Science, like most human activities, is based on a belief, namely the assumption that nature is understandable.
If we are faced with a puzzling experimental result, we first try harder to understand it with currently available theory, using more clever ways to apply that theory. If that really doesn't work, we try to improve or perhaps even replace the theory. We never conclude that a not-yet understood result is in principle un-understandable.
While some philosophers might draw a different conclusion—see the contribution by Nicholas Humphrey—as a scientist I strongly believe that Nature is understandable. And such a belief can neither be proved nor disproved.
Note: undoubtedly, the notion of what counts as "understandable" will continue to change. What physicists consider to be understandable now is very different from what had been regarded as such one hundred years ago. For example, quantum mechanics tells us that repeating the same experiment will give different results. The discovery of quantum mechanics led us to relax the rigid requirement of a deterministic objective reality to a statistical agreement with a not fully determinable reality. Although at first sight such a restriction might seem to limit our understanding, we in fact have gained a far deeper understanding of matter through the use of quantum mechanics than we could possibly have obtained using only classical mechanics.