Preface
A remark on notation
Acknowledgments
Chapter 1 Expository articles
1.1 An explicitly solvable nonlinear wave equation
1.2 Infinite fields, finite fields, and the Ax-Grothendieck theorem
1.3 Sailing into the wind or faster than the wind
1.4 The completeness and compactness theorems of first-order logic
1.5 Talagrand's concentration inequality
1.6 The Szemeredi-Trotter theorem and the cell decomposition
1.7 Benford's law, Zipf's law, and the Pareto distribution
1.8 Selberg's limit theorem for the Riemann zeta function on the critical line
1.9 P = NP, relativisation, and multiple-choice exams
1.10 Moser's entropy compression argument
1.11 The AKS primality test
1.12 The prime number theorem in arithmetic progressions, and dueling conspiracies
1.13 Mazur's swindle
1.14 Grothendieck's definition of a group
1.15 The "no self-defeating object" argument
1.16 From Bose-Einstein condensates to the nonlinear SchrSdinger equation
Chapter 2 Technical articles
2.1 Polymath1 and three new proofs of the density Hales-Jewett theorem
2.2 Szemeredi's regularity lemma via random partitions
2.3 Szemeredi's regularity lemma via the correspondence principle
2.4 The two-ends reduction for the Kakeya maximal conjecture
2.5 The least quadratic nonresidue, and the square root barrier
2.6 Determinantal processes
2.7 The Cohen-Lenstra distribution
2.8 An entropy Plunnecke-Ruzsa inequality
2.9 An elementary noncommutative Freiman theorem
2.10 Nonstandard analogues of energy and density increment arguments
2.11 Approximate bases, sunflowers, and nonstandard analysis
2.12 The double Duhamel trick and the in/out decomposition
2.13 The free nilpotent group
Bibliography
Index
