A known Chaitin's quote (*) can be succinctly expressed in a short phrase:
Understanding is programming
According to this statement, this very statement cannot be understood before we can program concepts: understanding and programming. If we were able to program these concepts, then it would be a discovery of true AGI. Hence the paradox is in the fact that its solution is not achievable before Technological Singularity.
(*) ... you understand something only if you can program it. (You, not someone else!) Otherwise you don't really understand it, you only think you understand it. [emphasis in the original]