The expansion of the complex field by the usual exponential function has been the subject of much research over the last twenty five years. Zilber conjectured that any subset of the complex numbers that is definable in this language (even in the extension of first order logic that allows countable conjunctions and disjunctions) is either countable or co-countable and he proved this under the assumption that certain conjectures concerning the solutions of algebra-exponential systems are true. I have long since proposed a conjecture concerning the analytic continuation of implicit solutions to such systems which might be more tractable and it is this that I propose to discuss. The method involves a tentative first step towards combining periodicity and o-minimality.