So far I have come up with high-dimensional spatial awareness (not sure how well we could get what happens in 1000 dimensions).
It might not be what you asked for but in practice "any sufficiently advanced technology is indistinguishable from magic" rule will come into play even with just quantitative advances. And we might get practical quantum computers at some point...
Control of (complex) nonlinear dynamical systems over long timescales will likely pose a problem and will require high-level unsavory shortcuts to work out. This may or may not include large-scale genetic engineering of mammals (including us) to express new characteristics later in life.
The moderate-scale genetic engineering, for example to uplift our cognitive capability or extend our lifespans could be easier for AIs, while for our own scientists it turned out to be barely tractable. Some will disagree here, noting the political red tape around the fields in question.