This is a translation into French of the author's English text, Math. Intell. 20, 7--15 (1998; Zbl 0947.01011). V. I. Arnold has written to a number of mathematicians with a suggestion that they describe some great problems for the 21st century. In this text Smale responds with a list of 18 problems, giving a brief discussion of each with necessary hints on literature. This list starts with: 1. The Riemann hypothesis, 2. The Poincaré conjecture\dots and ends with: 16. The Jacobian conjecture, 17. Solving polynomial equations, 18. Limits of intelligence.