Kolmogorov and Uspenskii in this paper 'http://epubs.siam.org/doi/pdf/10.1137/1132060' speculate P=BPP in 1986. They do this without getting into circuit lower bounds and from a different view which for people like me is more well grounded than basing on some other unknown and pure beliefs.
Is there a reference on P=BPP possibility earlier than this that goes into considerable depth?
On page 406 they state 'It should be clearly realized however that we have not seen a randomized algorithm which works faster than a deterministic one'. Now FPTAS for permanent came after this in 1988 and Toda's theorem came in 1991. Is there a philosophical take on what Kolmogorov would have thought if he had seen these before he passed away in 1987?
Note that our view of P=BPP is framed from circuit lower bounds. Kolmogorov's view was likely different and could not have come from circuit lower bounds.