P.S. Automated proof-checking may become an important issue in the future, now that we've seen at least one proof (Hales's computer portion of his proof of the Kepler conjecture) that has overwhelmed our combined computer and especially human resources. But as far as I know that is the only example so far; for all but measure zero among putative proofs, the old-fashioned system of peer-checking has worked well. (Aside to Steve: the Monthly is not included, since imo the outgoing Editor has taken an idiosyncratic view of the Editor's duties.) There are some examples of proofs erroneously believed valid for many years (e.g., Kempe's wrong proof of the four-color theorem (11 years), and Dulac's wrong proof of part of Hilbert's 16th problem* (58 years). But I've heard of only a handful of such examples. --Dan _____________________________________________________________________ * This is the conjecture that if a vector field in the plane is defined by real polynomials in x and y -- V(x,y) = (P(x,y), Q(x,y)) -- then its trajectories include only a finite number of limit cycles. It was finally proved in 1981 by Ilyashenko -- or so it is believed.