Drop your phone and it falls. It has always fallen, for everyone, everywhere, every single time. That is about as certain as anything gets, and you would be forgiven for calling it proof. But in the strict sense scientists use, there is no proof of gravity, and stranger still, no one has ever been able to say what it actually is.
Two different gaps hide inside that sentence, and they are worth pulling apart.
Science does not prove things
The first gap is about the word "proof." Proof belongs to mathematics; science does not deal in it. A physical law is a universal claim, something that is supposed to hold always and everywhere, and no pile of successful experiments can ever finish confirming a claim that large, while a single clean exception would kill it on the spot. The philosopher Karl Popper built his whole account of science on that lopsidedness:
"it is logically impossible to verify a universal proposition by reference to experience (as Hume saw clearly), but a single genuine counter-instance falsifies the corresponding universal law."
Stanford Encyclopedia of Philosophy, on Karl Popper
So every apple that falls only corroborates gravity. It never verifies it. In Popper's tradition every theory we have is permanently on probation: he held that "all knowledge is provisional, conjectural, hypothetical," and that "the universal theories of science can never be conclusively established." This is not a knock on gravity in particular. It is the price of admission for every law in physics. Gravity just happens to be the one we feel surest of.
We can describe it, but not explain it
The second gap is the genuinely strange one. We can write gravity down to staggering precision and still not know what makes it happen. This is old news, and not for lack of trying. Isaac Newton handed us the equation every schoolchild learns, and then, in the same book, openly admitted he had no idea what caused it:
"I have not been able to discover the cause of those properties of gravity from phaenomena, and I frame no hypotheses... it is enough, that gravity does really exist, and act according to the laws which we have explained."
Isaac Newton, General Scholium to the Principia, 1713
"I frame no hypotheses," hypotheses non fingo in the original Latin, became one of the most famous shrugs in the history of science. Nearly three centuries later, Richard Feynman, walking a room of students through gravity, hit exactly the same wall:
"All we have done is to describe how the earth moves around the sun, but we have not said what makes it go... No one has since given any machinery."
Richard Feynman, The Feynman Lectures on Physics, Vol. I
Every attempt to supply that missing machinery breaks, he noted: "No machinery has ever been invented that 'explains' gravity without also predicting some other phenomenon that does not exist."
And yet we measure it better than almost anything
None of this means gravity is shaky. The opposite. It is the best-tested idea we own. When two distant black holes collided, the LIGO detectors caught the ripple by measuring a change in their four-kilometre arms "smaller than one-ten-thousandth the diameter of a proton." Bench experiments confirm that everything falls in exactly the same way down to about fifteen decimal places. Spacecraft tracking agrees with Einstein's equations, in one careful survey of the evidence, "to 10-3 percent." We have pinned gravity down more tightly than almost anything else in the universe.
Einstein, for the record, did not explain it either. He re-described it, more beautifully, as the bending of spacetime: mass tells space how to curve, and things fall along the curve. But that picture rests on an assumption nobody can derive, only measure, namely that floating in deep space and falling freely in a gravitational field are truly the same situation. As the same survey puts it, "if [the equivalence principle] is valid, then gravitation must be a 'curved spacetime' phenomenon." It is an if. We feed it in by hand because that is what the experiments show, not because anyone understands why it must be so.
And at the largest scales the books do not balance at all. Galaxies spin too fast, and the universe flies apart too quickly, for the gravity we can actually account for, so physicists pencil in dark matter and dark energy to make the sums work. By NASA's own accounting the cosmos is "normal or visible matter (5%), dark matter (27%), and dark energy (68%)." Roughly 95% of what gravity appears to be doing out there is owed to something we have never seen and cannot explain. Gravity has also never been made to fit with quantum mechanics; "all attempts to quantize gravity and to unify it with the other forces," the survey concludes, "suggest that the standard general relativity of Einstein may not be the last word."
So the next time something falls, watch it for a second. You are looking at the most reliable, most precisely measured, least understood fact in all of science. We have pinned gravity to the width of a proton. We have never once explained it.
A clarification, because the opening line invites the wrong one: none of this says gravity is fake or in doubt. The phenomenon is as solid as facts get. What is missing is the explanation, a mechanism for why it happens, plus any final "proof" in the mathematical sense, which science does not actually trade in. The "science never proves, only fails to falsify" framing belongs to the falsificationist tradition and is not the only philosophy of science, but the underlying asymmetry is real. Sources, in order of appearance: the Stanford Encyclopedia of Philosophy on Karl Popper; Newton's General Scholium (1713, Motte's 1729 translation); the Feynman Lectures on Physics, Vol. I, ch. 7; the LIGO Laboratory; Clifford Will's review "The Confrontation between General Relativity and Experiment"; and NASA on the contents of the universe.