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 fGo curve for the formation of SiO2 lies above the Δ fGo curve for MgO, so, at temperature below 1683 K, Mg can reduce SiO¬2. On the other hand, above 1683 K, the  ΔfGo curve for MgO lies above  ΔfGo curve for SiO2. Hence, at a temperature above 1683 K, Si can reduce MgO to Mg.