  Describing minimal generating set of a toric ideal is a well-studied and
difficult problem. In 1980 White conjectured that the toric ideal associated to
a matroid is equal to the ideal generated by quadratic binomials corresponding
to symmetric exchanges. We prove White's conjecture up to saturation, that is
that the saturations of both ideals are equal. In the language of algebraic
geometry this means that both ideals define the same projective scheme.
Additionally we prove the full conjecture for strongly base orderable matroids.
