Mathematical problems for the next century
The author lists 18 problems, chosen with respect to three criteria: (i) Simple statement; (ii) Personal acquaintance with the problem; (iii) Belief that the question, its solution, partial results, or even attempts at its solution are likely to have great importance for mathematics and its development in the next century. The problems are: 1. The Riemann hypothesis, 2. The Poincaré conjecture, 3. Does P = NP?, 4. Integer zeros of a polynomial, 5. Height bounds for Diophantine curves, 6. Finiteness of the number of relative equilibria in celestial mechanics, 7. Distribution of points on the 2-sphere, 8. Introduction of dynamics into economic theory, 9. The linear programming problem, 10. The closing lemma, 11. Is one-dimensional dynamics generally hyperbolic?, 12. Centralizers of diffeomorphisms, 13. Hilbert's 16th problem, 14. Lorentz attractor, 15. Navier-Stokes equations, 16. The Jacobian conjecture, 17. Solving polynomial equations, 18. Limits of intelligence.
scientific article; zbMATH DE number 1516323
scientific article