Is it true that under certain conditions, Mg can reduce Al₂O₃ and Al can reduce MgO? What are those conditions?

Below 1683K, the melting point of silicon, the Δ _fG^o curve for the formation of SiO₂ lies above the Δ _fG^o curve for MgO, so, at temperature below 1683 K, Mg can reduce SiO₂. On the other hand, above 1683 K, the Δ_fG^o curve for MgO lies above Δ_fG^o curve for SiO₂. Hence, at a temperature above 1683 K, Si can reduce MgO to Mg.