  We study the number of ways to decompose a monic polynomial in F_q[t] of
degree n as a sum of two monic irreducible polynomials in F_q[t]. Our principal
result is an asymptotic formula for the number of such representations in the
case when q is large compared to n. In its range of validity, this formula
agrees with what is suggested by heuristic arguments from the rational setting.
We also present similar results towards an analogue of the twin prime
conjecture.
