In writing a biography, one question is always clear to the historian: what was the subject doing in the years from x to y? The answer to this question can be frustratingly elusive, however, if few sources, published or archival, remain. Taking the years from 1868 to 1876 in the life of the English algebraist, James Joseph Sylvester (1814--1897), as its case in point, this talk will explore ways of getting the ``right'' answers to the ``right'' questions about the life of a particularly interesting mathematician at a particularly crucial point in his life.