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Odifreddi P., Sangalli A., Dyson F. Ч The Mathematical Century: The 30 Greatest Problems of the Last 100 Years
Odifreddi P., Sangalli A., Dyson F. Ч The Mathematical Century: The 30 Greatest Problems of the Last 100 Years

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Ќазвание: The Mathematical Century: The 30 Greatest Problems of the Last 100 Years

јвторы: Odifreddi P., Sangalli A., Dyson F.


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.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2004

 оличество страниц: 223

ƒобавлена в каталог: 08.10.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
Geometry, Lie groups and      72Ч77
Geometry, minimal surfaces and      47Ч51
Geometry, negative numbers and      34
Geometry, Newton and      45Ч46
Geometry, number theory and      171
Geometry, orbital motion and      128Ч132
Geometry, structures and      15Ч21 71 57Ч59 126 see
Geometry, tensor calculus and      104Ч108
Geometry, three-body problem and      129Ч131
Geometry, topology and      37Ч39 56Ч59 78Ч79 see
Glashow, Sheldon      75 185
Gleason, Andrew      73
Glennie, Alick      150
Global programs      150Ч151
God      46 98
Goedel, Kurt, continuum hypothesis and      65
Goedel, Kurt, decision problem and      147
Goedel, Kurt, incompleteness theorem of      13Ч14 46Ч47 128 158 166
Goldbach conjecture      170 181Ч182
Gompf, Robert      58
Gorenstein, Daniel      77
Gowers, William      115 184
Grammar      125Ч128
Granada      98
Granville, Andrew      86
Graphics      144Ч145
Gravity      75 107Ч108
Gravity, orbital motion and      128Ч132
Gravity, three-body problem and      129Ч131
Greeks      9 40 49
Greeks, conic sections and      52
Greeks, geometry and      27Ч28 44Ч45
Greeks, negative numbers and      34
Greeks, perfect numbers and      167
Greeks, prime numbers and      168Ч169
Grothendieck, Alexandre      13 17 20Ч21 115 171 183
Group theory      182
Group theory, abelian groups and      73
Group theory, abstract groups and      72Ч73
Group theory, alternating groups and      76
Group theory, Burnside conjectures and      77
Group theory, continuous group and      xiv 73
Group theory, crystallography and      98Ч104
Group theory, cyclic groups and      76
Group theory, dimension and      73Ч74
Group theory, fundamental groups and      173Ч174
Group theory, Hilbert's fifth problem and      73
Group theory, homotopy and      173Ч175
Group theory, knot theory and      136Ч137
Group theory, Lie groups and      72 182
Group theory, permutations and      72
Group theory, simple groups and      73
Group theory, symmetry groups and      72 98Ч104
Group theory, theory of languages and      128
Group theory, unification and      75
Guthrie, Francis      154 181
Hadamard, Jacques      170
Haken, Wolfgang      142 157Ч158
Hamilton, William      35 49
Hardy, Godfrey      170
Harmonic ratios      39
Harriot, Thomas      87Ч88
Hausdorff, Felix      32Ч33 160Ч161
Heath-Brown, Roger      86
Heaviside, Oliver      53Ч54
Heawood, Percy      155
Hebrews      98
Heesch, Heinrich      102
Heisenberg, Werner      114Ч115 185
Helmholtz, Hermann      136
Hemion, Geoffrey      134
Hermite, Charles      42
Heron of Alexandria      49
Hilbert space      113Ч116
Hilbert, David      xii 4 6
Hilbert, David, decision problem of      145Ч148
Hilbert, David, eighteenth problem of      90 102
Hilbert, David, eighth problem of      170Ч171
Hilbert, David, electromagnetism and      107
Hilbert, David, fifth problem of      73
Hilbert, David, first problem of      63Ч66
Hilbert, David, fourth problem of      108
Hilbert, David, functional analysis and      112Ч113
Hilbert, David, general theory of integral equations and      112
Hilbert, David, geometry and      30 46
Hilbert, David, Lebesgue measure and      30Ч31
Hilbert, David, nineteenth problem of      50 55
Hilbert, David, Nullstellensatz of      180
Hilbert, David, Paris address of      165Ч166
Hilbert, David, second problem of      46Ч47
Hilbert, David, set theory and      14Ч15
Hilbert, David, seventh problem of      42Ч43
Hilbert, David, sixth problem of      107 114 119
Hilbert, David, summary of problems      182
Hilbert, David, tenth problem of      147Ч148
Hilbert, David, third problem of      30Ч31
Hilbert, David, transcendental numbers and      42Ч43
Hilbert, David, twentieth problem of      50
Hilbert, David, twenty-third problem of      50
Hipparchus      45
Hironaka, Heisuki      82 183
Hobbes, Thomas      108Ч109
Hoermander, Lars      55 183Ч184
Hoffman, David      50 144
Homotopy      173Ч176
Hubbard, John      163
Hurewicz, Witold      175
Huygens, Christian      116Ч117
Hyperbolic geometry, classification and      80Ч82
Hyperbolic geometry, development of      43Ч47
Hyperreal numbers      59Ч63
Hyperspheres      28 182
Hyperspheres, fixed-point theorem and      38
Hyperspheres, lattice configurations and      90Ч91
Hypoelliptic operators      55
Identity elements      16
Illinois Journal of Mathematics      158
imaginary numbers      see "Complex numbers"
Inaccessible set      13
Incompleteness theorem      13Ч14 46Ч47 128 158 166
Independence theorem      65Ч66
Index theorem      55Ч56
India      33Ч34
Indivisibles      60
Inertia      128Ч129
Infinite descent      83
Infinitesimals      28
Infinitesimals, model theory and      59Ч63
infinity      9
Infinity, Bourbaki group and      15Ч17
Infinity, complexity theory and      176Ч180
Infinity, continuum hypothesis and      65Ч66
Infinity, correspondence and      63Ч64
Infinity, functional analysis and      112Ч116
Infinity, hyperreal numbers and      59Ч63
Infinity, knot theory and      135
Infinity, Lie groups and      73Ч77
Infinity, polynomial time and      176Ч180
Infinity, Riemann zeta function and      170Ч172
Infinity, set theory and      13Ч15 63Ч66
Infinity, simplex method and      177
Infinity, theory of distributions and      52Ч56
Infinity, transcendental numbers and      43
Inflexions      68
Information theory      150 178Ч180
Inquiry into the Nature and Causes of the Wealth of Nations (Smith)      122
Instability      152
instantons      58
Integers      33Ч34
Integers, consistency and      46Ч47
Integers, Fermat's last theorem and      82Ч87
Integers, general theory of integral equations and      112
Integers, Hilbert's tenth problem and      147Ч148
Integers, programming and      121Ч122
Integers, transcendental numbers and      39Ч43
International Congress of Mathematicians      xiiЧxiii xvЧxvi 109 145
International Congress of Mathematicians of 1897      4
International Congress of Mathematicians of 1900      4
International Congress of Mathematicians, Fields Medal and      4Ч6
International Congress of Mathematicians, Hilbert and      4
Intuitionism      20 39
Invariance      29 134Ч138
Inverse operations      33
Invertibility      34
Irrational numbers      xx 34Ч35 166
Irrational numbers, transcendental numbers and      39Ч43
Isometry      46
Isomorphism      116
Janko, Zvonimir      76
Japanese      98 109
Jones, Vaughan      115 135Ч138 184
Jordan, Camille      31Ч32 50
Judaeus, Philo      167
Julia, Gaston      161Ч162
Junger, Itha      xiii
Jupiter      130
K-theory      55
Kakutani, Shizuo      39 124
Kam theorem      131Ч132
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      88Ч91
Kerekjarto, Bela      57
Kervaire, Michel      57
Khachian, L.G.      177
Khayyam, Omar      82
Killing, Wilhelm      74
Kleene, Stephen      23Ч24
Klein bottle      79Ч80 173
Klein, Felix      44 78Ч79
Knaster, B      39
Knot theory      132Ч138
Koch curve      54Ч55 160
Kodaira, Kunihiko      81 183Ч184
Kolmogorov, Andrei      119 131Ч132 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      122Ч123
Lambda calculus      21 23Ч24 185
Langlands, Robert      27 184
Large Cardinals      13
Larsen, Bent      151
Law of Large Numbers      117Ч118
Laws of motion      128
Laws of Thought, The (Boole)      140
Lawvere, William      19Ч20
Lebesque measure analysis and      29Ч33 113Ч114
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      60Ч61
Levi-Civita, Tullio      107Ч108
Levi-Strauss, Claude      126
Leviathan, The (Hobbes)      108Ч109
Levin, Leonid      177 180 182
Levy, David      151
Liber de Ludo Aleae (Cardano)      116
Lie groups      72 182
Lie groups, classification of      73Ч74
Lie groups, group theory and      73Ч77
Lie groups, infinity and      73Ч74
Lie groups, particle physics and      74Ч77
Lie, Sophus      xiv 73
Lindemann, Ferdinand      42Ч43
Linear language      127
Linear programming      120Ч122 185
Linear programming, complexity theory and      176Ч180
Linearity      xiv
Linguistics      125Ч128 145
Linguistics, Boolean algebra and      140Ч141
Liouville, Joseph      41 114
Lisp      146
Listing, Johann      78 133
Lobachevsky, Nikolai      44
Local programs      150Ч151
Logarithms      41Ч43 169
Logic      182
Logic, Aristotelian      20
Logic, artificial intelligence and      141 148Ч151
Logic, Boolean algebra and      140Ч141
Logic, categories and      17Ч21
Logic, computers and      139Ч143 see
Logic, connectives and      145
Logic, crystallography and      98Ч104
Logic, decision problem and      145Ч148
Logic, expert systems and      149
Logic, incompleteness theorem      13Ч14 46Ч47 128 158 166
Logic, intuitionistic      20 39
Logic, number theory and      43Ч47
Logic, prime numbers and      169
Logic, quantifiers and      145
Logic, set theory and      10Ч24
Logic, structures and      14Ч17
Logic, syntax and      141
Logic, truth tables and      145
Logic, Turing and      141
Lord Kelvin      136
Lorenz, Edward      143Ч144 153
MacLane, Saunders      18 20
Mandelbrot, Benoit      144Ч145 162Ч164 184
Manifolds      see also "Topology"
Manifolds, Calabi Ч Yau      82 137
Manifolds, classification and      81Ч82
Manifolds, Riemann      56Ч59 107Ч108
Markov, Anatoly      128
Mathematical Foundations of Quantum Mechanics (von Neumann)      114Ч115
Mathematics, applied, computers and      143Ч145 see
Mathematics, applied, crystallography and      98Ч104
Mathematics, applied, dual nature of      92
Mathematics, applied, dynamical systems theory and      128Ч132
Mathematics, applied, functional analysis and      112Ч116
Mathematics, applied, game theory and      108Ч112
Mathematics, applied, general equilibrium theory and      122Ч125
Mathematics, applied, knot theory and      132Ч138
Mathematics, applied, optimization theory and      120Ч122
Mathematics, applied, probability theory and      116Ч119
Mathematics, applied, tensor calculus      104Ч108
Mathematics, applied, theory of formal languages and      125Ч128
Mathematics, general, abstraction and      1
Mathematics, general, associative property and      73
Mathematics, general, Bourbaki group and      15Ч17
Mathematics, general, Cartesian versus Baconian view of      xiЧxvi
Mathematics, general, computers and      139Ч164
Mathematics, general, discovery versus invention      8Ч9
1 2 3 4 5
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