Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's famous list of problems presented in 1900 (Hilbert's problems), and in part in response to a suggestion by V. I. Arnold on behalf of the International Mathematical Union that mathematicians describe a number of outstanding problems for the 21st century.
1. The Riemann hypothesis.
2. The Poincaré conjecture.
3. Does 
(i.e., are P-problems equivalent to NP-problems)?
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 1-dimensional dynamics generally hyperbolic?
12. Centralizers of diffeomorphisms.
13. Hilbert's 16th problem.
14. Is the dynamics of the ordinary differential equations of Lorenz that of the geometric Lorenz attractor of Williams, Guckenheimer, and Yorke? Tucker (2002) answered this question in the affirmative.
15. Navier-Stokes equations.
16. The Jacobian conjecture.
17. Can a zero of 
complex polynomial equations in 
unknowns be found approximately, on the average, in polynomial
time with a uniform algorithm? Beltrán and Pardo (2008) answered this question
in the affirmative.
18. Limits of intelligence.
