Below `1623 K, Al` can reduce `MgO` to `Mg`, but above `1623 K`, reverse is true.

Explanation

To determine whether the statement "Below 1623 K, Al can reduce MgO to Mg, but above 1623 K, the reverse is true" is true or false, we can analyze the thermodynamic principles involved, particularly focusing on Gibbs free energy changes and the Ellingham diagram.

### Step-by-Step Solution:

1. **Understanding the Reduction Reaction**:
- The statement suggests that aluminum (Al) can reduce magnesium oxide (MgO) to magnesium (Mg) at temperatures below 1623 K. This means that Al is acting as a reducing agent, while MgO is being reduced.

2. **Oxidation of Aluminum**:
- When Al reduces MgO, it itself gets oxidized to aluminum oxide (Al2O3). The balanced chemical reaction for this process can be represented as:
\[ 3MgO + 2Al \rightarrow 3Mg + Al_2O_3 \]

3. **Gibbs Free Energy Consideration**:
- The feasibility of a reaction can be assessed using Gibbs free energy (ΔG). A reaction is spontaneous if ΔG is negative.
- For the reaction to occur, the ΔG for the reduction of MgO must be more negative than the ΔG for the oxidation of Al.

4. **Ellingham Diagram Analysis**:
- The Ellingham diagram plots the Gibbs free energy change (ΔG) for the formation of oxides as a function of temperature.
- According to experimental data and the Ellingham diagram, the ΔG for the formation of Al2O3 (oxidation of Al) is less negative than that for the formation of MgO (oxidation of Mg) at temperatures below 1623 K.

5. **Conclusion on the Statement**:
- Since ΔG for the formation of MgO is more negative than that for Al2O3 at temperatures below 1623 K, aluminum cannot reduce magnesium oxide in this temperature range.
- Therefore, the statement that "below 1623 K, Al can reduce MgO to Mg" is **false**.

6. **Reversal Above 1623 K**:
- Above 1623 K, the situation reverses. The ΔG for the oxidation of Al becomes more favorable, allowing Al to reduce MgO to Mg. Thus, the reverse statement holds true above this temperature.

### Final Answer:
The given statement is **false**.