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Pesic P. Ч Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability
Pesic P. Ч Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability

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Ќазвание: Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability

јвтор: Pesic P.


In 1824, a young Norwegian named Niels Henrik Abel proved conclusively that algebraic equations of the fifth order are not solvable in radicals. In this book, Peter Pesic shows what an important event this was in the history of thought. He also presents it as a remarkable human story. Abel was twenty-one when he self-published his proof, and he died five years later, poor and depressed, just before the proof started to receive wide acclaim. Abel's attempts to reach out to the mathematical elite of the day had been spurned, and he was unable to find a position that would allow him to work in peace and marry his fiancee. But Pesic's story begins long before Abel and continues to the present day, for Abel's proof changed how we think about mathematics and its relation to the "real" world. Starting with the Greeks, who invented the idea of mathematical proof, Pesic shows how mathematics found its sources in the real world (the shapes of things, the accounting needs of merchants) and then reached beyond those sources toward something more universal. The Pythagoreans' attempts to deal with irrational numbers foreshadowed the slow emergence of abstract mathematics. Pesic focuses on the contested development of algebra Ч which even Newton resisted Ч and the gradual acceptance of the usefulness and even beauty of abstractions that seem to invoke realities with dimensions outside human experience. Pesic tells this story as a history of ideas, with mathematical details incorporated in boxes. The book also includes a new annotated translation of Abel's original proof.

язык: en

–убрика: ћатематика/ѕопул€рные издани€/

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

ed2k: ed2k stats

√од издани€: 2003

 оличество страниц: 212

ƒобавлена в каталог: 22.03.2005

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ѕредметный указатель
"Completing the cube,"      36Ч37 120
"Completing the square,"      25Ч26 113
"Golden ratio"      28
"July monarchy,"      105Ч106
"Standard theory" (physics)      142 196n
"Treviso arithmetic"      29
Abbati Pietro      82
Abel, Niels Henrik      1-3 85Ч102 189nЧ190n
Abel, Niels Henrik, Abel-Ruffini Theorem      1Ч3 89Ч94 155Ч170 200n
Abel, Niels Henrik, Abelian Addition Theorem      151 200n
Abel, Niels Henrik, abelian equations      98Ч100
Abel, Niels Henrik, abelian groups      112Ч113
Abel, Niels Henrik, Abelian integrals      151 200n
Abel, Niels Henrik, and Cauchy      87 93Ч94 96
Abel, Niels Henrik, and Galois      105 108Ч109 130Ч131 145
Abel, Niels Henrik, and Gauss      88Ч89 95
Abel, Niels Henrik, and Hamilton      133
Abel, Niels Henrik, and Ruffini      87Ч89 97 190n
Abel, Niels Henrik, early life      85Ч89 189n
Abel, Niels Henrik, formulas of      88
Abel, Niels Henrik, illness and death of      101Ч102
Abel, Niels Henrik, notebooks of      97 152Ч153 200n
Abel, Niels Henrik, travels in Europe      95Ч97
Academie des Sciences      96 104Ч106
accounting      See Bookkeeping
al-Khwarizmi, Muhammed ibn-Musa      25Ч26 30 183nЧ184n
Algebra coefficient      1 44Ч45 91Ч93
Algebra variable      1 44
Algebra, Arabic      23Ч28 45 54
Algebra, noncommutative      131Ч143
Algebra, roots      1 92 98
Algebra, symbolic notation      40Ч45 132
Algebra, unknown      43
Algebraic functions      90Ч91
Alogon      9
Alternating groups      See Groups
Analytic mathematics      42 59
Anrta      9
Anticommutation      134Ч136 195n
Apollonius of Perga      42 51 59
Aporia      14 182n
Archimedes      32 60
Area problem      61Ч66
Aristotle      7 181n
Arithmos      9 181n
Athens      15
Ausdehnungslehre (Grassmann)      135Ч136
Ayoub, Raymond      189n 192nЧ193n
Babylonian mathematics      5 7 24Ч25 30 183n
Bacon, Francis      182nЧ183n
Basham, A.L.      181n
Beaumarchais, Pierre Augustin de      200n
Bell, Eric Temple      191n
Bernoulli Daniel      65
Bolyai, Janos      133 196n
Bombelli, Raphael      54Ч55 187n
Bookkeeping, double-entry      27Ч29 184nЧ185n
Boole, George      132Ч133 195n
Boole, George, Boolean algebra      132Ч133
Bourbaki, Nicolas (pseudonym)      188n 195n
Boyer, Carl      182nЧ195n
Bring, E.S.      67 188n
Brioschi, Fernando      146 98n
Brizio, Anna Maria      184n
Brown, R.G.      184n
Bryce, R.A.      189n
Buehler, W.K.      189n
Buergi, Jost      48Ч49
Bulletin (Baron de Ferussac)      96
Burkert, Walter      1981n
Burn, R.P.      193n
Burnside, William Snow      190n 192nЧ193n
Cajori, Florian      186n
Calculators      78 149Ч150
Calculus      60 62Ч63
Cantor, Georg      150 199n
Cardano, Girolamo      30Ч40 54 57 67 69 185n
Cartier, Pierre      197n
Cauchy, Augustin      83 87 96 104Ч105
Cauchy, Augustin, and commutativity      132 195n
Cauchy, Augustin, Cauchy's theorem      93 163 166 175Ч180 201n
Causality and noncommutativity      142 196n
Cayley, Arthur      112 126 136Ч138 195n
Cayley, Arthur, Cayley numbers      137
Cayley, Arthur, Cayley tables      112 119 122
Cervantes, Miguel de      23
Charles X      105
Chatfield, Michael      185n
Chinese mathematics      183n
Christiania      See Oslo
Cipher      27Ч28 33 42
circle      62
Code      See Cipher
Coleridge, Samuel Taylor      135
Commensurable      7Ч8 16
Commercial arithmetic      27Ч31
Commutativity      99 112
Computers      147 197nЧ198n
Conic sections      42
Connes, Alain      197n
Continuum      11 18
Cooke, Roger      200n
Cosa (coss)      27 44
Crelle, August      95-97
Crelle, August, Crelle's journal      95 101
Cross product      See Multiplication
cube      5Ч6
Cube, symmetries of      121
Cyclic groups and symmetries      113 117 122 195n
Dance      111Ч130
Dauben, Joseph Warren      199n
De Moivre, Abraham      149 197n
Dedekind, Richard      183n 199n
Dehn, Edgar      192n
del Ferro, Scipione      32Ч34
del Ferro-Cardano-Tartaglia method      32Ч35 48Ч49 54Ч55 77 174
DeMorgan, Augustus      132 195n
Descartes, Rene      50Ч59 68 187n
Descartes, Rene, "relativity" of roots      57 140
Descartes, Rene, and conic sections      64
Descartes, Rene, Descartes's rule of signs      53
Descartes, Rene, La Geometric      50Ч58
Dickson, Leonard E.      192n
Dimension (algebraic)      50Ч51
Dirac, Paul      141
Disquisitiones Arithmetics (Gauss)      79 189n
dodecahedron      5Ч6
Dodecahedron, symmetries of      124Ч125 126Ч130
Doerrie, Heinrich      188nЧ190n
Don Quixote (Cervantes)      23
Dunham, William      185n 199n
Duplication of cube      196n
dТAlembert, Jean le Rond      68
e      28 150 184n 199n
Ecole Polytechnique      105
Ecole Preparatoire (Ecole Normale Superieure)      105
Edwards, Harold M.      191n
Einstein, Albert      140 143
Eisenstein, E.L.      184n
Elements      See Euclid
Equations, algebraic, approximate solutions      66 147 198n
Equations, algebraic, cubic      3 28 30Ч37 90 113Ч120 148Ч149 185n
Equations, algebraic, general formulation      1Ч3
Equations, algebraic, quadratic      2 23 25Ч26 64 90Ч91 111Ч113 185n
Equations, algebraic, quartic      2 35 38Ч39 76Ч78 120Ч122
Equations, algebraic, quintic      2Ч3 77Ч78 91Ч99 122Ч129 198n
Equations, algebraic, roots      1
Erlangen Program (Felix Klein)      138Ч140 196n
Euclid      5 17Ч23 42 59 145Ч146 150 183n
Euclidian geometry      139
Eudoxus      17Ч18 183m
Euler, Leonhard      62 68 90 149 196n
Ewald, William B.      187n 195n 199n
Fauvel, John      184nЧ185n
Fearnly-Sander, Desmond      195n
Fermat's last theorem      87Ч88 189nЧ190n
Ferrari, Ludovico (Luigi)      34Ч35 37Ч39 57 69 76 122
fibonacci      See Leonardo of Pisa
Field, J.V.      186n 199n
Fields (mathematics)      139
Fields (physics), quantum theory of      142Ч143
Fine structure constant      197n
Fine, Benjamin      188n
Fontana, Niccolo      See Tartaglia
Fractions      7
France      45 96Ч97 102Ч108 190n
Fundamental theorem of algebra      56 68Ч73 79 146 188n
Galilei, Galileo      49Ч50 187n
Galois, Evariste      102Ч109 190nЧ191n
Galois, Evariste, and Abel      105Ч106 108Ч109 130Ч131 145
Galois, Evariste, and Cauchy      104Ч105
Galois, Evariste, and his father      104Ч105
Galois, Evariste, and Societe des Amis du Peuple      106Ч107
Galois, Evariste, and Stephanie Poterin-Dumotel      106
Galois, Evariste, death of      106Ч108
Galois, Evariste, education of      102Ч106 190n
Galois, Evariste, Galois theory      125Ч130 191nЧ193n
Galois, Evariste, legend of      108 191n
Galois, Evariste, posthumous writings of      108
Garding, Lars      190n
Gauge fields, nonabelian      142Ч143 196n
Gauss, Carl Friedrich      70Ч74 97 187nЧ189n
Gauss, Carl Friedrich, and Abel      89 95 100 151
Gauss, Carl Friedrich, and commutativity      131Ч132 195n
Gauss, Carl Friedrich, and unsolvability of quintic      79 88
Gazale, Midhat      183n
GelТfond, A.O.      197n
Gentzen, Gerhard      197n
Geometrie, La (Descartes)      50Ч54 187n
Geometry      50 60 66
Germain, Sophie      104
Gibbs, Josiah Willard      136
Gibbs, W. Wayt      195n
Gies, J. and E.      184n
Girard's identities      61 92
Girard, Albert      51 56 68 187n
Gleason, Andrew      187n
God      49 55
Goedel, Kurt      197n
Goldstine, Herman H.      198n
Gonzalez de Posada, Francisco      198n
Gorman, Peter      181n
Grafton, Anthony      185n
Grassmann, Hermann      135Ч136 195n
Gray, Jeremy      184nЧ185n 197n
Great Art (Cardano)      30Ч40
Greek mathematics      5Ч21
Greene, Brian      196n
Gregory, Duncan      132 195n
Grossmann, Israel      193n
groups      109 111Ч130 138Ч140 193nЧ195n
Groups and permutations      175Ч180
Groups cosets      176
Groups identity      112 119 125
Groups order      176
Groups, $A_3$      118Ч120
Groups, $A_4$      121Ч122
Groups, $A_5$      123Ч129 139
Groups, $S_2$      112Ч113
Groups, $S_3$      113Ч120 139
Groups, $S_4$      120Ч122 139
Groups, $S_5$      122Ч124
Groups, Abelian      112Ч113 129
Groups, continuous      140
Groups, cyclical      113 117 122 175Ч180 195n
Groups, definition of      125Ч126
Groups, invariant subgroups      119 129
Groups, Lagrange's Theorem      128 175Ч176
Groups, Lorentz      196n
Groups, monster group      130 195n
Groups, nonabelian      118 129 142Ч143
Groups, normal subgroups      119 129 193nЧ195n
Groups, philosophical aspects      193n
Groups, quotient      130 176Ч177 193nЧ194n
Groups, simple groups      130
Groups, solvable chains of      130 194nЧ195n
Groups, V      122
Groups, visualization of      193n
Guerard, Albert      190n
Hadlock, Charles Robert      192n
Hamilton, William Rowan      133Ч136 196n
Hankins, Thomas L.      196n
Harmony of the World (Kepler)      48 121 124 186n
Hartshorne, Robin      181n 191n 194n
Heath, Thomas      183n
Heisenberg uncertainty principle      141
Hellman, Morton J.      185n
Henry IV      45
Heptagon      48 186nЧ187n
Hermite, Charles      146 150 198n
Herrstein, I.N.      192n
Hexagon      48
Hilbert, David      197n
Hippias of Mesopontum      10
Hirano, Yoichi      193n
Hoe, J.      183n
Holder, Otto      130Ч131 177 194n
Holmboe, Berndt Michael      87 97 190n 200n
Holy Spirit      55
Huffman, C.A.      181n
Huntley, H.E.      181n
Hypergeometric functions      198nЧ199n
icosahedron      5Ч6
Icosahedron, symmetries of      123Ч129
incommensurability      7Ч14
Indian mathematics      9
Indistinguishability of quanta      142
infinity      22 146 148 151 153
Institut de France      100 106
Invariance      113 139
Invariant subgroups      See Groups
Irrational magnitudes      7Ч14 19Ч21 145Ч146 183n
Irreducible case (cubic equations)      54
Irreversibility      141
Isograph      147
Jacobi, Carl Gustav Jacob      100 146
Jacobson, Nathan      192n
Jerrard, George B.      67 133 188n 195n
Johnston, K.S.      184n
Jordan, Camille      130Ч131 133 146 177 194n
Kabbalists      48
Kaku, Michio      196n
Kant, Immanuel      200n
Karl XIII      85
Kemp, Christine      96 101Ч102
Kepler, Johannes      48Ч49 121 124 186nЧ187n
Khayyam, Omar      30 184n
Kiernan, B. Melvin      193n
King, R. Bruce      192n
Klein, Felix      138Ч140 143 189n 191n 196n 199n
Klein, Jacob      182n 187n
Kline, Morris      182n 192n
Knorr, Wilbur Richard      182n
Kronecker, Leopold      146 190n 198n
La Geometrie (Descartes)      50Ч58
La Nave, Federica      187n
Lafayette, General      105
Lagrange, Joseph-Louis      73Ч83 87 188n
Lagrange, Joseph-Louis, Lagrange resolvent      74Ч79
Lagrange, Joseph-Louis, Lagrange's Theorem      128 175Ч176 194n
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