given a vector field on a complex plane c^2 with polynomial coefficients one would like to know if all the integral curves of this vector field are algebraic. the problem seems to be very difficult. i will discuss an approach to this problem using the reduction to characteristic p, which produces a conjectural answer. also i will explain the relation with the famous grothendieck-katz p-curvature conjecture. probably the main beauty of the subject is its completely elementary nature, which makes it accessible to a first year student.