The precipitous loss of Arctic sea ice has far outpaced expert predictions. This decline impacts the rich ecosystems hosted by the sea ice pack and the Arctic Ocean below. In this seminar we will discuss how the mathematics of composite materials, statistical physics, and dynamical systems are being used to study key sea ice processes, to advance how sea ice is represented in climate models, and to improve projections of climate change. Moreover, we will explore some of the numerous related problems in the biology of sea ice, whose brine microstructure hosts extensive microbial communities which support the food web. For example, the fluxes of fluids, salts, nutrients, heat, and carbon dioxide are constrained by the connectivity of the brine phase, which depends strongly on temperature. Interestingly, in an example of "cross-pollination," we will show how analyzing brine connectivity in sea ice has inspired a novel approach to monitoring osteoporosis in human bone. Finally, we will show a video of a recent Antarctic expedition where sea ice properties were measured.