What are the latest breakthroughs? These posts summarize current mathematical research. They cover significant and influential results announced in talks, preprints and publications. These results are often preliminary, and their correctness may be as yet uncertain.
Author: Marjorie Senechal. “A longstanding open problem asks for . . . a shape that admits tilings of the plane, but never periodic tilings. We answer this problem for topological disk tiles by exhibiting a continuum of combinatorially equivalent aperiodic polygons.”
Thus begins the abstract of the preprint “An Aperiodic Monotile,” ﬁrst posted on arxiv.org on March 20, 2023 by David Smith, Joseph Myers, Craig Kaplan, and Chaim Goodman-Strauss (). Propelled by social media, lively international Zoom gatherings, on-line science magazines, and The New York Times, the news streaked around the globe at (nearly) the speed of light.
AUTHOR : F. Morgan : EDITORS : J. Hass, R. Ghrist : ART : R. Ghrist In 1884 Hermann Schwarz proved that
Floating bodies of equilibrium in 2D, the tire track problem, and electrons in a parabolic magnetic field
AUTHOR : S. Tabachnikov : EDITOR/ART : R. Ghrist : This review is for the preprint: F. Wegner, From elastica to floating
AUTHOR : S. Tabachnikov : EDITOR/ART : R. Ghrist : This review concerns the following preprint: M. Bialy and A. Mironov, The