WordPress Insert not working with ajax

Your AJAX callback method should be outputting something followed by a die() statement.

function wp_insert() {
    ..your code
    echo $whatever_your_results_are;
    //
    die();
}

I would also recommend against prefixing your custom methods with wp_. That should be reserved for WordPress and will cause confusion to other developers – and probably you 6 months down the road 🙂

Hope this helps