Index P = NP , 69 Ajtai-Szemer´ edi theorem, 143 AKS primality test, 85 Ax-Grothendieck theorem, 8 BBGKY hierarchy, 138 Benford’s law, 48 Burgess estimate, 187 Busy Beaver function, 125 Cantor’s theorem, 119 Cantor-Bernstein-Schr¨ oder theorem, 107 Cell decomposition, 43 Cohen-Lenstra heuristic, 201 Compactness theorem, 21 Connection, 109 Corners theorem, 143 Density increment argument, 76, 144 Determinantal process, 191 Dirichlet character, 179 Duhamel formula, 230 Energy increment argument, 76 Entropy Pl¨ unnecke-Ruzsa inequality, 204 Euclid’s theorem, 117 Fatou-Bieberback domain, 8 Fermat’s little theorem, 83 First-order logic, 31 Flat connection, 110 Free nilpotent group, 238 odel completeness theorem, 20 odel’s incompleteness theorem, 123 Gaudin-Mehta formula, 198 Gaussian concentration inequality, 40 Ginibre formula, 198 Gram identity, 191 Graph correspondence principle, 165 Greedy algorithm, 155 Gross-Pitaevskii hierarchy, 139 Grothendieck’s axiom, 113 Hales-Jewett theorem, 142 Hall-Witt identity, 235 Hamilton’s equations of motion, 131 Hamiltonian mechanics, 130 Harmless move, 127 Heisenberg’s equation of motion, 135 Hilbert’s nullstellensatz, 9 Hyperelliptic curve, 184 Infinitary regularity lemma, 168 Jacobian conjecture, 8 Kakeya maximal function conjecture, 172 Large deviation inequality, 36 Liouville equation, 2 Lorentz transformation, 3 Lov´ asz local lemma, 78 obius function, 94 247
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