Julia – Klee BIOGRAPHIES
Julia – Klee BIOGRAPHIES
Julia, Gaston (1893–1978) French hero of World War I who worked on DYNAMICAL SYSTEMS while recovering from his wounds in a hospital. Julia’s discovery of the important properties of JULIA SETS were appreciated only after BENOIT MANDELBROT
displayed Julia sets on the computer and showed their relevance to the study of FRACTALS .
K ¯aty ¯ayana (c. 200 B . C . E .) Vedic seer who wrote one of the main Sulba
Sutras, which are the oldest known writings on geometry. His work includes approximate squaring of the circle and computation of a value for √2– that is accurate to five decimal places.
Kauffman, Louis (b. 1945) American mathematician who discovered the KAUFFMAN POLYNOMIAL , an important knot invariant. He has made numerous other contributions to KNOT THEORY , applications of knot theory to statistical mechanics, quantum theory, abstract algebra, combinatorics, and the foundations of mathematics. He received his doctorate from Princeton University in 1972 and is professor of mathematics at the University of Illinois at Chicago.
Kepler, Johannes (1571–1630) German astronomer and cosmologist who discovered the laws governing the motion of the planets around the Sun. An accomplished and creative geometer, Kepler based his astronomical work on his deep understanding of the Platonic solids and the conic sections. Kepler was the first to study the REGULAR and ARCHIMEDEAN TILINGS and show their connection to the regular polyhedra. He discovered all 11 Archimedean tilings and proved there were no others. He discovered several regular polyhedra and appears to be the first mathematician interested in sphere PACKINGS .
Khayyam, Omar (c. 1048–c. 1131) Persian astronomer, mathematician, poet, and philosopher who made contributions
to arithmetic, algebra, and geometry. He solved the cubic Johannes Kepler
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equation by considering the solutions to be the intersection of conic sections and investigated the FIFTH POSTULATE of EUCLID .
Klee, Victor (b. 1925) American mathematician who has contributed to
a wide range of areas of mathematics, including CONVEX SETS ,
Julia – Klee BIOGRAPHIES
BIOGRAPHIES
Klein – Kuratowski
mathematical programming, combinatorics, the design and analysis of algorithms, and POINT SET TOPOLOGY . He received his doctorate from the University of Virginia in 1949 and is now professor emeritus at the University of Washington.
Klein, Felix (1849–1925) German mathematician who had a lasting impact on all areas of geometry. In 1872, at the age of 23,
Klein presented his ERLANGER PROGRAM , a way to unify different geometric theories using geometric TRANSFORMATIONS and their invariants. He later went on to make major contributions to PROJECTIVE GEOMETRY , TOPOLOGY , and ANALYSIS , in addition to continuing his work in transformation geometry. The KLEIN BOTTLE , a one-sided nonorientable surface that cannot exist in three-dimensional space, is named after him.
von Koch, Nils Fabian Helge (1870–1924) Swedish mathematician who is noted for creating the KOCH SNOWFLAKE to demonstrate
Felix Klein (Aufnahme von
the existence of a curve that is continuous but nowhere smooth.
Fr. Struckmeyer, Göttingen,
He studied at Stockholm University and later became a
courtesy AIP Emilio Segrè
professor there.
Visual Archives, Lardé Collection)
Kolmogorov, Andrei Nikolaevich (1903–87) Russian mathematician who did research in probability, TOPOLOGY , ALGEBRAIC TOPOLOGY , functional analysis, DYNAMICAL SYSTEMS , and the foundations of geometry.
Kovalevskaya, Sonya Vasilievna (1850–91) Russian mathematician who made outstanding contributions to PARTIAL DIFFERENTIAL
EQUATIONS and ANALYSIS . She studied in Germany under WEIERSTRASS and later accepted an academic position in Sweden.
Kuperberg, Krystyna (b. 1944) Polish-born American mathematician who studies TOPOLOGY , DISCRETE GEOMETRY , and DYNAMICAL SYSTEMS . She is a professor of mathematics at Auburn University.
Kuratowski, Kazimierz (1896–1980) Polish mathematician who was a leader of the Polish mathematical community and a world- renowned topologist. He worked on the foundations of POINT SET TOPOLOGY and developed the definition of TOPOLOGICAL
BIOGRAPHIES
Klein – Kuratowski
Laborde – Leech BIOGRAPHIES
SPACE that is now used. He also studied METRIC SPACES , COMPACT spaces, and GRAPH THEORY .
Laborde, Jean-Marie (b. 1945) French mathematician and computer scientist who led the development of the geometry software Cabri. He is research director of the Centre National de la Recherche Scientifique and head of the Cabri Geometry Project at the University of Grenoble.
Lagrange, Joseph Louis (1736–1813) Italian mathematician of French heritage who received great recognition for his work in DIFFERENTIAL EQUATIONS , algebra, NUMBER THEORY , and mechanics. Born in Turin, he became a professor of mathematics there at the age of 19, then spent 20 years in Berlin at the court of Frederick the Great before going to Paris, where he spent the rest of his life.
Lambert, Johann Heinrich (1728–77) German mathematician who proved that pi is IRRATIONAL . Of international renown, Lambert studied EUCLID ’s PARALLEL POSTULATE and its negation, laying the groundwork for ELLIPTIC GEOMETRY . He also wrote a definitive work on the mathematical theory of PERSPECTIVE .
Lamé, Gabriel (1795–1870) French engineer who developed the theory of CURVILINEAR COORDINATES while working on the conductance of heat. Lamé worked on many problems with mathematical aspects and was considered to be the leading mathematician in France during his lifetime.
Laplace, Pierre Simon de (1749–1827) French astronomer and mathematician who is noted for writing Celestial Mechanics, which uses mathematics to describe the motion of the moon and planets. He also made advances in DIFFERENTIAL EQUATIONS and probability.
Lebesgue, Henri (1875–1941) French mathematician who generalized concepts of CALCULUS to make them more widely applicable. He also studied the CALCULUS OF VARIATIONS , the theory of SURFACE AREAS , and DIMENSION THEORY .
Leech, John (1926–92) British computer scientist and mathematician who discovered the Leech lattice, a LATTICE corresponding to a
Laborde – Leech BIOGRAPHIES
BIOGRAPHIES
Lefschetz – Levi-Civita
sphere packing in 24-dimensional space. He also studied NUMBER THEORY , geometry and combinatorial group theory.
Lefschetz, Solomon (1884–1972) Russian-born American mathematician who began his career as an engineer but switched to mathematics in 1910 after the loss of both hands in an industrial accident. He was a leader in the fields of ALGEBRAIC GEOMETRY , ALGEBRAIC TOPOLOGY , and DYNAMICAL SYSTEMS . He spent most of his mathematical career at Princeton University.
Legendre, Adrien Marie (1752–1833) French mathematician who studied NUMBER THEORY , ELLIPTIC INTEGRALS , and geometry. His Eléments de géométrie was influential in the reform of secondary mathematics education in France. He gave the first proof of EULER ’ S FORMULA for polyhedra.
Leibniz, Gottfried Wilhelm (1646–1716) German philosopher and mathematician who independently developed CALCULUS . Leibniz studied law in Germany and became interested in mathematics while he was visiting France on a diplomatic mission. He introduced symbolic logic, constructed a mechanical calculator, and worked on DETERMINANTS , COMPLEX NUMBERS , binary numbers, and combinatorics.
Lemoine, Émile (1840–1912) Lemoine studied at the École Polytechnique in Paris and became a civil engineer, amateur
mathematician, and musician. He discovered that the SYMMEDIANS of a triangle meet at a point, now called the Lemoine point.
Leonardo da Vinci (1452–1519) Italian Renaissance painter, inventor,
Gottfried Wilhelm Leibniz
scientist, and engineer who was also a mathematician. In
(Image Select/Art Resource, NY)
studying the designs of symmetric buildings, he discovered that the SYMMETRIES of a finite design must be either CYCLIC or DIHEDRAL .
Levi-Civita, Tullio (1873–1941) Italian mathematician who worked in DIFFERENTIAL GEOMETRY , contributing to the development to tensors, which are important in the theory of general relativity.