| Résume||Certain reductions of the collection of ill-founded trees to well-studied objects in ergodic theory can be ``miniaturized" to give concretely computable maps from Godel numbers of lightface sentences in number theory to computable diffeomorphisms. This miniaturization process proves statements such as:
``The twin prime conjecture is equivalent to the associated computable transformation being isomorphic to its inverse."
Recently Marks and others pointed out that for universal number theoretic statements (such as Riemann's hypothesis) the proof can be greatly simplified.
The talk tells the story of a set theorist working in ergodic theory trying to get results in computable analysis.|