Darboux – Descartes BIOGRAPHIES
Darboux – Descartes BIOGRAPHIES
Darboux, Gaston (1842–1917) French mathematician who made important contributions to DIFFERENTIAL GEOMETRY and ANALYSIS . He studied the CYCLIDES and the shortest path between two points on a surface.
Daubechies, Ingrid (b. 1954) American mathematician who is a founder of the theory of WAVELETS . Born in Belgium, Daubechies was awarded a doctorate in physics and received a MacArthur fellowship in 1992. She is a member of the National Academy of Sciences and a professor at Princeton University.
Dedekind, Richard (1831–1916) German analyst who developed the DEDEKIND CUT , a precise way of constructing the REAL NUMBERS from the RATIONAL numbers using the language of SET THEORY .
Ingrid Daubechies
Dehn, Max (1878–1952) German mathematician who developed the
(Denise Applewhite)
procedure known as DEHN SURGERY in topology. When he was
a student of DAVID HILBERT at Göttingen, he solved the third of the problems proposed by Hilbert in 1900. In 1914, he proved that the left-hand and the right-hand TREFOIL knots are not equivalent to each other. In 1940, he came to the United States, where he taught at Black Mountain College in North Carolina.
Delaunay (Delone), Boris Nikolaevich (1890–1980) Russian mathematician who studied algebra, NUMBER THEORY , and the GEOMETRY OF NUMBERS . He introduced the DELAUNAY TRIANGULATION in the context of his work on the structure of crystals.
Democritus (c.460–c. 379 B . C . E .) Ancient Greek philosopher who
discovered formulas for the volume of a prism, pyramid, cylinder, and cone.
Desargues, Girard (1591–1661) French architect and military engineer who made many significant discoveries in
PROJECTIVE GEOMETRY , including the theorem named after him. The value of his work was recognized only many years
after his death. Descartes, René (1596–1650) French philosopher, scientist, and
René Descartes (Réunion
mathematician who was interested in the deepest and most
des Musées Nationaux/
universal principles of knowledge and how they could be
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Darboux – Descartes BIOGRAPHIES
BIOGRAPHIES
Devaney – Douglas
discovered. His invention of COORDINATE GEOMETRY and ANALYTIC GEOMETRY allowed the powerful techniques of symbolic algebra to be used to uncover and understand properties of geometric shapes. Today, analytic geometry is an essential tool for mathematicians and the coordinate plane is
called the Cartesian plane to honor Descartes for his discovery. Devaney, Robert (b. 1948) American mathematician who has made
significant contributions to the study of FRACTALS and DYNAMICAL SYSTEMS . He is a professor of mathematics at Boston University, where he has developed computer graphics software for viewing and studying fractals.
Diocles (c. 210–190 B . C . E .) Greek mathematician who studied the CONIC SECTIONS . He discovered the properties of the CISSOID and discovered the relationship between the focus and the directrix of a PARABOLA .
Dirichlet, Peter Lejeune (1805–59) Of Belgian ancestry, Dirichlet was raised in Germany, studied in France, and returned to Germany to teach at the University of Berlin and later at Göttingen. He worked in NUMBER THEORY , DIFFERENTIAL EQUATIONS , and FOURIER SERIES . He initiated the development of analytic number theory and proposed the definition of FUNCTION that is used today. He originated the pigeonhole principle, which states that if n objects are placed in fewer than n pigeonholes, at least one pigeonhole must contain more than one object.
Donaldson, Simon K. (b. 1957) British mathematician who proved that there are different smooth structures on four-dimensional real space, opening up questions about the relationships between algebraic and topological properties in the fourth dimension. He was awarded the Fields Medal in 1986 for this result and is professor of mathematics at Imperial College in London.
Douady, Adrien (b. 1935) French mathematician who has extensively studied the MANDELBROT SET . The rabbit-shaped FRACTAL that
he studied is named Douady’s rabbit after him. He is a professor at the École Normale Supérieure in Paris.
Douglas, Jesse (1897–1965) American mathematician who independently solved PLATEAU ’ S PROBLEM and made other
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Devaney – Douglas
Dupin – Dürer BIOGRAPHIES
contributions to the study of MINIMAL SURFACES . He was awarded the Fields Medal in 1936.
Dupin, François Pierre Charles (1784–1873) French naval engineer who made his famous discovery of the Dupin’s CYCLIDES as a student of MONGE at the École Polytechnique in Paris. He made other contributions to DIFFERENTIAL GEOMETRY , including the Dupin indicatrix, while pursuing a career in the navy, eventually becoming the French minister of maritime affairs.
Dürer, Albrecht (1471–1528) German artist who was interested in the use of mathematics as a foundation for his art. While traveling in Italy to learn more about art, he became acquainted with the theory and practice of PERSPECTIVE and proportion. After his second trip to Italy, Dürer wrote a four-volume work, the first German books on mathematics. These books described the
From About the Art of Measurement by Albercht Dürer (Dover)
Dupin – Dürer BIOGRAPHIES
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Eratosthenes – Euclid
construction of curves, including the SPIRAL OF ARCHIMEDES , the LOGARITHMIC SPIRAL , and the CONCHOID , discussed the PLATONIC SOLIDS and the SEMIREGULAR POLYHEDRA , and gave an introduction to the theory of PERSPECTIVE . Dürer also invented NETS to describe the structure of polyhedra.
Eratosthenes (c. 276–c. 195 B . C . E .) Greek mathematician, astronomer, poet, and athlete who made a remarkably accurate calculation of the circumference of the Earth and created the sieve of Eratosthenes, a way to determine which numbers are prime. Born in Cyrene, now part of Libya, Eratosthenes studied in Athens and then went to Alexandria, where he spent the rest of his life.
Erdös, Paul (1913–96) Itinerant mathematician who was born and educated in Hungary but then traveled the world, seeking out mathematicians and mathematics problems. His work is remarkable for its depth and breadth, covering the areas of NUMBER THEORY , combinatorics, GRAPH THEORY , and discrete mathematics.
Escher, M. C. (1898–1970) Dutch artist who made frequent use of TILINGS , spheres, POLYHEDRA , HYPERBOLIC GEOMETRY , and other mathematical ideas in his work. Escher also made important mathematical discoveries and was the first to study and classify COLOR SYMMETRIES .
Euclid (c. 330–c. 270 B . C . E .) Greek mathematician whose name is synonymous with the study of geometry. He first studied at PLATO ’s Academy in Athens and then went to Alexandria
around 300 B . C . E ., where he wrote the Elements and other works on the CONIC SECTIONS , SPHERICAL GEOMETRY , PERSPECTIVE , and optics. The Elements included all the fundamental theorems in plane geometry, NUMBER THEORY , and SOLID GEOMETRY that were known at the time. The original contributions of Euclid presented in the Elements include a theory of parallel lines, a proof of the Pythagorean theorem, a proof of the infinitude of prime numbers, and the Euclidean algorithm for finding the greatest common denominator of two numbers. Because of its clarity, comprehensiveness, and logical sequence, it has become the standard for mathematical exposition. Euclid is famous for
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Eratosthenes – Euclid
Eudoxus of Cnidus – Feigenbaum BIOGRAPHIES
telling the ruler Ptolemy that there is “no royal road to geometry.”
Eudoxus of Cnidus (c. 391–338 B . C . E .) Philosopher, physician,
mathematician, and astronomer who traveled widely in the ancient world before eventually returning to his native city, Cnidus, in what is today Turkey. His theory of PROPORTIONS was the first step in the mathematical understanding of the REAL NUMBERS and resolved questions about the nature of INCOMMENSURABLES . His method of exhaustion was widely used to find the area and volume of CURVILINEAR figures.
Euler, Leonhard (1707–83) Swiss-born mathematician who made discoveries in all areas of mathematics and is regarded as one of the greatest mathematicians of all time. Born in Basel, where he was a friend of the Bernoulli family, Euler spent most of his life in Saint Petersburg at the court of Catherine the Great. His analysis of the Konigsberg Bridge Problem marked the beginning of TOPOLOGY and GRAPH THEORY . His other contributions to geometry include the EULER NUMBER , the EULER LINE , and Euler’s formula for normal curvature.
Fano, Gino (1871–1952) Italian-born mathematician who studied in Göttingen under FELIX KLEIN . After his studies, he returned to Italy, where he taught for more than 40 years before moving to Switzerland. Fano was a pioneer in the study of FINITE GEOMETRY and discovered the first finite projective geometry, which now bears his name.
Fatou, Pierre (1878–1929) French mathematician who studied at the
Leonhard Euler (Image
École Normale Supérieure in Paris and was awarded a doctoral
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degree in 1906 for results in the theory of complex functions. His work in the iterations of complex functions marked the beginning of the study of FRACTALS .
Federov, Efgraf Stepanovich (1853–1919) Russian crystallographer who independently discovered the 230 CRYSTALLOGRAPHIC GROUPS .
Feigenbaum, Mitchell Jay (b. 1944) American physicist who discovered the FEIGENBAUM NUMBER and its role in CHAOS theory. He received a doctoral degree in physics from the Massachusetts Institute of Technology (MIT) and then joined
Eudoxus of Cnidus – Feigenbaum BIOGRAPHIES
BIOGRAPHIES
Ferguson – Freedman
the staff at Los Alamos National Laboratory. Feigenbaum is now a professor of physics at Rockefeller University.
Ferguson, Helaman (b. 1940) American mathematician and sculptor who has used his knowledge of geometry and TOPOLOGY to create beautiful and inspiring sculptures. His work helps the viewer understand the nature of abstract topological concepts and is displayed at many mathematical institutions throughout the country.
Fermat, Pierre de (1601–65) French judge and amateur mathematician who made significant and lasting contributions to NUMBER THEORY . He independently developed ANALYTIC GEOMETRY and the beginnings of CALCULUS . Along with BLAISE PASCAL , he founded the study of probability. His study of optics led to Fermat’s principle of least time: A ray of light going from one point to another takes the path that requires the least time.
Feuerbach, Karl Wilhelm (1800–34) German mathematician who discovered the NINE - POINT CIRCLE when a student 22 years of age. He continued to work in geometry until forced to retire because of poor health.
Pierre de Fermat (Getty)
Fibonacci (1180–1240) Italian merchant who contributed to many areas of mathematics. Leonardo Pisano or Leonardo of Pisa,
better known as Fibonacci, discovered the Fibonacci series, 1,
1, 2, 3, 5, 8, . . . , which is used to model natural growth and has many deep mathematical properties.
Fourier, Joseph (1768–1830) French mathematician and scientist who introduced Fourier series, which are series of sines and cosines that sum to a specific periodic function, and made contributions to the theory of heat and linear differential equations. Fourier accompanied Napoleon to Egypt, where he had an opportunity to study Egyptian antiquities.
della Francesca, Piero (c. 1420–92) Italian Renaissance painter and mathematician who refined and furthered the use of the checkerboard in PERSPECTIVE geometry.
Freedman, Michael H. (b. 1951) American mathematician who was awarded the Fields Medal in 1986 for his solution of the
Michael Freedman (MSR)
POINCARÉ CONJECTURE for four-dimensional manifolds.
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Ferguson – Freedman
Fuller – Gergonne BIOGRAPHIES
Freedman received his doctoral degree from Princeton University in 1973 and is now a researcher in the Theory Group at Microsoft Research, where he is working on quantum computation.