Some things keep staying in mind, no matter how intractable they may be.
When I read Roger Penrose's "The Emperor's New Mind" in 1989, I was quite taken by the argument in it. The main thesis was that some parts of human thought, especially those carried out consciously, are non-algorithmic. Citing Goedel's theorem and the enigmas of wave function collapse in quantum mechanics, Penrose argued that human thinking, the process of understanding something in particular, could not be broken down in terms of algorithms which could be carried out by a digital computer.
Although attacked by people from various fields, the Penrose thesis appeared to be essentially correct for me, not in an immediately provable way, but in poignant threads of thinking the gist of which will become only apparent after many years of elaboration and effort by humans. Roger Penrose in that sense is a predictor. It is moving how the sense becomes a forerunner of logic, in that what turns out to be logically correct afterwards is perceived by the sense as intuitively pointing the right way.
Roger Penrose visited Cambridge while I was doing postdoc there. I have written an essay a "Roger Penrose visits Cambridge" based on the experiences at that occasion.
With Roger Penrose in Oxford, U.K.