Gravity just might be the most interesting thing out there, second only to Prime Numbers, IMNSHO. As a fledgling "amateur-mathematician" (don't ask), I am astonished that centuries after the Newtonian Revolution kicked off all of science, we still don't know what underlies the very basis of Newton's discovery. Even today, measure the amount of "force" of gravity on very large or small scales is damned near impossible. But we must believe in it nonetheless!

We sure take a lot of our hindsight knowledge for granted.

What is gravity? We sure think we have pinned it down because we can measure its effects on very precise scales. But measuring a thing is not at all the same as understanding a thing, in a teleological sense. I am not a physicist, but then again, I'm pretty sure most physicists are equally in the dark about what gravity is, so there's little harm to be done firing blindly in the dark.

The way I understand it so far, the explanation of gravity is intimately tied into the way we measure, model and predict the behavior of gravity. And all of that is equivalent to our mathematical formulation of gravity.

Newton was fortunate enough that the precision of measurements in his era were orders of magnitudes worse than now. So he could create calculus to explain his notion of gravitational force, assuming all space and time in the universe were a single, absolute "reference frame", and not run into any real problems. I've always seen the creation of the calculus and the formulation of the central force field hypothesis as being flip sides of the same coin—without the notion of one, you would never arrive at the idea of the other. So that's one way of explaining it.

In Netwon's day, the primary objection to gravity was that you had to believe in "action-at-a-distance", and that the force of gravity "travels" instantaneously across the entire Universe. I don't recall, but there was some Aristotilean or Scholastic hang-up on this point. And we still have this problem—it'sonly slightly alleviated by General Relativity sweeping it under the rug of "things-we-can't-hope-to-measure-until-we-get-intergalactic-starships"

Einstein's genius lay in being a great connector of existing ideas. He managed to take Newton's gravity, a dash of Bolztmann's atomic hypothesis & statistical mechanics, a pinch of Riemann's non-euclidean metrical ideas, and notice the very staggering pattern that Lorentz transforms and Minkowski space on paper exactly match how gravity appears to work, even with relaxing Newton's assumption of a single, universe-wide, unchanging space-time. It does seem far, far too convenient that of all the possible models the Universe could take, it "chose" to make gravity appear locally Euclidean, yet globally Minkowski, and that the hyperbolic metric of non-euclidean geometry can be made to exactly model the behavior of gravity in non-inertial-frames. All of that explanation exists only on paper too.

As an aside, I cannot recommend this book enough for a not-too-difficult, motivated-sophomore-level calculus based explanation of gravity—just 60 pages in and you will "get it", as least the bigger picture of gravity: The Geometry of Spacetime: An Introduction to Special and General Relativity
http://www.amazon.com/gp/product/B000YJ4ZTE/ref=pd_lpo_k2_dp...

I also highly recommend Westfall's definitive biography of Newton, "Never at Rest." He spends a lot of time picking apart Newton's conceptual problems with gravity. It's like looking over Newton's shoulder, with added commentary, so you can glimpse a lot more about the weird nature of gravity without being drowned in mathematical equations.

So again, the explanation is almost entirely mathematical. While this may turn off a lot of folks who (incorrectly) believe they can never understand enough calculus to even glimpse what Newton & Einstein were saying, I personally believe the opposite—wanting to know what gravity really is serves as a great motivation for learning more math
Which everyone ought to do!

It was about 6 months ago that a paper was published(and linked to on HN) saying no separate effect of gravity could be detected even right down to the Planck scale(the smallest theoretical "distances" we can ever hope to measure!). Gravity, being the weakest of the 4 forces, is even weaker than we thought, and yet it is the "prime mover" of the entire Universe. If gravity cannot be easily detected even on the Planck scale, this is going to be a huge, huge problem in figuring out gravity. What the gist of the experiment seemed to suggest is that we have no hope of ever detecting "gravitons." I am not a physicist, so I may not fully understand this new research, but I think that's what it was implying if you read between the lines.

We may never know what gravity is. But I would say it's all about the journey anyways, and never the destination. So all of the mathematics you have to pick up along the way to grok that we don't know what gravity is, is itself of more possible value than knowing what gravity really is. (Of course I might be wrong—a gravity manipulation machine would be most excellent!).