Proofs from THE BOOK

Table of Contents

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   Book Overview
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   Chapter 1 Six proofs of the infinity of primes
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   Chapter 2 Bertrand’s postulate
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   Chapter 3 Binomial coefficients are (almost) never powers
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   Chapter 4 Representing numbers as sums of two squares
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   Chapter 5 The law of quadratic reciprocity
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   Chapter 6 Every finite division ring is a field
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   Chapter 7 The spectral theorem and Hadamard’s determinant problem
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   Chapter 8 Some irrational numbers
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    Chapter 9 Three times Π²/6
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    Chapter 10 Hilbert’s third problem: decomposing polyhedra
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    Chapter 11 Lines in the plane and decompositions of graphs
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    Chapter 12 The slope problem
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    Chapter 13 Three applications of Euler’s formula
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    Chapter 14 Cauchy’s rigidity theorem
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    Chapter 15 The Borromean rings don’t exist
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    Chapter 16 Touching simplices
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    Chapter 17 Every large point set has an obtuse angle
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    Chapter 18 Borsuk’s conjecture
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    Chapter 19 Sets, functions, and the continuum hypothesis
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    Chapter 20 In praise of inequalities
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    Chapter 21 The fundamental theorem of algebra
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    Chapter 22 One square and an odd number of triangles
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    Chapter 23 A theorem of Pólya on polynomials
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    Chapter 24 On a lemma of Littlewood and Offord
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    Chapter 25 Cotangent and the Herglotz trick
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    Chapter 26 Buffon’s needle problem
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    Chapter 27 Pigeon-hole and double counting
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    Chapter 28 Tiling rectangles
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    Chapter 29 Three famous theorems on finite sets
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    Chapter 30 Shuffling cards
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    Chapter 31 Lattice paths and determinants
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    Chapter 32 Cayley’s formula for the number of trees
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    Chapter 33 Identities versus bijections
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    Chapter 34 The finite Kakeya problem
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    Chapter 35 Completing Latin squares
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    Chapter 36 The Dinitz problem
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    Chapter 37 Permanents and the power of entropy
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    Chapter 38 Five-coloring plane graphs
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    Chapter 39 How to guard a museum
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    Chapter 40 Turán’s graph theorem
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    Chapter 41 Communicating without errors
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    Chapter 42 The chromatic number of Kneser graphs
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    Chapter 43 Of friends and politicians
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    Chapter 44 Probability makes counting (sometimes) easy