How to curry a function across an unknown number of parameters

It’s sort of possible but you need to define the terminating condition because the problem is essentially the same problem as writing a recursive function. The function needs a way to tell whether it should return a function or a value.

How you signal the need for values is up to you. One way of doing it is to check if an argument is passed:

// Using add instead of multiplyDivide to simplify example:

function add (num) {
    function adder (n) {
        if (n !== undefined) {
            num += n;
            return adder;
        }
        else { // terminate
            return num;
        }
    }
    return adder;
}

Now you can do:

var sum = add(1)(2)(3)(4)();

Otherwise it would return a function which you can keep calling:

var x = add(1)(2)(3)(4);
x = x(5)(6)(7);
x = x(8)(9)(10);

var sum = x();

Since in js functions are objects, you can also implement the value getter as a static method. It won’t be purely functional but makes the “API” a bit more explicit and easier to read:

function add (num) {
    function adder (n) {
        num += n;
        return adder;
    }
    adder.value = function(){
        return num
    };
    return adder;
}

Which would allow you to do:

var sum = add(1)(2)(3)(4).value();

You can even get fancy by overriding the built-in .valueOf() and .toString() methods:

function add (num) {
    function adder (n) {
        num += n;
        return adder;
    }
    adder.valueOf = function(){
        return num
    };
    adder.toString = function(){
        return '' + num
    };
    return adder;
}

Which would allow you to do:

var sum = add(1)(2)(3)(4) + 5; // results in 15
var txt = add(1)(2)(3)(4) + "hello"; // results in "10hello"

The key here is that you need a way to tell the function to stop returning functions.