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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 |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
"Computing Machines and Intelligence" (Turing) 149 "Foundations of Mathematics for the Working Mathematician" (Bourbaki group) 15 "Invisible hand" 122—123 "Publish or perish" 2 53—54 43 Abel, Niels 72 Abelian groups 73 Abstraction 1 72—73 Abstraction, categories and 18 Abstraction, fields and 33—36 Abstraction, functions and 21—24 Abstraction, Lebesgue measure and 29—33 Abstraction, set theory and 10—24 Abstraction, topology and 37—39 Adian, S.I. 77 Aeneid 47 Airplanes 48 Alexander the Great 132—133 Alexander, James 134—135 138 Algebra automorphisms 137 Algebra automorphisms, Boolean 140—142 182 Algebra automorphisms, fields and 33—36 Algebra automorphisms, finite groups and 71—77 Algebra automorphisms, fundamental theorem of 34—35 Algebra automorphisms, geometry and 45—46 171—172 Algebra automorphisms, grammatical productions and 128 Algebra automorphisms, invariants and 134—138 Algebra automorphisms, knot theory and 137 Algebra automorphisms, natural numbers 33—34 Algebra automorphisms, singularity theory and 66—71 Algebra automorphisms, structures and 16—17 Algebra automorphisms, transcendental numbers 39—43 Algebra automorphisms, von Neumann operators 115 Algebraic closure 36 Algebraic extension 35 Algebraic manifolds 81—82 Algorithms' complexity theory and 176—180 Algorithms' complexity theory and, computers and 145—148 Algorithms' complexity theory and, decision problem and 145—148 Algorithms' complexity theory and, exponential time and 180 Algorithms' complexity theory and, factorization and 178—180 Algorithms' complexity theory and, polynomial time and 176—180 Algorithms' complexity theory and, simplex method and 177 Algorithms' complexity theory and, Turing's definition of 176 Alhambra 98 Alternating groups 76 Analysis 9 11 182 Analysis, dynamical systems theory and 128—132 Analysis, fixed-point theorem and 37—39 Analysis, game theory and 108—112 Analysis, infinitesimals and 59—63 Analysis, knot theory and 132—138 Analysis, Lebesgue measure and 29—33 Analysis, nonstandard 62—63 Analysis, quantum axioms and 112—116 Analysis, Riemann hypothesis and 168—172 Analysis, set theory and 10—14 Analysis, social choice and 108—112 Analysis, theory of distributions and 52—56 Analytic geometry 45—47 Appel, Kenneth 142 157—158 Arabs 34 98 Archimedes 31 59 Area 29—33 Aristotelian logic 20 Arithmetic 9 11 Arithmetic (Diophantus) 26 Arithmetic, modular 35 179 182 Arnol'd, Vladimir 131—132 Arrow, Kenneth 96 124 185 Ars Conjectandi (Bernoulli) 117 artificial intelligence 141 185 Artificial intelligence, chess and 149—151 Artificial intelligence, exaggerations of 148—149 Artificial intelligence, expert systems and 149 Artificial intelligence, Shannon and 150 Artificial intelligence, Turing test and 149—151 Artin, Emil 171 Aspect, Alain 95 Associative property 73 Astronomy 45 Astronomy, orbital motion and 128—132 151—154 Astronomy, three-body problem and 129—131 Atiyah, Michael 55 176 183 Atomic bomb 142 atoms xii 1 Atoms, complex numbers and xiii—xiv Atoms, Lie groups and 74—77 Attractors 152 162—163 Augustine 167 Austrians 109 Automata 127 Automatic Computing Engine (ACE) 142 Automorphisms 137 Axioms 107 Axioms, categories and 19—20 Axioms, computers and 142 Axioms, decision problem and 145—148 Axioms, hyperbolic geometry and 43—47 Axioms, incompleteness theorem and 13—14 Axioms, probability theorem and 116—119 Axioms, quantum mechanics and 112—116 Axioms, set theory and 65—66 Babbage, Charles 150 Babylonians 71 83 92 Bacon, Francis xi—xvi Baire, Rene 53 Baker, Alan 43 147—148 183 Banach spaces 114—116 Banach, Stefan 33 39 114 Barycenter 130 Bayes's law 118 Bayes, Thomas 118 Bell, John 94—95 BELLE program 150—151 Beltrami, Eugenio 44 Berger, Robert 102 Berkeley, Bishop 60 Bernoulli, Daniel 117 Bernoulli, Jacques 117 Bernoulli, Jean 48 Bernstein, Serge 55 Bible, the 98 Bieberbach, Ludwig 102 Bifurcations 69—71 Bohr, Niels 93 Bolyai, Janos 30—31 44 Bolzano, Bernhard 63 Bombelli, Raffaele 34 Bombieri, Enrico 50 104 183 Boolean algebra 140—142 182 Boone, William 128 Borcherds, Richard 137 184 Borel, Emile 110 Botvinnik, Mikhail 150 Bourbaki group xii—xiii Bourbaki group, categories and 18—19 Bourbaki group, philosophy of 15—17 Bourbaki group, structure and 15—17 Bourgain, Jean 115 184 Brachistochrone 48 Bravais, Auguste 99 Breuil, Christophe 87 Brouwer, Luitzen 20 Brouwer, Luitzen, fixed-point theorem and 37—39 124 Brownawell, Dale 180 Burnside conjectures 77 182 Butterfly effect 143—144 Calabi — Yau manifolds 82 137 Calculus 182 Calculus, dynamical systems theory and 128—132 Calculus, functional analysis and 112—116 Calculus, infinitesimal 28 59—63 Calculus, lambda 21 23—24 185 Calculus, maxima/minima and 47—51 Calculus, Steiner problem and 179—180 Calculus, tensor 104—108 Calculus, Turing and 141 Calculus, variations and 47—51 Cantor, Georg 181 Cantor, Georg, decision problem and 146—147 Cantor, Georg, dimension and 37 Cantor, Georg, infinity and 63—66 Cantor, Georg, number theory and 46 Cantor, Georg, set theory and 10—15 Cantor, Georg, transcendental numbers and 41 Capitalism 120 125 Cardano, Gerolamo 34 72 116 Cartan, Elie 74 Carter, Jimmy 95 Cartesian thought xi—xvi Castelnuovo, Guido 81 Catastrophe theory 69—71 Categories 17—21 Categories for the Working Mathematician (MacLane) 20 Cauchy, Augustin 61 Cavalieri, Bonaventura 60 Cayley, Arthur 72 Celestial Mechanics (Laplace) 130 Chaos theory 71 Chaos theory, attractors and 152 162—163 Chaos theory, butterfly effect and 143—144 Chaos theory, computers and 143—144 151—154 Chaos theory, instability and 152 Characteristics 36 40 Chess 149—151 Chevalley, Claude 76 Chomsky, Noam 126—127 Chromodynamics 58 Church, Alonzo 21 23—24 128 145—147 circles 27—28 31 Circles, fixed-point theorem and 38 Circles, hyperbolic geometry and 44 Circles, infinitesimals and 59 Circles, Kepler's problem and 87—91 Circles, lattice onfigurations and 87—91 Circles, Lebesgue measure and 33 Circles, Queen Dido and 47 Circles, tensor calculus and 104—108 City of God, The (Augustine) 167 Classes 11—12 Classes, catastrophes and 69—71 Classes, categories and 17—21 Classes, dimensional space and 78—82 Classes, elliptic curves and 66—71 Classes, finite groups and 71—77 Classes, P = NP problem and 176—180 Cobham, A. 176 Cobordism theory 55 176 Codimension 70 Cohen, Paul 65—66 183 Communism 120 Compactness 38 Complete metric spaces 39 Complete partial orders 39 complex numbers xiii—xiv Complex numbers, fractals and 162 Complex numbers, introduction of 34—35 Complex numbers, transcendental numbers and 42 Complexity theory 176—180 185 Comprehension principle 10—12 22 Computers ACE 142 Computers ACE, algorithms and 145—148 Computers ACE, artificial intelligence and 141 148—151 185 Computers ACE, atomic bomb and 142 Computers ACE, Babbage and 150 Computers ACE, beginnings of 140—141 Computers ACE, Boole and 140—141 Computers ACE, calculating power of 142—143 Computers ACE, chaos theory and 43—44 151—154 Computers ACE, CRAY 159 Computers ACE, cryptography and 178—180 Computers ACE, dynamic systems and 143 Computers ACE, ENIAC 142 Computers ACE, exaggeration of 139—140 Computers ACE, expert systems and 149 Computers ACE, four-color theorem and 142 154—159 Computers ACE, fractals and 144—145 159—164 Computers ACE, functions and 21—24 Computers ACE, graphics and 144—145 152—153 156—164 Computers ACE, languages and 127—128 146 Computers ACE, mindless use of 139—140 Computers ACE, polynomial time and 176—177 Computers ACE, prime number searches and 139 Computers ACE, proofs and 142 154—159 Computers ACE, topology and 39 Computers ACE, Turing and 141—142 149—151 185 Condorcet, Marquis of 95 Conic sections 46 52 Conic sections, algebraic curves and 66 Conic sections, elliptic curves and 66—71 Connectives 145 Connes, Alain 115 184 Conrad, Brian 87 Constructible numbers 40—41 65 Context-free language 127—128 Context-sensitive language 127 Continuous groups xiv 73 Continuum Hypothesis 65—66 181—182 Contractable compact complexes 39 Convergence 123 Convexity 38 Conway, John 63 91 137 182 Cook, Stephen 177 180 182 185 Coordinate systems 45 108 Coordinate systems, functional analysis and 112—116 Coordinate systems, Lie groups and 72—77 Corank 70 Countable additivity 119 Cournot, Antoine-Augustin 122 Cours de linguistique generate (Saussure) 125 Cox, Donna 144 CRAY supercomputer 159 Creation of the World, The (Judaeus) 167 Crick, Francis 97 185 Cryptography 178—180 Crystallography xiv—xv 88 182 Crystallography, symmetry groups and 98—104 Cubics 66 Curbastro, Gregorio Ricci 107 Curie, Marie xii Curves: algebraic 66—71 Curves: attractors and 152—153 Curves: boundary problems and 142 154—159 Curves: calculus ofvariations and 47—51 Curves: catastrophe theory and 69—71 Curves: chaos theory and 151—154 Curves: classification and 81 Curves: corank and 70 Curves: derivatives and 68—71 Curves: elliptic 66—71 85 137 182 Curves: Fermat's last theorem and 82—87 Curves: fixed-point theorem and 37—39 Curves: fractals and 144—145 159—164 Curves: Gauss and 105—106 Curves: minimal surfaces and 47—51 Curves: Newton's definition and 105 Curves: probability theory and 118—119 Curves: tensor calculus and 104—108
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