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Odifreddi P., Sangalli A., Dyson F. — The Mathematical Century: The 30 Greatest Problems of the Last 100 Years
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Íàçâàíèå: The Mathematical Century: The 30 Greatest Problems of the Last 100 YearsÀâòîðû: Odifreddi P., Sangalli A., Dyson F.Àííîòàöèÿ: The twentieth century was a time of unprecedented development in mathematics, as well as in all sciences: more theorems were proved and results found in a hundred years than in all of previous history. In The Mathematical Century , Piergiorgio Odifreddi distills this unwieldy mass of knowledge into a fascinating and authoritative overview of the subject. He concentrates on thirty highlights of pure and applied mathematics. Each tells the story of an exciting problem, from its historical origins to its modern solution, in lively prose free of technical details.
Odifreddi opens by discussing the four main philosophical foundations of mathematics of the nineteenth century and ends by describing the four most important open mathematical problems of the twenty-first century. In presenting the thirty problems at the heart of the book he devotes equal attention to pure and applied mathematics, with applications ranging from physics and computer science to biology and economics. Special attention is dedicated to the famous ''23 problems'' outlined by David Hilbert in his address to the International Congress of Mathematicians in 1900 as a research program for the new century, and to the work of the winners of the Fields Medal, the equivalent of a Nobel prize in mathematics.
This eminently readable book will be treasured not only by students and their teachers but also by all those who seek to make sense of the elusive macrocosm of twentieth-century mathematics.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 2004Êîëè÷åñòâî ñòðàíèö: 223Äîáàâëåíà â êàòàëîã: 08.10.2014Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Geometry, Lie groups and 72—77 Geometry, minimal surfaces and 47—51 Geometry, negative numbers and 34 Geometry, Newton and 45—46 Geometry, number theory and 171 Geometry, orbital motion and 128—132 Geometry, structures and 15—21 71 57—59 126 see Geometry, tensor calculus and 104—108 Geometry, three-body problem and 129—131 Geometry, topology and 37—39 56—59 78—79 see Glashow, Sheldon 75 185 Gleason, Andrew 73 Glennie, Alick 150 Global programs 150—151 God 46 98 Goedel, Kurt, continuum hypothesis and 65 Goedel, Kurt, decision problem and 147 Goedel, Kurt, incompleteness theorem of 13—14 46—47 128 158 166 Goldbach conjecture 170 181—182 Gompf, Robert 58 Gorenstein, Daniel 77 Gowers, William 115 184 Grammar 125—128 Granada 98 Granville, Andrew 86 Graphics 144—145 Gravity 75 107—108 Gravity, orbital motion and 128—132 Gravity, three-body problem and 129—131 Greeks 9 40 49 Greeks, conic sections and 52 Greeks, geometry and 27—28 44—45 Greeks, negative numbers and 34 Greeks, perfect numbers and 167 Greeks, prime numbers and 168—169 Grothendieck, Alexandre 13 17 20—21 115 171 183 Group theory 182 Group theory, abelian groups and 73 Group theory, abstract groups and 72—73 Group theory, alternating groups and 76 Group theory, Burnside conjectures and 77 Group theory, continuous group and xiv 73 Group theory, crystallography and 98—104 Group theory, cyclic groups and 76 Group theory, dimension and 73—74 Group theory, fundamental groups and 173—174 Group theory, Hilbert's fifth problem and 73 Group theory, homotopy and 173—175 Group theory, knot theory and 136—137 Group theory, Lie groups and 72 182 Group theory, permutations and 72 Group theory, simple groups and 73 Group theory, symmetry groups and 72 98—104 Group theory, theory of languages and 128 Group theory, unification and 75 Guthrie, Francis 154 181 Hadamard, Jacques 170 Haken, Wolfgang 142 157—158 Hamilton, William 35 49 Hardy, Godfrey 170 Harmonic ratios 39 Harriot, Thomas 87—88 Hausdorff, Felix 32—33 160—161 Heath-Brown, Roger 86 Heaviside, Oliver 53—54 Heawood, Percy 155 Hebrews 98 Heesch, Heinrich 102 Heisenberg, Werner 114—115 185 Helmholtz, Hermann 136 Hemion, Geoffrey 134 Hermite, Charles 42 Heron of Alexandria 49 Hilbert space 113—116 Hilbert, David xii 4 6 Hilbert, David, decision problem of 145—148 Hilbert, David, eighteenth problem of 90 102 Hilbert, David, eighth problem of 170—171 Hilbert, David, electromagnetism and 107 Hilbert, David, fifth problem of 73 Hilbert, David, first problem of 63—66 Hilbert, David, fourth problem of 108 Hilbert, David, functional analysis and 112—113 Hilbert, David, general theory of integral equations and 112 Hilbert, David, geometry and 30 46 Hilbert, David, Lebesgue measure and 30—31 Hilbert, David, nineteenth problem of 50 55 Hilbert, David, Nullstellensatz of 180 Hilbert, David, Paris address of 165—166 Hilbert, David, second problem of 46—47 Hilbert, David, set theory and 14—15 Hilbert, David, seventh problem of 42—43 Hilbert, David, sixth problem of 107 114 119 Hilbert, David, summary of problems 182 Hilbert, David, tenth problem of 147—148 Hilbert, David, third problem of 30—31 Hilbert, David, transcendental numbers and 42—43 Hilbert, David, twentieth problem of 50 Hilbert, David, twenty-third problem of 50 Hipparchus 45 Hironaka, Heisuki 82 183 Hobbes, Thomas 108—109 Hoermander, Lars 55 183—184 Hoffman, David 50 144 Homotopy 173—176 Hubbard, John 163 Hurewicz, Witold 175 Huygens, Christian 116—117 Hyperbolic geometry, classification and 80—82 Hyperbolic geometry, development of 43—47 Hyperreal numbers 59—63 Hyperspheres 28 182 Hyperspheres, fixed-point theorem and 38 Hyperspheres, lattice configurations and 90—91 Hypoelliptic operators 55 Identity elements 16 Illinois Journal of Mathematics 158 imaginary numbers see "Complex numbers" Inaccessible set 13 Incompleteness theorem 13—14 46—47 128 158 166 Independence theorem 65—66 Index theorem 55—56 India 33—34 Indivisibles 60 Inertia 128—129 Infinite descent 83 Infinitesimals 28 Infinitesimals, model theory and 59—63 infinity 9 Infinity, Bourbaki group and 15—17 Infinity, complexity theory and 176—180 Infinity, continuum hypothesis and 65—66 Infinity, correspondence and 63—64 Infinity, functional analysis and 112—116 Infinity, hyperreal numbers and 59—63 Infinity, knot theory and 135 Infinity, Lie groups and 73—77 Infinity, polynomial time and 176—180 Infinity, Riemann zeta function and 170—172 Infinity, set theory and 13—15 63—66 Infinity, simplex method and 177 Infinity, theory of distributions and 52—56 Infinity, transcendental numbers and 43 Inflexions 68 Information theory 150 178—180 Inquiry into the Nature and Causes of the Wealth of Nations (Smith) 122 Instability 152 instantons 58 Integers 33—34 Integers, consistency and 46—47 Integers, Fermat's last theorem and 82—87 Integers, general theory of integral equations and 112 Integers, Hilbert's tenth problem and 147—148 Integers, programming and 121—122 Integers, transcendental numbers and 39—43 International Congress of Mathematicians xii—xiii xv—xvi 109 145 International Congress of Mathematicians of 1897 4 International Congress of Mathematicians of 1900 4 International Congress of Mathematicians, Fields Medal and 4—6 International Congress of Mathematicians, Hilbert and 4 Intuitionism 20 39 Invariance 29 134—138 Inverse operations 33 Invertibility 34 Irrational numbers xx 34—35 166 Irrational numbers, transcendental numbers and 39—43 Isometry 46 Isomorphism 116 Janko, Zvonimir 76 Japanese 98 109 Jones, Vaughan 115 135—138 184 Jordan, Camille 31—32 50 Judaeus, Philo 167 Julia, Gaston 161—162 Junger, Itha xiii Jupiter 130 K-theory 55 Kakutani, Shizuo 39 124 Kam theorem 131—132 Kantorovich, Leonid 121 185 Karp, Richard 177 180 182 185 Kasparov, Gary 151 Kempe, Alfred 155 157 Kepler, Johannes 129 159 181 Kepler, Johannes, lattice configurations and 88—91 Kerekjarto, Bela 57 Kervaire, Michel 57 Khachian, L.G. 177 Khayyam, Omar 82 Killing, Wilhelm 74 Kleene, Stephen 23—24 Klein bottle 79—80 173 Klein, Felix 44 78—79 Knaster, B 39 Knot theory 132—138 Koch curve 54—55 160 Kodaira, Kunihiko 81 183—184 Kolmogorov, Andrei 119 131—132 180 184 Kontsevich, Maxim 135 137 184 Koopmans, Tjalling 121 185 Korchnoi, Viktor 151 Kreigspiel game 109 Kronecker, Leopold 46 Kuhn, Harold 122 Kummer, Ernst 83 l-adic cohomology 171 Lacan, Jacques 126 Laczkovich, Miklos 33 Lagrange, Joseph Louis 49 130 Laissez-faire 122—123 Lambda calculus 21 23—24 185 Langlands, Robert 27 184 Large Cardinals 13 Larsen, Bent 151 Law of Large Numbers 117—118 Laws of motion 128 Laws of Thought, The (Boole) 140 Lawvere, William 19—20 Lebesque measure analysis and 29—33 113—114 Lebesque measure analysis and, probability theory and 119 Leclerc, Georges Louis 118 Leech, John 91 Lefschetz, Solomon 39 Legendre, Adrien-Marie 83 Leibniz, Gottfried Wilhelm 10 Leibniz, Gottfried Wilhelm, brachistochrone and 48 Leibniz, Gottfried Wilhelm, infinitesimals and 60—61 Levi-Civita, Tullio 107—108 Levi-Strauss, Claude 126 Leviathan, The (Hobbes) 108—109 Levin, Leonid 177 180 182 Levy, David 151 Liber de Ludo Aleae (Cardano) 116 Lie groups 72 182 Lie groups, classification of 73—74 Lie groups, group theory and 73—77 Lie groups, infinity and 73—74 Lie groups, particle physics and 74—77 Lie, Sophus xiv 73 Lindemann, Ferdinand 42—43 Linear language 127 Linear programming 120—122 185 Linear programming, complexity theory and 176—180 Linearity xiv Linguistics 125—128 145 Linguistics, Boolean algebra and 140—141 Liouville, Joseph 41 114 Lisp 146 Listing, Johann 78 133 Lobachevsky, Nikolai 44 Local programs 150—151 Logarithms 41—43 169 Logic 182 Logic, Aristotelian 20 Logic, artificial intelligence and 141 148—151 Logic, Boolean algebra and 140—141 Logic, categories and 17—21 Logic, computers and 139—143 see Logic, connectives and 145 Logic, crystallography and 98—104 Logic, decision problem and 145—148 Logic, expert systems and 149 Logic, incompleteness theorem 13—14 46—47 128 158 166 Logic, intuitionistic 20 39 Logic, number theory and 43—47 Logic, prime numbers and 169 Logic, quantifiers and 145 Logic, set theory and 10—24 Logic, structures and 14—17 Logic, syntax and 141 Logic, truth tables and 145 Logic, Turing and 141 Lord Kelvin 136 Lorenz, Edward 143—144 153 MacLane, Saunders 18 20 Mandelbrot, Benoit 144—145 162—164 184 Manifolds see also "Topology" Manifolds, Calabi — Yau 82 137 Manifolds, classification and 81—82 Manifolds, Riemann 56—59 107—108 Markov, Anatoly 128 Mathematical Foundations of Quantum Mechanics (von Neumann) 114—115 Mathematics, applied, computers and 143—145 see Mathematics, applied, crystallography and 98—104 Mathematics, applied, dual nature of 92 Mathematics, applied, dynamical systems theory and 128—132 Mathematics, applied, functional analysis and 112—116 Mathematics, applied, game theory and 108—112 Mathematics, applied, general equilibrium theory and 122—125 Mathematics, applied, knot theory and 132—138 Mathematics, applied, optimization theory and 120—122 Mathematics, applied, probability theory and 116—119 Mathematics, applied, tensor calculus 104—108 Mathematics, applied, theory of formal languages and 125—128 Mathematics, general, abstraction and 1 Mathematics, general, associative property and 73 Mathematics, general, Bourbaki group and 15—17 Mathematics, general, Cartesian versus Baconian view of xi—xvi Mathematics, general, computers and 139—164 Mathematics, general, discovery versus invention 8—9
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