It's backed by math and computational complexity, which is decidedly not "nothing." If, as you say, it is backed by nothing, go ahead and forge some Bitcoins. Except, of course, you cannot forge them. You can only create them via the investment of hardware, electricity, time, and luck.
It's not like gold is actually worth $1,500 an ounce due to its value in making jewelry or in manufacturing. The value of gold is set by the speculative market, just like Bitcoin.
Of course, you're right that it's volatile. But that has nothing to do with its "backing" and everything to do with the fact that 99% of the world has no idea what the hell to make of it yet. That, and the fact that there has never been a decentralized digital currency before, so nobody knows what's going to happen.