To set the tone for the very first research programme on the history of mathematics at the Isaac Newton Institute, this opening workshop will feature experts from several different areas of the discipline all of whom have been asked to address the following: “What do you consider to be the most significant open question, or lacuna, in your area of the history of mathematics?” Speakers will be encouraged to outline the background to their chosen question or lacuna, outline the challenges that lie ahead for current research, suggest some possible strategies and approaches that could be applied, and possibly speculate on potential or anticipated findings.