This is an announcement for the paper "An arithmetic proof of John’s ellipsoid theorem" by Peter M. Gruber and Franz E. Schuster. Abstract: Using an idea of Voronoi in the geometric theory of positive definite quadratic forms, we give a transparent proof of John’s characterization of the unique ellipsoid of maximum volume contained in a convex body. The same idea applies to the ‘hard part’ of a generalization of John’s theorem and shows the difficulties of the corresponding ‘easy part’. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 52A21, 46B07, 52A27 Citation: Arch. Math. (Basel) 85 (2005), 82–88 Submitted from: franz.schuster@tuwien.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.7246 or http://arXiv.org/abs/1207.7246