Science can only prove things statistically for a person who believes in this methodology. A physical reality to one person might appear a "magic", unexplained coincidence, or simply incoherent "noise" to someone else.
Science can't prove the existance of individual subjective experiences because, by definition, these can't be repeatably demonstrated to others. Science is also something defined subjectively by individuals. What's "science" to one person may not be considered so to someone else.
Also, science should be more in regard to observations and predictions than models. The value of science is in its predictive ability. Models can be useful but often prove misleading and limiting.
I had an almost religious experience recently while trying to find a model that unified gravity and quantum observations. There's little way to "prove" something to someone else with the same certainty that comes when you search for something you believe should exist and eventually find it on your own. I believe there's only 1 absolute to the universe - change/transience. Existance is difference/contrast and non-existance can't exist with a contrast. It simply takes the possibility of anything else to create a universe of possibilities, and we're in the middle of it all. (For fun I actually simulated the idea of the universe being created from a decision between 2 choices, and using this selection to further seed the possible universes and the growth progressed like the "Golden ratio"/PHI, the same as seen in galaxy arms, hurricanes, seashells ... it's a number that never repeats, like pi). Spacetime is a memory of what's happened, to keep things from repeating - you can't calculate an endless number without potentially infinite storage (hence why we see space expanding). Energy is the source of possibilities - once we examine something, we find we can't ever repeat the exact same observations. This is why time goes in one direction - no loops are possible. The speed of light is less of a real barrier than a necessary protection. There are many experiments that demonstrate that as long as we isolate something being affected by faster than light actions, other things can operate effectively faster. Without the speed of light limitations, and on average conservation of energy there would be nothing protecting existance from a division by 0 and starting over (a division by 0 is in a way how things started ... the Big Bang for example). Maybe some universes have experienced this ... but those would obviously not be ones we currently inhabit, just as we can't inhabit a planet inhospitable to life.
Anyway, I see things in these terms but there are so many analogies that exist saying effectively the same thing. I can't describe the number of things that just clicked into place. There's a common theme to so many thoughts but basically we're all part of the same thing ... we're every part of it, from the mind of God to the most frozen particle of dust in the void. From as simple sunlight to as complex as a fractalize representation of 24th dimensional leech space. The whole thing is our playground and we only see the surface of what's possible. I've found a pattern to science - everytime we try to prove why you can't do something, we instead succeed in showing how few limits truly exist.
The next "big thing", in my opinion, is the recognition of a fractalized universe. They've been failing to unify observed phenomenon, because they see the universe as detached and flat whereas it only takes one single recognition to realize this is almost impossible. Everything is composed of wave energies and the interference patterns alone from these would create the appearance of multiple objects from a single one. If you want to witness this first hand, grab a laser pointer and shine it on a white surface. Hold steady and look closely at where the beam hits the wall. You'll see black dots floating in space ... real or imaginary? Either way you answer this says the same thing - what we see doesn't agree with our typical internal view of things and just like a fish in water, it's hard to realize what things are like until you've exerienced the air above it.
I noticed a fractal pattern, sort of like the Fibonacci sequence to the elements and had tried putting together a table for this and found someone else already did it:
Notice the self-replicating shape. You could likely extend this below hydrogen to find traits of subatomic particles,(though this shape could repeat at stellar and galactic scales, to give an alchemy of the universe)and use "chemistry" to predict interactions of quarks or planetary bodies or interactions in the weather.
Similar characteristics for magnetism etc. would likely hold true over at least some scales.
But why is this pattern to the elements overlooked? Because we prefer straight lines, whereas nature uses fractal curves.
I've seen pictures of galaxies colliding that look just like the orbital shells of helium. There's even a claim, things scale well too:
http://www.amherst.edu/~rlolders/NOF.HTM 
http://www.fractaluniverse.org
How could galaxies look so much like storms on Earth unless they followed a very similar process? There's an "absorption spectrum", just like absorption bands for light in elements to asteroids in our solar system (I couldn't find the graph but it shows asteroid orbital periods versus Jupiter rotation and makes sense why some periods are unsustainable) It seems extremely unlikey that such complex phenomon don't share similar key functions and topologies. If you altered your viewpoint a bit (to shrink horizontally the storm on Earth), these two would be almost identical. Considering if there's a small set of principles by which the universe operates, then it seems almost impossible to see anything but such fractalized versions of things. Consider the spirals of a storm in themselves are fractal in that the arms extend in greater and greater circles, just as the elemental characteristics do. There's a simple math to the universe that just needs to be unfolded.
I was posting about this on another site and can't repeat everything here, but I think I've got a very simple model along the lines of the Higgs field that explains so much of this, but it seems to have so many implications along religious lines that mainstream science isn't likely to want to recognize the simplicity of it. (I listed about 13 observations that seem to have gone relatively unexplained in science and they all seem to match the idea that we're missing how interconnected everything is).