Preface : what is mathematics?
Structure and randomness in the prime numbers / Terence Tao
How to solve a Diophantine equation / Michael Stoll
From sex to quadratic forms / Simon Norton
Small divisors : number theory in dynamical systems / Jean-Christophe Yoccoz
How do IMO problems compare with research problems? Ramsey theory as a case study / W. Timothy Gowers
How do research problems compare with IMO problems? A walk around games / Stanislav Smirnov
Graph theory over 45 years / László Lovász
Communication complexity / Alexander A. Razborov
Ten digit problems / Lloyd N. Trefethen
The ever-elusive blowup in the mathematical description of fluids / Robert M. Kerr and Marcel Oliver
About the Hardy inequality / Nader Masmoudi
The lion and the Christian, and other pursuit and evasion games / Béla Bollobás
Three mathematics competitions / Günter M. Ziegler
Complex dynamics, the Mandelbrot set, and Newton's method : or, On useless and useful mathematics / Dierk Schleicher.
