People write that the Erlangen Program is a "program" (like the "Langlands Program"), i.e. a series of related conjectures, which in this case were all solved. There are various intuitive accounts, describing that this program is about relating algebra and geometry, about relating transformation groups of spaces (Lie groups) and different geometries, invariants, etc.

What I haven't been able to find is a precise statement in modern language (e.g. not that of his original paper) of what Klein's conjectures were. What precisely were his conjectures, or equivalently, what results constitute their resolution? Or was there never truly a precise statement?

precisely, does the Langlands Program over number fields state? :) $\endgroup$ – user30379 Jan 15 '13 at 19:36realname) ] $\endgroup$ – Qfwfq Jan 15 '13 at 22:53