Grünbaum – Helly BIOGRAPHIES
Grünbaum – Helly BIOGRAPHIES
Grünbaum, Branko (b. 1929) American mathematician who was born in Yugoslavia, received his doctorate from Hebrew University and is now is professor emeritus at the University of Washington. He is a leading researcher in tilings, spatial patterns, polyhedra, polytopes, convexity, COMBINATORIAL GEOMETRY , and GRAPH THEORY .
Haken, Wolfgang (b. 1928) American mathematician who solved the FOUR - COLOR PROBLEM together with his colleague KENNETH APPEL at the University of Illinois. Their proof required more than 1,000 hours of computer calculations. Haken has also given an algorithm for determining whether or not a given KNOT DIAGRAM represents the UNKNOT .
Hales, Thomas (b. 1958) American mathematician who proved two important theorems, that the KEPLER CONJECTURE about the densest PACKING of spheres in space is true, and that the most efficient partition of the plane into equal areas is the regular hexagonal honeycomb. He is a professor of mathematics at the University of Pittsburgh.
Hamilton, William Rowan (1805–65) Irish mathematician and physicist who was an inventor of LINEAR ALGEBRA and vector calculus. A child prodigy, Hamilton had mastered 12 foreign languages by the age of 12. He developed the QUATERNION number system as a generalization of the complex numbers and was the Astronomer-Royal of Ireland.
Hausdorff, Felix (1868–1942) German mathematician who studied ANALYSIS , TOPOLOGY , and SET THEORY . He introduced the concepts of partially ordered set, METRIC SPACES , and HAUSDORFF DIMENSION .
Heawood, P. J. (1861–1955) English mathematician who is noted for his work in GRAPH THEORY and on the FOUR - COLOR PROBLEM .
Heesch, Heinrich (1906–1995) German mathematician who studied REGULAR TILINGS of the plane and the SYMMETRIES of colored tilings. He classified the 28 types of asymmetric tiles that can
be used to create ISOHEDRAL TILINGS . Helly, Eduard (1884–1943) Austrian-born mathematician who studied
in Germany after completing his doctorate in Vienna. Helly’s
Grünbaum – Helly BIOGRAPHIES
BIOGRAPHIES
Helmholtz – Hipparchus
promising career in mathematics was interrupted by World War I, after which he immigrated to the United States and was able to resume his study of mathematics. He proved HELLY ’ S THEOREM about CONVEX SETS in 1923 and made important contributions to ANALYSIS .
Helmholtz, Hermann von (1821–94) A German mathematician, naturalist, and physician who worked in DIFFERENTIAL GEOMETRY and initiated the study of the INTRINSIC geometry of a surface.
Heron (c. 62) Greek mathematician and scientist residing in Alexandria who contributed to surveying, mechanics, pneumatics, and the study of mirrors. He developed numerical methods for computing square roots and cube roots and the Heron formula for the area of a triangle in terms of its sides. He is also known as Hero of Alexandria.
Hess, Edmund (1843–1963) German mathematician who studied POLYTOPES in depth and discovered the 10 regular STAR POLYTOPES .
Hessel, Johann (1796–1872) German crystallographer who determined the 32 CRYSTAL CLASSES and discovered the CRYSTALLOGRAPHIC RESTRICTION in three-dimensional space. He was a professor of mineralogy and mining technology at the University of Marburg.
Hilbert, David (1862–1943) German mathematician; one of the greatest mathematicians of all time. He worked in many areas, including geometry, algebra, NUMBER THEORY , ANALYSIS , the CALCULUS OF VARIATIONS , theoretical physics, and the foundations of mathematics. He developed a new system of axioms for Euclidean geometry that resolved problems that had been found in Euclid’s Elements. Hilbert championed the axiomatic approach to mathematics and sought to strengthen the logical foundations of mathematics. In 1900, he gave a list of 23 problems that provided direction to 20th-century
David Hilbert (Aufnahme
mathematics.
von Fr. Schmidt, Göttingen, courtesy AIP Emilio Segrè
Hipparchus (c. 175–125 B . C . E .) Greek astronomer and mathematician
Visual Archives, Lardé
who developed a simple form of TRIGONOMETRY , using the
Collection)
ratio of a chord to the diameter of a circle rather than the ratio
BIOGRAPHIES
Helmholtz – Hipparchus
Hippias of Elis – Hurwitz BIOGRAPHIES
of the sides of a right triangle, to assist in his astronomical calculations. He also discovered the precession of the equinoxes, which is due to the difference between the sidereal year and the solar year.
Hippias of Elis (c. 400 B . C . E .) Greek mathematician who invented the
quadratrix, a curve that can be used to trisect an angle.
Hippocrates of Chios (c. 460–380 B . C . E .) Greek mathematician who
computed the area of a LUNE . He also wrote a comprehensive textbook on geometry that has since been lost. Born on the island of Chios in the Aegean Sea, Hippocrates studied and taught mathematics in Athens.
de la Hire, Philippe (1640–1718) French geometer who wrote two books about the conic sections in the context of PROJECTIVE GEOMETRY . Originally an artist, de la Hire became interested in geometry while studying perspective during a trip to Italy. After returning to France, he was appointed to the chair of mathematics at the Collège Royale, where he continued his study of geometry.
Hopf, Heinz (1884–1971) German mathematician who worked in ALGEBRAIC TOPOLOGY and HOMOLOGY and created the algebraic structures known as Hopf algebras, which are used in algebraic topology and theoretical physics. After serving as an officer in World War I, Hopf completed his studies in Germany and traveled to France and the United States before settling at the Federal Institute of Technology in Zurich, Switzerland.
Hubbard, John (b. 1945) American mathematician who is a specialist in DYNAMICAL SYSTEMS and properties of the MANDELBROT
SET . He received his doctorate from the University of Michigan and is now professor of mathematics at Cornell University.
Huntington, Edward V. (1874–1952) American mathematician who was interested in the axiomatic foundations of mathematics and developed several systems of axioms, including one for geometry.
Hurwitz, Adolf (1859–1919) German mathematician who was interested in NUMBER THEORY , COMPLEX ANALYSIS , and
Hippias of Elis – Hurwitz BIOGRAPHIES
BIOGRAPHIES
Ibn Qurra – Jordan
RIEMANN SURFACES . Hurwitz was a student of FELIX KLEIN and teacher of DAVID HILBERT .
Ibn Qurra, Th¯abit (d. 901) Syrian mathematician at the court in Baghdad who translated works by EUCLID , ARCHIMEDES , and APOLLONIUS into Arabic and made original contributions to plane and SOLID GEOMETRY , TRIGONOMETRY , and algebra. He translated many classical Greek works into Arabic and wrote commentaries on them.
Ibn Y ¯unus (d. 1009) Egyptian astronomer who developed an interpolation procedure for calculating sines at half-degree intervals and compiled many numerical tables useful for astronomers.
Jackiw, Nick (b. 1966) American software designer who created the Geometer’s Sketchpad dynamic geometry software and continues to refine it. Jackiw studied English literature and computer science at Swarthmore College before becoming interested in computer geometry.
Jacobi, Carl (1804–51) German mathematician who did research in many areas, including NUMBER THEORY , elliptic functions, DIFFERENTIAL EQUATIONS , and DIFFERENTIAL GEOMETRY . He developed the DETERMINANT now called the JACOBIAN .
Jones, Vaughn F. R. (b. 1952) American mathematician who was born in New Zealand and completed his graduate work in Switzerland. Jones was awarded the Fields Medal in 1990 for his work in KNOT THEORY and the discovery of the JONES POLYNOMIAL , a knot invariant that has connections with many different areas of mathematics and physics. He is now professor of mathematics at the University of California at Berkeley.
Jordan, Camille (1838–1922) French mathematician who made many contributions to algebra as well as geometry and calculus for higher-dimensional spaces. Jordan was the first mathematician to recognize the importance of the work of his compatriot ÉVARISTE GALOIS and wrote a monograph on the work of
Vaughn F. R. Jones
Galois to present it to other mathematicians. JORDAN CURVES