Everyone's assuming

>! that $AWE$, $SOME$, and $MATH$ are formed by concatenating the single-digit integers of $A$, $W$, etc. 

But 

>! this is a math equation, and ordinarily $xy$ means $x$ times $y$, not $10x+y$.

Which means that the maximum *potential* value of $MATH$ is

>! $9^4=6561$, achieved when $M=A=T=H=9$. 

Can we achieve this?

>! Sure! With some quick algebra, the equation becomes $9WE+9SOE=9^4$, which we can simplify to $E(W+SO)=9^3$. Speculatively plugging in $E=9$, we get $W+SO=81$, which is achievable with $W=S=9$ and $O=8$.