Mathematicians and computer scientists who have developed a clear vision of the relation between lambda calculus and cartesian-closed categories, as Jonathan Burns evidently has, may wish to consider the following PROBLEM: 1. There is a great deal of technical development of the presentational machinery of lambda calculus. 2. Lately, there have been interesting advances in the study of the algebraic theory of exponential rigs, which Tarski called "the high school" theory. (See papers of Stanley Burris et al. on counter examples by Wilkie et al. to naive completeness conjectures.) 3. There are many objectively (or semantically) arising examples of cartesian-closed categories in the form of presheaf toposes, such as that of finite directed graphs or of discrete dynamical systems (as explained in our recent elementary book published by Cambridge). 4. The rich variety of models mentioned in 3. has apparently NEVER BEEN DIRECTLY RELATED to the abstract theory of lambda calculus, nor to the theory of exponential rigs. In the latter case, although specific models are of great interest, they have been constructed by formal syntactical means, rather than through the "objective number theory" means via Steiner-Cantor- Burnside-Grothendieck-Schanuel abstraction from these concrete categories of combinatorial structures, in which the exponent- iation operation has a very explicit mathematical content and construction. Although the exponential rigs capture only the "existence of isomorphisms" equations between objects as opposed to the detailed knowledge of given morphisms (usually not iso) between the combinatorial structures and the detailed particular operations that lambda calculus eventually wants to apply to, nonetheless already at that level nontrivial equational questions arise. For example, there are often "connected" objects A which satisfy equations B^A + C^A = (B+C)^A, and there are sometimes sufficiently separating "figures" or "elements" of connected shapes. As another example, exponential objects occasionally are actually polynomial in the sense that B^A is actually iso- morphic to F(A,B) where F is a combination of products and co-products; two cases that I know of are, with B = A, F = 2A^2 and F = 1+A. The latter has a clear intuitive interpretation that the only internally definable endomaps are either identity or constant. But it is an open PROBLEM whether there are any other polynomials F for which there exists a finite presheaf topos, in which there exist objects A enjoying such isomorphisms.