From: Fred W. Helenius Subject: Re: Dodekaederproblem or Dodekaeder Hypothesis Date: Tue, 14 Mar 2000 02:03:43 -0500 Newsgroups: sci.math Summary: [missing] Wilhelm Sternemann wrote: >There exists a Dodekaeder Hypothesis out of the last years. It is >related to the problem of the best package of balls and the tries of a >proof of Mr. Hsiang since 1993 (Univ. Kalifornien) that the package of >Kepler is the best. From what I've read, I'm not sure that anyone other than Hsiang believes his proof is complete and correct. For one very negative assessment, see http://www.math.lsa.umich.edu/~hales/muder_on_hsiang . >I would be very thankful about a link or a given literature to inform >myself about the Dodekaederproblem or Dodekaeder Hypothesis o.a. Thomas C. Hales and his student, Samuel Ferguson, announced a lengthy, computer-assisted proof of the Kepler conjecture in autumn 1998. I haven't heard anything negative about it, but given its imposing length, there's still plenty of room for potential errors. The entire proof is available online at the Math ArXiv; the abstract of the first part (and pointers to the rest) can be found at http://arxiv.org/abs/math.MG/9811071 . The paper includes a historical introduction and many references. A proof of the related dodecahedral conjecture appears in a paper by Hales and Sean McLaughlin, http://arxiv.org/abs/math.MG/9811079 . You can also get to this and related information via Hales' web site, http://www.math.lsa.umich.edu/~hales/countdown/ . -- Fred W. Helenius