An Invitation to Mathematics

1. Structure and Randomness in the Prime Numbers
Terence Tao

2. How to Solve a Diophantine Equation
Michael Stoll

3. From Sex to Quadratic Forms
Simon Norton

4. Small Divisors: Number Theory in Dynamical Systems
Jean-Christophe Yoccoz

5. How do IMO Problems Compare with Research Problems?
W. Timothy Gowers

6. How do Research Problems Compare with IMO Problems?
Stanislav Smirnov

7. Graph Theory Over 45 Years
László Lovász

8. Communication Complexity
Alexander A. Razborov

9. Ten Digit Problems
Lloyd N. Trefethen

10. The Ever-Elusive Blowup in the Mathematical Description of Fluids
Robert M. Kerr, Marcel Oliver

11. About the Hardy Inequality
Nader Masmoudi

12. The Lion and the Christian, and Other Pursuit and Evasion Games
Béla Bollobás

13. Three Mathematics Competitions
Günter M. Ziegler

14. Complex Dynamics, the Mandelbrot Set, and Newton’s Method — or: On Useless and Useful Mathematics
Dierk Schleicher

Keywords: Mathematics, Mathematics, general