Answer
Isaiah 65:17 is the text you probably have in mind: "For behold, I create new heavens and a new earth; And the former things will not be remembered or come to mind." But in the context of this verse, it is God who will not remember these things, not us (cf. Isa. 65:16). Clearly God's omniscience will not be compromised, though. "Remember" in this passage does not refer to knowledge, but to consideration and legal weight. That is, God will forgive our sins, ceasing to hold them against us (cf. the uses of "remember" in Ezek. 3:20; 18:22,24).
The Bible never actually teaches that we will not retain knowledge of this life in the next life (either in heaven, or later in the new earth when our bodies are resurrected). Further, it provides some evidence that we will remember. For example, Revelation 6:9-10 seems to indicate that martyred saints cry out for holy vengeance, indicating that they remember at least their martyrdom and their murderers. And in 1 Samuel 28:16ff, when the witch of Endor conjures Samuel's spirit to speak with Saul, Samuel refers to a prophecy he had given to Saul while Samuel was still alive, demonstrating knowledge of things he did before he died.
I would also add that it is a bit difficult to conceive of a continued personal existence in which prior knowledge is not retained. Our sense of individual identity would seem to require some knowledge of our past "self" in order for it to be said that we are the same people. Even considering cases of real amnesia, in which people certainly are the same individuals they were before their amnesia, if they have lost all prior knowledge, they have also lost self-identity — they no longer know who they are — which would not seem to be the case in heaven.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.