There are so many elements, that it seems impossible to capture them all. To do that, a lot of people think of intelligence like so:
We use a range of tests and tasks to gauge certain dimensions of mental capability, and we establish a scale of comparison by juxtaposing peoples' scores.
I prefer to look at intelligence like this:
Those are fractals, if you aren't already familiar with them. The thing about fractal structures is that they are extremely beautiful not in spite of, but as a result of a few simple rules. The rules that you choose determine the fractal that you get.
I think of the mind in this frame. I can change how "coarse" my measures of the mind are, in the same way that I could look at different sizes of chunks in these fractals. Now, in a real fractal, changing the scale that you look at doesn't actually change the fractal structure at all. You just see a replication of the same thing on any scale.
In the mind, this is not true. I can look at several different scales, along several dimensions. In a fractal, dimensions are weird. You don't always have 1D or 2D objects, you can easily find structures that are 1.33 dimensional. If you want to understand how that works, you need to read about fractals (because they're awesome) but for now, assume that the dimensions of the mind are weird too. Not only that, but like different fractals, the dimensions of different minds are not necessarily the same.
This is how I view the differentiating characteristics of individual minds. The beauty and uniqueness lies in the structure, rather than the measurements along a fixed axis. You can't measure something like color density in a Mandelbrot set and learn much about the fractal structure of the set; it seems just as silly to say that any of our current set of measures can classify a mind successfully. Our tests may indicate a person's suitability for a particular line of work, but that's akin to a chemical test in water that determines the amount of chlorine in it. You may know that there is chlorine in the water, but that tells you nothing of the pH, the calcium hardness, the alkalinity, and so on. You have to use multiple orthogonal measures to understand something completely.
And so this leaves us at a crossroads. If we wish to continue to use standardized testing to find intelligence, then we will be forced to define intelligence as the thing that we are testing for. Otherwise, intelligence will have to be reconceptualized as something deeply related to the structure of the mind, the nature of which cannot be determined by a single test. Intelligence would require a much more dynamic form of measurement, something attended to just as closely and experimentally as the measurements that scientists make. Note, that scientists aren't looking for a single measurement to solve every problem. Instead, the point is to find throw new measurement methods at a problem to learn more about the thing that you're looking at.