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 $O=8$.

Incidentally,

Note that the question (as currently posted) does not limit $M$ to an integer between 0 and 9. If we exploit this loophole, we can set $A=E=S=O=T=H=1$ and $W=0$ which simplifies the equation to $M=M$, making the maximum value unbounded.

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 $O=8$.

Incidentally,

Note that the question (as currently posted) does not limit $M$ to an integer between 0 and 9.

If we exploit this loophole,

we can set $A=E=S=O=T=H=1$ and $W=0$ which simplifies the equation to $M=M$, making the maximum value unbounded.

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 $O=8$.

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 $O=8$.

Incidentally,

Note that the question (as currently posted) does not limit $M$ to an integer between 0 and 9. If we exploit this loophole, we can set $A=E=S=O=T=H=1$ and $W=0$ which simplifies the equation to $M=M$, making the maximum value unbounded.