...

• Apollonius of Perga fl. 247-205 BC, Greek mathematician of the Alexandrian school. He produced a treatise on conic sections that included, as well as his own work, much of the work of his predecessors, among whom was...

• Archimedes 287-212 BC, Greek mathematician, physicist, and inventor. He is famous for his work in geometry (on the circle, sphere, cylinder, and parabola), physics, mechanics, and hydrostatics. He lived most...

• Babbage, Charles 1792-1871, English mathematician and inventor. He devoted most of his life and expended much of his private fortune and a government subsidy in an attempt to perfect a mechanical calculating...

• Banach, Stefan 1892-1945, Polish mathematician. He was educated at the Institute of Technology in Lviv; his doctoral thesis laid the foundations of modern functional analysis, which he continued to work at...

• Banu Musa family of Arab mathematicians and astronomers of the 9th cent. AD The name means "sons of Musa" and refers to the three brothers, Muhammad, Ahmad, and al-Hasan. They supervised the translation of Greek scientific works into Arabic and helped to found the Arabic school of mathematics. The most...

• Barrow, Isaac 1630-77, English mathematician and theologian. His method of finding tangents prefigured the differential calculus developed by Isaac Newton. He was professor of mathematics at Cambridge from 1663...

• Bayes, Thomas 1702-61, English clergyman and mathematician. The son of a Nonconformist minister, he was privately educated and earned his livelihood as a minister to the Nonconformist community at Tunbridge...

• Beltrami, Eugenio 1835-99, Italian mathematician. He is famous for his work on non-euclidean geometry, electricity, and magnetism.

• Benedetti, Giovanni Battista 1530-90, Italian mathematician and physicist. An important forerunner of Galileo, Benedetti had diverse interests, including mechanics, music, hydrostatics, astronomy, astrology, and gnomonics...

• Bernoulli or Bernouilli , name of a family distinguished in scientific and mathematical history. The family, after leaving Antwerp, finally settled in Basel, Switzerland, where it grew in fame. Jacob, Jacques, or James Bernoulli, 1654-1705, became professor at Basel in 1687. One of the chief developers both of the ordinary calculus and of the calculus of variations , he was the first to use the word integral in solving Leibniz's problem of the isochronous curve. He wrote an important treatise on the theory of probability (1713) and discovered the series of numbers that now bear his name, i.e., the...

• Bhaskara called Acarya [Skt.,=learned], b. 1114, Indian mathematician and astronomer. According to the custom, he put his learned treatises into verse, adding, however, explanations in prose. His work Siddhantasiromani includes chapters on arithmetic, algebra, and astronomy that have been translated into English. He gives the first systematic exposition of the decimal system. By mentioning such items as rates of...

• Birkhoff, Garrett 1911-, American mathematician, b. Princeton, N.J.; son of George David Birkhoff. He was educated at Harvard (B.A., 1932) where he was elected a fellow in 1933 and taught until his retirement in...

• Birkhoff, George David 1884-1944, American mathematician, b. Overisel, Mich.; father of Garrett Birkhoff. The son of a physician, he was educated at Harvard (B.A., 1905) and the Univ. of Chicago (Ph.D., 1907) After...

• Bolyai family of Hungarian mathematicians. The father, Farkas, or Wolfgang, Bolyai, 1775-1856, b. Bolya, Transylvania, was educated in Nagyszeben from 1781 to 1796 and studied in Germany during the next three years at Jena and Göttingen, where he began a lifelong friendship with...

• Bolzano, Bernard 1781-1848, Czech philosopher, mathematician, and theologian. Though as a Catholic priest he himself was primarily concerned with religious and ethical questions, he is known today for his work in...

• Boole, George 1815-64, English mathematician and logician. He became professor at Queen's College, Cork, in 1849. Boole wrote An Investigation of the Laws of Thought (1854) and works on calculus and differential...

• Borel, Félix Édouard Émile 1871-1956, French mathematician. He is noted for his work in infinitesimal calculus and the calculus of probabilities. He was professor at the Univ. of Paris (1904-41), director of the Henri...

• Bowditch, Nathaniel 1773-1838, American navigator and mathematician, b. Salem, Mass. He had no formal schooling after the age of 10. In 1795 he went to sea, and on five long voyages he carried out his studies in...

• Bradwardine, Thomas c.1295-1349, English mathematician, natural philosopher, and theologian. He was chaplain to Edward III (c.1338) and later Archbishop of Canterbury. As a mathematician he is known for his Tractatus de proportionibus velocitatum (1328), which attempted to derive novel quantitative relations between speed and force; as a natural philosopher he defended Aristotle's concept of the plenum against atomistic views. His major...

• Briggs, Henry 1561-1630, English mathematician. He was the first professor of geometry at Gresham College, London (1596-1619), and Savilian professor of astronomy at Oxford (from 1619). After publication of...

• Calderón, Alberto 1920-98, Argentine mathematician, b. Mendoza, Argentina, grad. Univ. of Buenos Aires (B.S. 1947), Univ. of Chicago (Ph.D. 1950). He is known for his contributions to mathematical analysis and the...

• Cantor, Georg 1845-1918, German mathematician, b. St. Petersburg. He studied under Karl Weierstrass and taught (1869-1913) at the Univ. of Halle. He is known for his work on transfinite numbers and on the...

• Cardano, Geronimo 1501-76, Italian physician and mathematician. His works on arithmetic and algebra established his reputation. Barred from official status as a physician because of his illegitimate birth, he...

• Cartan, Élie Joseph 1869-1951, French mathematician. The son of a village blacksmith, he graduated from the École normale and taught at the universities of Montpellier, Lyons, Nancy, and finally Paris, where he was...

• Cauchy, Augustin Louis, Baron 1789-1857, French mathematician. He was professor simultaneously (1816-30) at the École polytechnique, the Sorbonne, and the Collège de France in Paris. While a political exile (1830-38) he taught...

• Cavalieri, Francesco Bonaventura 1598-1647, Italian mathematician, a Jesuit priest. Professor at Bologna from 1629, he invented the method of indivisibles (1635) that foreshadowed integral calculus.

• Cayley, Arthur 1821-95, English mathematician. He was admitted to the bar in 1849. In 1863 he was appointed first Sadlerian professor of mathematics at Cambridge. His researches, which covered the field of pure...

• Chern, Shiing-Shen 1911-2004, Chinese-American mathematician, b. Kashing (now Jiaxing), China, D.Sc. Hamburg, 1936. While undertaking graduate studies in China (1932-34), Chern developed what became a lifelong...

• Ch'in Chiu-shao c.1202-1261, Chinese mathematician. He pioneered in the study of indeterminate analysis in his Mathematical Treatise in Nine Sections of 1247. The text existed only in manuscript form for several centuries and still has not been fully translated or investigated. Like many traditional Chinese mathematical works, it reflects a...

• Chu Shih-chieh fl. 1280-1303, Chinese mathematician. He contributed to the study of arithmetic and geometric series and to that of finite differences. His two mathematical works, Introduction to Mathematical Studies...

• Chuquet, Nicolas c.1450-1500, French mathematician, probably b. Paris. Little is known of Chuquet's life. At Lyons in 1484 he composed a manuscript on the science of numbers, which was finally published in two...

• Clairaut, Alexis Claude 1713-65, French mathematician. He assisted P. L. M. de Maupertuis in measuring (1736) a degree of an arc of a meridian in Lapland. He is noted for his work on differential equations and on curves...

• Clavius, Cristoph 1537-1612, German astronomer and mathematician. He entered the Jesuit order in 1555 and studied at Coimbra and Rome. He taught mathematics at the Collegio Romano from 1565. In a commentary on...

• Condorcet, Marie Jean Antoine Nicolas Caritat, marquis de 1743-94, French mathematician, philosopher, and political leader, educated at Reims and Paris. He became a member of the Academy of Sciences in 1769 and of the French Academy in 1782. His work on...

• Conon 3d cent. BC, Greek astronomer and mathematician of Samos. He traveled in the western part of the Greek world making astronomical observations, then settled at Alexandria. He was a student of solar...

• Cournot, Antoine Augustin 1801-77, French mathematician and economist. He developed mathematical theories of chance and probability and was one of the first to attempt the application of mathematics to economic problems...

• d'Alembert, Jean le Rond see Alembert.

• Darboux, Jean Gaston 1842-1917, French mathematician. He is known for his work on orthogonal surfaces and for his application of infinitesimal calculus to geometry. From 1880 until his death he held the chair of...

• de Moivre, Abraham see Moivre, Abraham de.

• De Morgan, Augustus 1806-71, English mathematician and logician, b. India. A noted teacher, he was professor of mathematics (1828-31, 1836-66) at University College (now part of the Univ. of London) and a founder and...

• Dedekind, Julius Wilhelm Richard 1831-1916, German mathematician. Dedekind studied at Göttingen under the German mathematician Carl Gauss and in 1852 received his doctorate there for a thesis on Eulerian integrals. In 1858 he...

• Desargues, Gérard 1591-1661, French mathematician and engineer, a founder of modern geometry. He discovered the theorems on involutions and transversals known by his name and worked on conic sections. His writings,...

• Dickson, Leonard Eugene 1874-1954, American mathematician, b. Independence, Iowa, grad. Univ. of Texas, 1893. He studied in Leipzig and Paris and joined the staff of the Univ. of Chicago in 1900. A leading American...

• Diophantus fl. AD 250, Greek algebraist. He pioneered in solving a type of indeterminate algebraic equation where one seeks integer values for the unknowns; work in this field is known as Diophantine...

• Erdös, Paul 1913-96, Hungarian mathematician, b. Budapest. A child prodigy, he was mostly home-schooled by his parents—both teachers of mathematics—until he entered the Univ. of Budapest in 1930. He graduated...

• Euclid fl. 300 BC, Greek mathematician. Little is known of his life other than the fact that he taught at Alexandria, being associated with the school that grew up there in the late 4th cent. BC He is...

• Euler, Leonhard 1707-83, Swiss mathematician. Born and educated at Basel, where he knew the Bernoullis, he went to St. Petersburg (1727) at the invitation of Catherine I, becoming professor of mathematics there...

• Fermat, Pierre de 1601-65, French mathematician. A magistrate whose avocation was mathematics, Fermat is known as a founder of modern number theory and probability theory. He also did much to establish coordinate geometry (see Cartesian coordinates ) and invented a number of methods for determining maxima and minima that were later of use to Newton in applying the calculus. He noted without proof, although he claimed to have discovered one,...

• Fibonacci, Leonardo b. c.1170, d. after 1240, Italian mathematician, known also as Leonardo da Pisa. In Liber abaci (1202, 2d ed. 1228), for centuries a standard work on algebra and arithmetic, he advocated the adoption of Arabic notation. In Practica geometriae (1220) he organized and extended the material then known in geometry and trigonometry. The sequence of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, … , formed by adding consecutive members, is named for...

• Fisher, Sir Ronald Aylmer 1890-1962, English statistician and geneticist, b. East Finchley, Middlesex, England; educated at Cambridge Univ. (1909-1915; Sc.D., 1926). From 1919 to 1933 he worked at the Rothamsted...

• Fourier, Jean Baptiste Joseph, Baron 1768-1830, French mathematician and physicist. He was noted for his researches on heat and on numerical equations. He originated Fourier's theorem on vibratory motion and the Fourier series, which...

• Gödel, Kurt 1906-78, American mathematician and logician, b. Brünn (now Brno, Czech Republic), grad. Univ. of Vienna (Ph.D., 1930). He came to the United States in 1940 and was naturalized in 1948. He was a...

• Galois, Évariste 1811-32, French mathematician. At the age of 17 he had evolved original concepts on the theory of algebra. He made important contributions to the theory of equations, the theory of numbers, and...

• Gassendi, Pierre 1592-1655, French philosopher and scientist. A teacher and priest, Gassendi taught at Digne, Aix, and the Royal College at Paris and held several church offices. He ranked with the leading...

• Gauss, Carl Friedrich born Johann Friederich Carl Gauss, 1777-1855, German mathematician, physicist, and astronomer. Gauss was educated at the Caroline College, Brunswick, and the Univ. of Göttingen, his education and...

• Germain, Sophie 1776-1831, French mathematician. Although self-taught, she mastered mathematics and corresponded with J. L. Lagrange and C. F. Gauss. She is known especially for her study of the vibrations of...

• Green, George 1793-1841, English mathematician and physicist. He was largely self-taught until, in 1833, he entered Caius College, Cambridge. In addition to making a number of contributions to the calculus,...

• Gregory, James 1638-75, Scottish mathematician. He invented a reflecting telescope (1661), which he described in his Optica promota (1663). In 1668 he became professor of mathematics at the Univ. of St. Andrews and, in 1674, professor of mathematics at the Univ. of Edinburgh. He originated a photometric mode of measuring the...

• Gunter, Edmund 1581-1626, English mathematician and astronomer, educated at Westminster School, London, and Christ Church, Oxford. He invented (1618) a small portable quadrant and discovered (1622) the variation...

• Habash al-Hasib d. c.870, Arab mathematician and astronomer. Habash al-Hasib was born in what is now Mary, Turkmenistan, and worked in Baghdad. He calculated tables of sines, tangents, and standard astronomical...

• Hamilton, Sir William Rowan 1805-65, Irish mathematician and astronomer, b. Dublin. A child prodigy, he had mastered 13 languages by the age of 13 and was still an undergraduate when he became professor of astronomy at the...

• Harriot, Thomas 1560-1621, English mathematician and astronomer. He was tutor to Sir Walter Raleigh, who sent him in 1585 to Virginia as surveyor with Sir Richard Grenville. Returning to England, Harriot wrote A Brief...

• Hermite, Charles 1822-1901, French mathematician. A professor at the École polytechnique, Paris (1869-76), and at the Faculty of Sciences (1869-97), he exerted a strong influence on the French school of...

• Hero Greek mathematician: see Heron of Alexandria.

• Heron of Alexandria or Hero, mathematician and inventor. The dates of his birth and death are unknown; conjecture places them between the 2d cent. BC and the 3d cent. AD He is believed to have lived in Alexandria; although he...

• Hilbert, David (1862-1943), German mathematician, professor at Königsberg (1886-95) and Göttingen (1895-1930), b. Königsberg, Germany. His proof of the theorum of invariants (1890) supplanted earlier computational...

• Ibn al-Haytham or Alhazen , 965-c.1040, Arab mathematician. Ibn al-Haytham was born in Basra, Persia, but made his career in Cairo, where he supported himself copying scientific manuscripts. Among his original works, only...

• Jacobi, Carl Gustav Jacob 1804-51, German mathematician. He was an outstanding teacher and was professor of mathematics at Königsberg (1827-42) and lectured at Berlin from 1844. One of the greatest algorists of all time,...

• John of Hollywood see Sacrobosco, Johannes de.

• Jungius, Joachim 1587-1657, German mathematician, logician, and systematizer of natural history. In 1608 he made his inaugural dissertation at the Univ. of Giessen, proclaiming in it the doctrine, endorsed by...

• Kakutani, Shizuo 1911-2004, Japanese mathematician, b. Osaka, Japan, grad. Tohoko Univ, Ph.D. Princeton, 1941. Kakutani repatriated to Japan during World War II, but returned to Princeton in 1948 and joined the...

• Kircher, Athanasius 1601?-1680, German Jesuit archaeologist, mathematician, biologist, philologist, astronomer, musicologist, and physicist. One of the world's great polymaths, he knew Hebrew, Aramaic, Coptic,...

• Klein, Christian Felix 1849-1925, German mathematician. He is noted for his work in geometry and on the theory of functions. His Erlangen program (1872) for unifying the diverse forms of geometry through the study of...

• Kovalevsky, Sonya 1850-91, Russian mathematician. She studied at the universities of Heidelberg and Berlin (under K. T. Weierstrass) and in 1874 received a Ph.D. in absentia from the Univ. of Göttingen for her...

• Kronecker, Leopold 1823-91, German mathematician. After making a fortune in business he devoted his attention to mathematics and became professor at the Univ. of Berlin in 1883. Noted as an algebraist, he was a...

• Lagrange, Joseph Louis, Comte 1736-1813, French mathematician and astronomer, b. Turin, of French and Italian descent. Before the age of 20 he was professor of geometry at the royal artillery school at Turin. With his pupils...

• Lambert, Johann Heinrich 1728-77, German-French philosopher and scientist, b. Alsace. He developed many basic concepts in mathematics, including that of the hyperbolic functions in trigonometry. In physics he achieved...

• Legendre, Adrien Marie 1752-1833, French mathematician. He is noted especially for his work on the theory of numbers, on which he wrote an essay (1798) containing the law of quadratic reciprocity as well as several...

• Leonardo da Pisa see Fibonacci, Leonardo.

• Levi-Civita, Tullio 1873-1942, Italian mathematician. He taught at the universities of Padua (1898-1919) and Rome (1919-38) and was noted for his researches in pure geometry, hydrodynamics, celestial mechanics, and...

• Lie, Marius Sophus 1842-99, Norwegian mathematician. He is noted for his contributions to the theories of differential equations and continuous transformation groups.

• Lobachevsky, Nikolai Ivanovich 1793-1856, Russian mathematician. A pioneer in non-Euclidean geometry, he challenged Euclid's fifth postulate that one and only one line parallel to a given line can be drawn through a fixed point...

• Möbius, Augustus Ferdinand (1790-1868), German mathematician and astronomer, b. Schulpforta, Saxony. A professor of astronomy at the Univ. of Leipzig, he made important contributions to theoretical astronomy with his...

• Müller, Johannes von 1752-1809, Swiss historian. He spent much of his life in Germany, where he held political posts under the elector of Mainz, the king of Prussia, and King Jérôme Bonaparte of Westphalia. His...

• Maclaurin, Colin 1698-1746, Scottish mathematician and natural philosopher, one of the greatest mathematicians of his time. He was professor at Aberdeen and from 1725 at the Univ. of Edinburgh. He was an authority...

• Mandelbrot, Benoit B. 1924-, French mathematician, b. Warsaw, Poland. Largely self-taught and considered a maverick in the field of mathematics, he is uncomfortable with the rigorously pure logical analysis prescribed...

• Maupertuis, Pierre Louis Moreau de 1698-1759, French mathematician and astronomer. For his skillful support of Newton's theory he was admitted to the Royal Society of London in 1728. He headed (1736-37) an expedition of...

• Miller, George Abram 1863-1951, American mathematician, b. Lehigh co., Pa., grad. Muhlenberg College (B.A., 1887), Ph.D. Cumberland Univ., 1893. He was professor at the Univ. of Illinois (1907-31). His chief work was...

• Minkowski, Hermann 1864-1909, Russian mathematician. He was educated in Germany and was professor at the Univ. of Königsberg (1894-96), the Federal Institute of Technology, Zürich (1896-1902), and the Univ. of...

• Mittag-Leffler, Magnus Gösta 1846-1927, Swedish mathematician. He was (1877-81) professor at Helsingfors (Helsinki) and at the Univ. of Stockholm from 1881. In 1882 he founded Acta Mathematica, which he edited until his death. He made important contributions to analysis (including the Mittag-Leffler theorem on single-valued functions) and to linear differential equations and greatly...

• Moivre, Abraham de 1667-1754, French-English mathematician. He fled to England after the revocation of the Edict of Nantes. He was called upon by the Royal Society to help decide the issue between Newton and Leibniz...

• Monge, Gaspard, comte de Péluse 1746-1818, French mathematician, physicist, and public official. He was distinguished for his geometrical research, which laid the foundations of modern descriptive geometry, a field essential to...

• Napier, John 1550-1617, Scottish mathematician. He invented logarithms and wrote Mirifici logarithmorum canonis descriptio (1614), containing the first logarithmic table and the first use of the word logarithm. His Rabdologiae (1617) gives various methods for abbreviating arithmetical calculations. One method of multiplication uses a system of numbered rods called Napier's rods, or Napier's bones; this was a major...

• Nash, John Forbes, Jr. 1928-, American mathematician, b. Bluefield, W.Va., grad. Carnegie Institute of Technology (now Carnegie-Mellon Univ., B.A. and M.A. 1948), Ph.D. Princeton 1950. During a five-year period,...

• Nonius, Petrus see Nunes, Pedro.

• Nunes, Pedro Lat. Petrus Nonius, 1502-1578, Portuguese mathematician, geographer, and writer on navigation and geometry. He was the first (1534) to demonstrate an instrument for measuring angles and was the reputed inventor of the...

• Painlevé, Paul 1863-1933, French statesman and mathematician. A mathematical prodigy when a child, he entered on a career devoted to science. He was a professor at the Sorbonne and the École Polytechnique when...

• Pappus fl. c.300, Greek mathematician of Alexandria. He recorded and enlarged on the results of his predecessors, including Euclid and Apollonius of Perga, in his Mathematical Collection (8 books; date conjectural). The six and a half extant books, edited and translated into Latin by Commandinus (1588), stimulated a revival of geometry in the 17th cent.; Descartes expounded several...

• Pascal, Blaise 1623-62, French scientist and religious philosopher. Studying under the direction of his father, a civil servant, Pascal showed great precocity, especially in mathematics and science. Before he...

• Peirce, Benjamin 1809-80, American mathematician and astronomer, b. Salem, Mass., grad. Harvard, 1829. From 1833 he was a professor at Harvard; he helped establish the Harvard Observatory and was an organizer of...

• Plücker, Julius 1801-68, German mathematician and physicist. He became professor of mathematics (1836) and of physics (1847) at the Univ. of Bonn. He is known for his work in analytical geometry, in magnetic and...

• Poincaré, Jules Henri 1854-1912, French mathematician, physicist, and author. He was from 1881 connected with the faculty of sciences at the Univ. of Paris. One of the greatest mathematicians of his age, Poincaré, by...

• Poisson, Siméon Denis 1781-1840, French mathematician and physicist. From 1802 he taught at the École polytechnique, Paris, and was also on the faculty of sciences at the Univ. of Paris from 1809. His chief interest...

• Poncelet, Jean Victor 1788-1867, French mathematician and army engineer. He taught at the school of mechanics at Metz and at the Faculté des Sciences and the École Polytechnique, both in Paris. While a prisoner of war...

• Ramanujan, Srinivasa 1889-1920, Indian mathematician. He was a self-taught genius in pure mathematics who made original contributions to function theory, power series, and number theory with the training gained from a...

• Regiomontanus [Lat.,=belonging to the royal mountain, i.e., to Königsberg], 1436-76, German astronomer and mathematician, b. Königsberg. His original name was Johannes Müller. In 1461 he went to Rome with...

• Riemann, Bernhard (Georg Friedrich Bernhard Riemann) , 1826-66, German mathematician. He studied at the universities of Göttingen and Berlin and was professor at Göttingen from 1859. His great contributions to mathematics include his work on the...

• Sacrobosco, Johannes de or John of Hollywood, c.1200-1256, English mathematician and astronomer. He wrote several widely read and influential books: Algorismus, a study of arithmetic; a treatise on the calendar; and...

• Shannon, Claude Elwood 1916-2001, American applied mathematician, b. Gaylord, Michigan. A student of Vannevar Bush at the Massachusetts Institute of Technology (MIT), he was the first to propose the application of symbolic logic to the design of relay circuitry with his paper "A Symbolic Analysis of Relay and Switching Circuits" (1938). His insight that all data could be encoded as a series of 1's and 0's pioneered the breakthrough in digital electronics that led to the modern digital computer and telecommunications...

• Smith, Henry John Stephen 1826-83, British mathematician. He was a lecturer in mathematics (1850-73) and, from 1860 to 1883, Savilian professor of geometry at Oxford Univ. He is especially noted for his work on the theory...

• Snell, Willebrord 1591-1626, Dutch mathematician. He is generally credited with the discovery (1621) of the law of the refraction of light. In 1613 he became professor of mathematics at the Univ. of Leiden. His two...

• Snellius, Willebrord see Snell, Willebrord.

• Steiner, Jakob 1796-1863, Swiss mathematician. He was largely self-taught and was professor of geometry at the Univ. of Berlin from 1834. A pioneer in the development of synthetic, or pure, geometry (i.e.,...

• Stevin, Simon 1548-1620, Dutch engineer and mathematician. His experiments in hydrostatics showed that the pressure exerted by a liquid is dependent only on its vertical height and not on the shape of the...

• Sylvester, James Joseph 1814-97, English mathematician. He studied at Cambridge for four years after 1831, but because degrees were limited to members of the Church of England and he was a Jew, he was not granted a degree...

• Tait, Peter Guthrie 1831-1901, Scottish physicist and mathematician. He was professor of natural philosophy at Edinburgh from 1860 and conducted important investigations in thermodynamics and the kinetic theory of...

• Tartaglia, Niccolò c.1500-1577, Italian engineer and mathematician. Largely self-educated, he taught mathematics at Verona, Brescia, and Venice. A pioneer in applying mathematics to artillery, he recorded his...

• Taylor, Brook 1685-1731, English mathematician. He originated Taylor's theorem, a formula important in differential calculus, which relates a function to its derivatives by means of a power series. This theorem...

• Turing, Alan Mathison 1912-54, British mathematician and computer theorist. While studying at Cambridge Univ. he began work in predicate logic that lead to a proof (1937) that some mathematical problems are not...

• Viète, François 1540-1603, French mathematician. As a founder of modern algebra, he introduced the use of letters as algebraic symbols and correlated algebra with geometry and trigonometry. A prominent lawyer, he...

• Von Neumann, John 1903-57, American mathematician, b. Hungary, Ph.D. Univ. of Budapest, 1926. He came to the United States in 1930 and was naturalized in 1937. He taught (1930-33) at Princeton and after 1933 was...

• Wallis, John 1616-1703, English mathematician. He was Savilian professor of geometry at Oxford Univ. from 1649. He systematized the use of formulas, introduced the symbol ∞ for infinity, and made a study of...

• Weaver, Warren 1894-1978, American scientist, b. Reedsburg, Wis., grad. Univ. of Wisconsin. He taught mathematics at Wisconsin (1920-32), was director of the division of natural sciences at the Rockefeller...

• Weierstrass, Karl Wilhelm Theodor 1815-97, German mathematician. From 1864 he was professor of mathematics at the Univ. of Berlin. His development of the modern theory of functions is described in his Abhandlungen aus der Funktionenlehre...

• Whitehead, Alfred North 1861-1947, English mathematician and philosopher, grad. Trinity College, Cambridge, 1884. There he was a lecturer in mathematics until 1911. At the Univ. of London he was a lecturer in applied...

• Wiener, Norbert 1894-1964, American mathematician, educator, and founder of the field of cybernetics, b. Columbia, Mo., grad. Tufts College, 1909, Ph.D. Harvard, 1913. In 1920 he joined the faculty of the...

• Zygmund, Antoni 1900-1992, Polish-American mathematician, b. Warsaw, Ph.D. Univ. of Warsaw, 1923. In 1940 he escaped from German-controlled Poland to the United States. He served in a number of posts before he...