Zilber's trichotomy conjecture asserts that the "geometry" of a strongly minimal set which is defined in terms of basic notions of logic is actually a manifestation of geometry in the physical sense. If one takes the pseudoplanes and other combinatorial geometries connected with strongly minimal sets seriously as geometric objects, then via geometric operations, such as composition of tangent vectors, one may recover the field whose algebraic geometry explains the complicated combinatorial geometry of the strongly minimal set.

Alas, the Hrushovski-Fraïssé structures witness the failure of Zilber's conjecture, but they do not refute the program of recognizing the geometer's (if not exactly Euclid's) geometry in the complicated combinatorial geometry of non-locally modular strongly minimal sets.

Firstly, as tangents work well only for smooth geometric objects, one should expect good results from combinatorial tangency only for "smooth" strongly minimal sets, namely Zariski geometries. Secondly, while the failure to anticipate the exotic strongly minimal sets exhibits a prior blindness to the potential structure of strongly minimal sets, it may, Zilber proposes, actually reflect too narrow a perspective on geometry.