Considering that every new human more or less starts off as a blank slate (or rather, that which we do start with doesn't improve with each generation) and there is only so much a human can learn within a lifetime (unless we consider genetic engineering or control over death/prolonging life), I'd expect that progress becomes slower and slower over time. I don't see how a takeoff (where progress speeds up again, and drastically so) could be achieved without either mind uploads, anti-death measures which greatly prolong life, or genetic engineering/breeding of humans. Or major breakthroughs in education, to the point where you don't need brains to observe and pattern-match, but can teach them directly.

A data point: Even today, in highly explored areas such as mathematics, it takes a significant fraction of a normal human life to acquire the skillset needed to tackle the hard problems.