'… a fascinating and exciting overview of contemporary mathematics.' L'Enseignement Mathématique

• 1. The Independent University of Moscow and student sessions at the IUM; 2. Mysterious mathematical trinities V. I. Arnold; 3. The principle of topological economy in algebraic geometry V. I. Arnold; 4. Rational curves, elliptic curves, and the Painléve equation Yu. I. Manin; 5. The orbit method and finite groups A. A. Kirillov; 6. On the development of the theory of dynamical systems during the past quarter century D. V. Anosov; New or 'renewed' directions; 'Named' problems; Some other achievements; 7. Foundations of computational complexity theory A. A Razborov; 8. The Schrödinger equation and symplectic geometry S. P. Novikov; 9. Rings and algebraic varieties Miles Reid; 10. Billiard table as a playground for a mathematician A. B. Katok; 11. The Fibonacci numbers and simplicity of 2127 minus 1 A. N. Rudakov; 12. On problems of computational complexity Stephen Smale; 13. Values of the -function Pierre Cartier; 14. Combinatorics of trees Pierre Cartier; 15. What is an operad Pierre Cartier?; 16. The orbit method beyond Lie groups A. A. Kirillov; Infinite-dimensional groups; 17. The orbit method beyond Lie groups A. A. Kirillov; Quantum groups; 18. Conformal mappings and the Ehitham equations I. M. Krichever; 19. Projective differential geometry: old and new V. Yu. Ovsienko; 20. Haken's method of normal surfaces and its applications to classification problem for 3-dimensional manifolds - the life story of one theorem S. V. Matveev.

'… a fascinating and exciting overview of contemporary mathematics.' L'Enseignement Mathématique

• 1. The Independent University of Moscow and student sessions at the IUM; 2. Mysterious mathematical trinities V. I. Arnold; 3. The principle of topological economy in algebraic geometry V. I. Arnold; 4. Rational curves, elliptic curves, and the Painléve equation Yu. I. Manin; 5. The orbit method and finite groups A. A. Kirillov; 6. On the development of the theory of dynamical systems during the past quarter century D. V. Anosov; New or 'renewed' directions; 'Named' problems; Some other achievements; 7. Foundations of computational complexity theory A. A Razborov; 8. The Schrödinger equation and symplectic geometry S. P. Novikov; 9. Rings and algebraic varieties Miles Reid; 10. Billiard table as a playground for a mathematician A. B. Katok; 11. The Fibonacci numbers and simplicity of 2127 minus 1 A. N. Rudakov; 12. On problems of computational complexity Stephen Smale; 13. Values of the -function Pierre Cartier; 14. Combinatorics of trees Pierre Cartier; 15. What is an operad Pierre Cartier?; 16. The orbit method beyond Lie groups A. A. Kirillov; Infinite-dimensional groups; 17. The orbit method beyond Lie groups A. A. Kirillov; Quantum groups; 18. Conformal mappings and the Ehitham equations I. M. Krichever; 19. Projective differential geometry: old and new V. Yu. Ovsienko; 20. Haken's method of normal surfaces and its applications to classification problem for 3-dimensional manifolds - the life story of one theorem S. V. Matveev.

'… a fascinating and exciting overview of contemporary mathematics.' L'Enseignement Mathématique

• 1. The Independent University of Moscow and student sessions at the IUM; 2. Mysterious mathematical trinities V. I. Arnold; 3. The principle of topological economy in algebraic geometry V. I. Arnold; 4. Rational curves, elliptic curves, and the Painléve equation Yu. I. Manin; 5. The orbit method and finite groups A. A. Kirillov; 6. On the development of the theory of dynamical systems during the past quarter century D. V. Anosov; New or 'renewed' directions; 'Named' problems; Some other achievements; 7. Foundations of computational complexity theory A. A Razborov; 8. The Schrödinger equation and symplectic geometry S. P. Novikov; 9. Rings and algebraic varieties Miles Reid; 10. Billiard table as a playground for a mathematician A. B. Katok; 11. The Fibonacci numbers and simplicity of 2127 minus 1 A. N. Rudakov; 12. On problems of computational complexity Stephen Smale; 13. Values of the -function Pierre Cartier; 14. Combinatorics of trees Pierre Cartier; 15. What is an operad Pierre Cartier?; 16. The orbit method beyond Lie groups A. A. Kirillov; Infinite-dimensional groups; 17. The orbit method beyond Lie groups A. A. Kirillov; Quantum groups; 18. Conformal mappings and the Ehitham equations I. M. Krichever; 19. Projective differential geometry: old and new V. Yu. Ovsienko; 20. Haken's method of normal surfaces and its applications to classification problem for 3-dimensional manifolds - the life story of one theorem S. V. Matveev.