Simple math using arrays
You should avoid mixing calculations with input/output. It would be better if your doMath() would not call the output function ap() directly, but instead would just return the result of its calculations:

ap(doMath({'numbers': [10,5,2,2], 'method':'subtract'}));


Of course the ap itself is a lousy name for a function, but it's more of a helper in here I guess.

I see no reason why you would use and options object instead of passing in just two parameters, but even when you use an options object, it would be simpler to extract its values into local variables and work with these. One can also easily drop the use of $.extend in favor of simple || operator, which is the canonical way of implementing default values for parameters:

    var method = options.method || "add";
    var numbers = options.numbers;


Another step to simplify code is to filter out the invalid numbers before doing any calculations on them. Array.filter helps us here:

var validNumbers = numbers.filter(isNumber);


The actual calculation can be easily implemented with Array.reduce. First we can define functions add and subtract

var methods = {
    add: function(a, b) { return a + b; },
    subtract: function(a, b) { return a - b; }
};


And then using Array.reduce we can apply them for the whole array:

validNumbers.reduce(methods.add);
// or
validNumbers.reduce(methods.subtract);


Pulling it all together:

function doMath(options) {
    var method = options.method || "add";
    var numbers = options.numbers;

    var validNumbers = numbers.filter(isNumber);

    var methods = {
        add: function(a, b) { return a + b; },
        subtract: function(a, b) { return a - b; }
    };

    return validNumbers.reduce(methods[method]);
}