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.