Stephen G. Simpson
 Department of Mathematics
 Penn State University

 APA/ASL Meeting
 University of Minnesota
 May 3-5, 2001
 Symposium on Reverse Mathematics and Computability Theory 

 Title: Why the Recursion Theorists Should Thank Me


 Foundations of mathematics (f.o.m.) is the study of the most basic
 concepts and logical structure of mathematics.  G"odel, Turing, Post
 and Kleene pioneered recursion theory (a.k.a. computability theory)
 in an f.o.m. context.  Over a period of forty years, recursion theory
 lost touch with its f.o.m. roots.  More recently, reverse mathematics
 came to the rescue.  Reverse mathematics is an explicitly
 foundational research program which aims to discover which axioms are
 necessary and sufficient to prove standard theorems of core
 mathematics.  For recursion theorists, reverse mathematics represents
 a rich problem area where some (but probably not all) highly
 developed recursion-theoretic techniques can be applied to draw
 f.o.m. conclusions which are of general intellectual interest.
 Confronted with this opportunity, many leading recursion theorists
 react favorably, while others such as Robert I. Soare exhibit intense
 hostility.  We comment on scientific and sociological aspects of the