How can the concentration of a solid be constant during a reaction? The molar concentration is given by the ratio between density and molar mass. I understand the proof. 
But how does this remain true during a reaction? 

For example consider the reaction, 

$$\ce{4Al(s) + 3O2 (g) -&gt; 2Al2O3(s)}$$

If the amount of Al and O2 moles are equal, according to stoichiometry Al ought to be the reactant to end first. But, being a solid, Al’s concentration must be constant. 
How can this be? What is wrong in my reasoning?

**Please note that I mistakenly assumed that the amount of Al and O2 are equal, without stating it, leading to the confusion that Al ends first at all times, I have edited the question appropriately
In physical chemistry one does not use the concentration of a chemical but its activity (see https://en.m.wikipedia.org/wiki/Thermodynamic_activity)

In a solid the standard condition is the pure chemical. In case of the solid block of aluminum it is therefore in its standard condition which leads to the fact that the activity is 1 (the chemical potential is equal to the chemical potential in the standard condition as the block of aluminium is in its standard condition - see the link I provided for the definition of the activity).

Therfore it doesn't need to be considered in calculations like the law of mass action as multiplying or diving by 1 does not affect the result.

However in "real chemistry" one does not calculate with activities too often and uses concentrations instead and in order to apply the same trick one simply says that the concentration is constant.

So in the end it's just a result of sloppiness because one doesn't want to work with activities.