Things fall apart. From the moment solid rock or ice is formed, stresses inexorably fragment this material into ever more intricate fracture mosaics. At the smallest scales, mm-thin layers of drying mud give rise to cm-size mudcracks. At the largest scales, the lithospheres of entire planets are torn asunder by tidal and thermal stresses. Surface fracture patterns are at the center of some of the deepest mysteries of planetary evolution. Did Earth's tectonic plates -- unique in the solar system -- form from a primordial, catastrophic cracking of Earth's crust; or are they merely the reflection of underlying mantle convection cells? Did martian mudcracks require a prolonged hydrologic cycle to form? And, are the unusual ridged cracks on Europa a portal to a subsurface ocean of water that harbors life (Fig. 1)? We examine crack networks through the lens of ``convex mosaics'', in which a fracture pattern can be completely described statistically using two measured quantities that are derived from integers -- that is, by counting cracks and their intersections. This approach allows us to see hidden similarities among apparently different mosaics, and to reveal the formative stresses of those networks. We discover that certain fracture patterns betray the presence of water, providing a new tool for detecting potentially habitable environments on other planets. Fragments also form the initial conditions for river rocks, which round in a universal manner as they are eroded by collisions. Thus, the history of a pebble is encoded in its shape, which allows us to unravel environmental conditions on Mars and Titan from geometry.
For Dr. Douglas Jerolmack, Geology is too important to be left to geoscientists alone. He is one of the founders of the newly emerging discipline called Soft Earth Geophysics; this involves the extension of emerging frameworks in soft matter physics to geoscience while also using geoscience problems to shine light into dark corners of physics that may influence other areas. He engages in a range of activities that promote cross-disciplinary exchange and the inclusion of diverse voices in support of creative science.