Our global atmosphere and ocean have been observed to warm moderately over the past century, and are reliably projected to warm more significantly over the coming century.  The vast amounts of ice stored in the Greenland and Antarctic Ice Sheets are thereby under threat of partially melting and significantly raising global sea level over the present century and beyond, potentially flooding low lying cities like New York and Abu Dhabi.  A scientific research program is outlined that seeks to transform our present ignorance of basic earth science processes relating to ice sheets and sea level into a fundamental new understanding and predictive capability. David Holland Professor of Mathematics, Courant Institute of Mathematical Sciences and Director, Center for Atmosphere Ocean Science, NYU