Li – Lorenz BIOGRAPHIES

Li – Lorenz BIOGRAPHIES

Li Ye (1192–1279) Chinese mathematician who wrote the Sea Mirror of Circle Measurements, in which he used quadratic and cubic equations to solve problems of finding the diameters of circles that satisfy various given conditions.

Lie, Sophus (1842–99) Norwegian mathematician who developed LIE GROUPS and Lie algebras and made many other brilliant contributions to geometry and PARTIAL DIFFERENTIAL EQUATIONS . Lie became close friends with FELIX KLEIN during his student years in Berlin. Once, while traveling through France, he was arrested as a spy because his mathematical work looked like secret code.

Lindemann, Ferdinand von (1852–1939) German mathematician who proved that pi is TRANSCENDENTAL . Lindemann was a student of FELIX KLEIN at Erlangen and then continued his studies in England and France before returning to Germany to teach.

Liu Hui (c. 260) Chinese mathematician who made contributions to algebra and geometry. He wrote the Sea Island Mathematical Manual and the Commentary on the Nine Chapters, where he provides explanation and justification of material in the Nine

Chapters and gives one of the earliest known proofs of the Pythagorean theorem. He computed a value of 3.14 for pi and computed the volume of a TETRAHEDRON , the FRUSTUM of pyramid, and many other solids.

Sophus Lie (Scanpix Norway)

Lobachevsky, Nicolai (1792–1856) Russian mathematician who independently discovered HYPERBOLIC GEOMETRY and many of its properties. Lobachevsky served as rector of the University of Kazan, where he was a popular teacher and administrator.

Lorentz, Hendrik Antoon (1853–1928) Dutch physicist who worked on the FitzGerald-Lorentz contraction used in special relativity and developed a mathematical theory of the electron for which

he received the Nobel Prize in physics in 1902. A student and later professor at Leiden University in the Netherlands, Lorentz was primarily interested in theoretical physics.

Lorenz, Edward (b. 1917) American meteorologist at MIT who

Nicolai Lobachevsky

discovered the BUTTERFLY EFFECT and the phenomenon of

(The Granger Collection,

CHAOS by studying a mathematical model of a weather system

New York)

Li – Lorenz BIOGRAPHIES

BIOGRAPHIES

Madhava of Sangamagramma – Minkowski

on a primitive computer. As of 2002 he was professor emeritus at MIT.

Madhava of Sangamagramma (c. 1340–1425) Astronomer and mathematician of southern India who wrote many astronomical treatises. He gave power series expansions for pi and for the SINE , COSINE , and INVERSE TANGENT functions. He created a table of the sine function accurate to eight or nine decimal places.

Mandelbrot, Benoit (b. 1924) American mathematician who is famous for the discovery of FRACTALS and the MANDELBROT SET . He was born in Poland, moved to France at the age of 12, and finally moved to the United States in 1958, where he was an IBM fellow. As of 2002 he was professor of mathematics at Yale University.

Mascheroni, Lorenzo (1750–1800) Italian priest, poet, and

Benoit Mandelbrot

mathematician who is best known for proving that all

(Michael Marsland/Yale

Euclidean constructions can be made with compass alone.

University)

Menaechmus (c. 350 B . C . E .) Greek mathematician who discovered the conic sections. He was a student of EUDOXUS and later tutor to

Alexander the Great.

Menelaus (c. 100 C . E .) Greek astronomer residing in Alexandria who made extensive use of TRIGONOMETRY in his astronomical calculations and established trigonometry and SPHERICAL

TRIGONOMETRY as distinct branches of mathematics. Milnor, John (b. 1931) American mathematician who has been

influential in the development of DIFFERENTIAL TOPOLOGY , ALGEBRAIC TOPOLOGY , MORSE THEORY , KNOT THEORY , and DYNAMICAL SYSTEMS . Appointed to the faculty of Princeton

University at the age of 23, Milnor was awarded the Fields Medal in 1962 for his discovery of the EXOTIC SPHERES . He is now professor of mathematics at the State University of New York (SUNY) at Stony Brook.

Minkowski, Hermann (1864–1909) Russian-born mathematician who

John Milnor (John Griffin/

was the founder of the GEOMETRY OF NUMBERS and

SUNY SB)

established the geometric framework for special relativity.

BIOGRAPHIES

Madhava of Sangamagramma – Minkowski

Möbius – Moufang BIOGRAPHIES

Minkowski studied mathematics in Germany, where he became close friends with DAVID HILBERT .

Möbius, August Ferdinand (1790–1868) German astronomer and mathematician who spent most of his life in Leipzig, where he was the director of the observatory. His major contributions to geometry include HOMOGENEOUS COORDINATES , BARYCENTRIC COORDINATES , INVERSION , and the MÖBIUS STRIP .

Mohr, Georg (1640–97) Danish mathematician who proved that all compass and straightedge constructions can be done with compass alone. Mohr studied in Holland, France, and England.

Moivre, Abraham de (1667–1754) French-born English mathematician who developed the formula (cos θ + i sin θ) n = (cos nθ + i sin nθ) for COMPLEX NUMBERS . He also studied ANALYTIC GEOMETRY and probability.

Monge, Gaspard (1746–1818) French mathematician who was a founder of PROJECTIVE GEOMETRY and DIFFERENTIAL GEOMETRY . He helped establish the École Polytechnique in Paris and made important contributions to ALGEBRAIC

Gaspard Monge (Réunion

GEOMETRY and the geometry of curves and surfaces. Born the

des Musées Nationaux/Art

son of a shopkeeper in a small town in Burgundy, Monge

Resource, NY)

attended a French military school where he showed early promise with discoveries in DESCRIPTIVE GEOMETRY .

Moore, Robert L. (1882–1974) American mathematician and educator who made contributions to POINT SET TOPOLOGY and the foundations of topology. He developed the innovative Moore Method for teaching research skills in mathematics.

Morgan, Frank (b. 1952) American mathematician who studies minimal surfaces and was a collaborator on the proof of the double bubble theorem in 2000. He received his doctorate from Princeton University in 1977 and is now professor of mathematics at Williams College.

Moufang, Ruth (1905–77) German mathematician who contributed to the algebraic study of projective planes and theoretical physics. Moufang received her doctorate in 1931 for a thesis in PROJECTIVE GEOMETRY and was an industrial mathematician

Frank Morgan (courtesy

before being joining the University of Frankfurt, where she

Frank Morgan)

Möbius – Moufang BIOGRAPHIES

BIOGRAPHIES

Mydorge – Pappus

was the first woman in Germany to be appointed as a full professor.

Mydorge, Claude (1585–1647) French lawyer who devoted most of his life to mathematics. He wrote books on optics, the CONIC SECTIONS , and recreational mathematics. He was a friend of RENÉ DESCARTES and made many optical instruments for him.

Newton, Isaac (1643–1727) British physicist and mathematician who developed CALCULUS in order to solve problems in physics. He discovered gravity and used his newly invented calculus to

show that his theory of gravity had as a consequence the elliptic orbits of the planets.

Noether, Emmy (1882–1935) German algebraist who pioneered the

Isaac Newton (AIP Emilio

modern abstract approach to the study of groups. She proved

Segrè Visual Archives, Physics Today Collection)

that every conservation law in physics is related to a symmetry of space and also worked on the general theory of relativity. She was the first to recognize the algebraic nature of certain topological structures, thus contributing to the development of algebraic topology. She spent the last one and a half years of her life at Bryn Mawr College in Bryn Mawr, Pennsylvania.

Novikov, Sergei Petrovich (b. 1938) Soviet topologist who has made important contributions to DIFFERENTIAL TOPOLOGY , DYNAMICAL SYSTEMS , ALGEBRAIC TOPOLOGY , mathematical physics, and GAUGE FIELD theories. He was awarded the Fields Medal in 1970. Since 1996 he has been professor at the

University of Maryland at College Park.

Emmy Noether (The

Pacioli, Luca de (1445–1514) Italian mathematician and Franciscan

Granger Collection, NY)

friar who traveled throughout Italy studying and teaching mathematics. A student of LEON ALBERTI , Pacioli was a close friend of LEONARDO DA VINCI , who made the drawings for his book on the golden ratio, Divina proportione (The Divine Proportion).

Pappus (c. 300–c. 350) Greek mathematician who taught at the school in Alexandria and was the last great geometer of antiquity. His discoveries include three theorems that are now part of