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Íàçâàíèå: Stalking the Riemann Hypothesis
Àâòîð: Rockmore D.
Àííîòàöèÿ:
In 1859 a German professor named Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the baffling occurrence of prime numbers; coming up with its proof has been the holy grail of mathematicians ever since. In 'Stalking the Riemann Hypothesis, Dan Rockmore, a prominent mathematician in his own right, takes us from Euclid's pondering of the infinitude of the primes through modern efforts to prove the Riemann hypothesis-efforts that astonishingly connect the primes to the statistics of solitaire, chaos theory, and even the mysteries of quantum mechanics. Along the way, he introduces us to the many brilliant and fascinating thinkers who have contributed to this work, from the most famous mathematician of all time, Carl Friedrich Gauss (Riemann's teacher), to the intellectual giants David Hilbert and Freeman Dyson.
A lively, comprehensive, and accessible examination of one of the most compelling unsolved problems in mathematics, 'Stalking the Riemann Hypothesis tells us the full story of the quest to find that elusive solution.
Moses93 Mosteller, Fred224225 Mount Holyoke244—245 Multivalued function147—148 Nachlass (Riemann)140 Nahin, Paul72 Napoleon81—82 Nash, John, Jr.152—153 Natal University211 Natural logarithm34—35 Natural numbers7—20 Natural numbers, as "God given"770111137 Natural numbers, composites12—13 Natural numbers, defined7 Natural numbers, primessee “Prime numbers” Ncudcckcr, Werner152 negative numbers71 Nevanlinna, R.145 New York Times148149 New York University3—6241243261—263 Newlands, John108 Newman, Charlie262263 Newton, described46—47 Newton, Isaac3848505282236 Nobel prize102150152155163171174257 Nobel Prize, mathematics and141—142 Nobel, Alfred141—142 Non-Euclidean geometry39123201203—205 Noncommutative geometry230 Noncommutative multiplication169n230 Nonlinear differential equations238 Nonobstructive proof265 Nonoricntable surface97 Nontrivial zeta zeros89—92 Nonzero11 An Nuclear weapons249—250255 NUMBER259 Number theorists10 Number theory1053265 Numerical methods250 Numerosity, pattern of8—10 Occam's razor221 Odlyzko, Andrew179n198199218258263 Odlyzko, described180—181 Odlyzko, Dyson — Moncgomery — Odlyzko Law180—185 On the Propagation of Heat in Solid Bodies (Fourier)81 Operator177 Operator theory234 Operator, integral178—179 Operator, zeta zeros and180220 Origin of Species, The (Darwin)63 orthogonal matrices219 Overfitting data3840 p-adic numbers229—230 Pacific Institute of Mathematical Sciences265 Painlcve equations237238 Painleve transcendants237—240256 Painleve, described238—239 Painleve, Paul237—240246 Pair correlations157—160164 Parallel postulate203—204 Partial differential equation82 Patience sorting253—254 Patterns8—14 Patterns, figurate numbers and10—11 Patterns, numerosity8—10 Patterns, patterns within11—14 Pavlovskii, V.V228 Peer review148 Perfect number12 Perfect shuffles249 Periodic functions83 Periodic orbit191192 permutations245—259 Permutations, computer science and247—249 Petain, Marshal238 Philosophy10 Physics171 Physics, bridge between quantum mechanics andsee “Scmidassical limit” Physics, physicists217 Physics, statistical233 Pi 5870—7172 Planar domains196 Planck's constant187—188 Planck, Max187 Plato1363 Poe, Edgar Allan24236 Poincare conjecture202 Poincare disk200—209 Poincare disk, chaos in207—209 Poincare, described202 Poincare, Henri102 Point204n Poisson process158—160 Poisson, Simeon — Denis158 Polya Prize260 Polya — Hilbert approach179—180185198—199227232 Polya, described177—178 Polya, George177—180259—260 Polya, integral operators and178—179 Polynomial72 Polytechnical School of Delft95—96 Pomerance, Carl264 Pons, Jean — Louis40 Population density41 Poussin, Nicholas107119120 Preprocessing248 Primal curve28—2932 Primal waves86—87 Primality tests15—16264 Prime distribution analyzer (PDA)76—77 Prime distribution analyzer (PDA), Dirichlet's7781 Prime distribution analyzer (PDA), Eulcr's7781 Prime distribution analyzer (PDA), Riemannian77—81 Prime factorization1420 Prime number theorem6391—9495 Prime Number Theorem, Cramer primes and138—139 Prime Number Theorem, Gauss and42—4469106119120126132—133137141185 Prime Number Theorem, Lcgendre and35—3869 Prime Number Theorem, mathematically written36n Prime Number Theorem, proof of105106—107116118119129139 Prime Number Theorem, statement of35 Prime numbers, algorithms for checking264 Prime numbers, as the integral atoms14—15 Prime numbers, asymptotic study of23—3051118—129 Prime numbers, cardinality of22—23 Prime numbers, composites and12—13 Prime numbers, Cramer137—139151 Prime numbers, defined4 Prime numbers, digital cryptography and17—18 Prime numbers, error correction and16—17 Prime numbers, Euclid s proof of the infinitude of18—202124285051 Prime numbers, first cartographers of30—45 Prime numbers, Gauss andsee “GaussCarl Prime numbers, Gaussian112—123 Prime numbers, graphs of occurrence of25—29 Prime numbers, harmonic series and55—61 Prime numbers, Hawkins151—152 Prime numbers, infinity of18—20215159—62 Prime numbers, irregular appearance of23—29 Prime numbers, Lcgendre andsee“LegendreAdrien23—29Marie” Prime numbers, music of81—85 Prime numbers, pattern within the pattern11—14 Prime numbers, periodic tables for59—61107—110 Prime numbers, Riemann hypothesis andsee “Riemann hypothesis” Prime numbers, search for14—16 Prime numbers, series of reciprocals of51—59 Prime numbers, shape of21—29 Prime numbers, slowing occurrence of41—42 Prime numbers, speaking in16—18
Prime numbers, twin23—24 Prime numbers, zeta zeros andsee “Zeta zeros” Princeton University154155174195214218219242—243262 Probabilistic number theory137 Probability theory223 Proof (Auburn)50 Proof of Riemann hyporhesis, code breaking and149—152 Proof of Riemann hyporhesis, Cramer and136—139 Proof of Riemann hyporhesis, de la Vallee — Poussin and107—110 Proof of Riemann hyporhesis, early twentieth century pursuit of120—127 Proof of Riemann hyporhesis, eigenvalues andsee “Eigenvalues” Proof of Riemann hyporhesis, epilogue263—266 Proof of Riemann hyporhesis, first steps in128—153 Proof of Riemann hyporhesis, Hadamardand107—110 Proof of Riemann hyporhesis, Hamiltonian matrix and227—228 Proof of Riemann hyporhesis, limits of computation132—134 Proof of Riemann hyporhesis, Millennium meeting and3—6261—263 Proof of Riemann hyporhesis, Nash and152—153 Proof of Riemann hyporhesis, rwo-pronged assault129 Proof of Riemann hyporhesis, search for131 Proof of Riemann hyporhesis, Sicgel and139—140 Proof of Riemann hyporhesis, Stieltjes and95—99104—105 Proof of Riemann hyporhesis, true, false, or neither134—136 Pseudosphere207 Ptolemy I.1350 Purdue University262265 Putnam Exam234 Pythagoras (Pythagoreans)10—1354 Pythagoras (Pythagoreans), theorem of113n114115 Quadratic formula72 Quantization196—200 Quantum chaos187—190 Quantum chaos, basic conjecture of197—200 Quantum chaos, Berry and187188—189197—198 Quantum chaos, billiard tabic analogysee “Billiard tables for physicists” Quantum chaos, comparison of distributions222 Quantum chaos, making order out of213—231 Quantum chaos, Sarnak and217—221 Quantum chaos, zeta zeros and199 Quantum chromodynamics (QCD)237 Quantum electrodynamics (QED)163171237 Quantum gravity236—237 quantum mechanics115136—137see Quantum mechanics, classical physics and171 Quantum mechanics, Planck's constant and187—188 Quantum mechanics, spectral lines and172—173 Quantum mechanics, uncertainty principle and135187—188 Quantum mechanics, wave function and171—172176—179 Rademachcr, Hans147—149 RAF Bomber Command162—163 Rains, Eric258 Random matrices173—175177—180218 Random Matrices (Mchta)218239244245 Random matrices, Deift and244—246 Random matrices, RSK and258—259 Random matrices, Tracy — Widom distributions and234—241 Random walk100—104177178 Random Walk Down Wall Street, A (Malkiel)102 Randomness157—160 Randomness, understanding through173—175 Rational integers114 Rational numbers70116 Real axis74 Real numbers116 Real part of complex numbers7374 Reciprocals, of logarithms41—42 Reciprocals, of Riemann's zeta function96—99 Reeds, Jim248 Reid, Constance179260n Relative (percentage) error126—127 Relativity theory, general136236—237 Relativity theory, special202 Repulsion160 Reseating data158—160 Rhind papyrus246—247 Rhind, Henry246 Rhodes University242 Richter scale33 Riemann hypothesis88—94125 Riemann hypothesis, as "very likely"91—94 Riemann hypothesis, as possibly undecidable134—136 Riemann hypothesis, attempts to provesee “Proof of Riemann hypothesis search for” Riemann hypothesis, claimed proofs (dc Branges)262—263265—266 Riemann hypothesis, complex numbers and70—73 Riemann hypothesis, complex plane and73—76 Riemann hypothesis, defined4—54788—91 Riemann hypothesis, equivalence to eigenvalue properties of matrix179185 Riemann hypothesis, extended219 Riemann hypothesis, for function fields145—147 Riemann hypothesis, for L-series110 Riemann hypothesis, generalized120—121 Riemann hypothesis, incorrect refutation (Rademache)147—149 Riemann hypothesis, Polya — Hilbert approach179—180 Riemann hypothesis, publication of63—64 Riemann hypothesis, quest to settle4—6 Riemann hypothesis, raw material for53 Riemann hypothesis, road to64—69 Riemann hypothesis, web of connections to259—260 Riemann hypothesis, zeta function andsee “Riemanns zeta function” Riemann hypothesis, zeta zeros and4588—91 Riemann surfaces147 Riemann — Hilbert problems243—244 Riemann — Siegel formula139—140150—151 Riemann's zeta function5seesearch Riemann's zeta function, "zoo" of zeta functions and142—143218 Riemann's zeta function, creation of76—81 Riemann's zeta function, Fourier analysis and81—85 Riemann's zeta function, integral form of80—81129 Riemann's zeta function, logarithm of81 Riemann's zeta function, music of the prime powers and81—85 Riemann's zeta function, reciprocal of96—99 Riemann's zeta function, Riemann hypothesis and88—94 Riemann's zeta function, zeros of85—92119125—126 Riemann, academic mentors of455961—6265—6976—78 Riemann, Bemhard4—663—94 Riemann, death of6592—93 Riemann, early life65—66 Riemann, formulation of zeta function80 Riemann, notes of64—65 Riemann, reinvention of space66—69 Riemann, statement of Riemann hypothesis88—91 Riemannian geometry66—69 Riemannian manifold68 Riemannian prime distribution analyzer77—81 Riemanns Zeta Function (Edwards)140 Riffle shuffling248 Rising sequence252—259 Robinson — Schensted — Knuth (RSK) construction257—259 Robinson, Gilbert de Beauregard257 Rosser, John Barkery151 Royal Danish Academy75 Royal Society150 Rubinstein, Michael219 Rudnick, Zeev218—229 Rutgers University233 Saddle point207 Samak, Cohen and214—226 Samak, described214263 Samak, Katz and219—221 Samak, Peter143185227231244260262 Samak, quantum chaos and217—221 Samak, Rudnick and218—229 Sato, M.237239—240 Saxena, Nitin264 Scattering theory242—243 Schcnsted, Craige257 Schmit, Charles198 Schoenfeld, Lowell151 Scholcs, Myron102 Schrodinger, Erwin179
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