Hi Dan, To my surprise, the referee of my 2003 paper made a favorable comment ("original and interesting") but had exactly one very minor correction or substantive comment. After I received the paper back from the editor and went over it again, I found at least 20 typos, notation inconsistencies, and other small annoyances. I think the referee spent maybe 20 minutes or less reading it. The editor must have noticed this, but I imagine referees are so hard to find that he didn't want to find someone else. I'm now working on a problem in discrete geometry that I got interested in right before the first conference on experimental math. Part of it was and is doing a computer run which so far has taken 18 months of almost continuous running. It's 90% done, but regardless of the result, I won't have a paper ready for at least another year. I don't know whether to hope for the same referee next time or not! In my one referee job so far, I commented on the first half of a paper and said that I wasn't qualified to judge the second half. (I don't have a math degree.) The paper was published with my comments incorporated; maybe they also sent it to someone else. Or not. They haven't asked me again. Have you heard of any next meeting on experimental math? (I should write to Bailey or Borwein.) Steve ----- Original Message ----- From: <dasimov@earthlink.net> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Friday, March 03, 2006 11:04 AM Subject: Re: [math-fun] Most influential mathematician?
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.