That old curmudgeon H. L. Mencken had it right: "Penetrating so many secrets, we cease to believe in the unknowable. But there it sits nevertheless, calmly licking its chops."
Consider the theory of quantum electrodynamics, an amalgam of quantum mechanics and special relativity. Half a century ago Richard Feynman, Julian Schwinger and Sin-itiro Tomonaga used the theory to predict the magnetic moment of the electron, a measure of the magnetic field associated with this tiny bit of spinning charge. At about the same time, and independently, Willis Lamb measured the magnetic moment of the electron. And, wonder of wonders, the predicted and measured values agreed to an accuracy, of, oh say, one part in a hundred billion. Talk about penetrating secrets!
At which point one might reasonably suppose that there is no secret the human mind can't penetrate. Stephen Hawking looks forward to knowing (metaphorically, of course) the "mind of God," and Steven Weinberg dreams of a "final theory." And indeed physicists might be forgiven a bit of hubris.
We may know the magnetic moment of the electron, but the mystery of knowability sits there licking its chops.