There's a big difference between

$$
\int\int
$$

and \AmSTeX's

$$
\iint
$$

\AmSTeX\ also offers

$$
\iiint,\quad\iiiint,\quad\oint,\quad\text{and}\quad\idotsint
$$

\AmSTeX\ offers superior typesetting of mathematics.

$$
\iiint\limits_M d\omega=\iint\limits_{\partial M} \omega
$$

$$
\int\limits_{\partial(M-\cup_{i=1}^n U_i)} r^*\Pi
=\sum_{i=1}^n\int_{\partial U_i} r^*\Pi
$$

$$
\sum\Sb 0\le i\le m\\ 0\le j\le n \endSb P(i,j)
$$

\bye