If one understands the Bible to have shown man that He simply can not know all the manifest works of God, and if on the other hand, some come and say, "Urethra! I have found it" to announce that they do indeed know all such things (or are on the path to such knowledge, expected to be full and filled by their own efforts), then yes, there does seem to be a conflict. What does the Bible say about that? Look not at the detail, but instead look in a broad overview and hear what is said from the "mouth of God" about man's insolence. I'm using the term insolence or "cheek" or being audacious not because many will like to look at what may be seen, that's okay, it's natural, but instead because many take the observations to mean that God did not do as He declared. Too often there is twisting involved. People wind two strands together and that's okay too, except when it produces something other than the original intent. Each person must look and be responsible for their thoughts in these matters, hopefully guided not by their own "wisdom" but instead by the Lord who spoke and speaks to each of us.
By the way, this comment isn't directed at Intelligent Design, but instead at those who would go as far as to say, "There is no God." Or to those who wish to declare that there is a path apart from Jesus that brings men into god-like nature. Our perception of "truth" without thanks and acknowledgement of who Jesus is is not sufficient. No twisting allowed when Jesus says, "No man comes to the Father except through me." That does not mean that men may take their observations of "truth," so-called, or pseudo-knowledge as their salvation, nor may they rightly preach such things.