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Index Theory is one of the most exciting and consequential accomplishments of twentieth-century mathematics. ""The Founders of Index Theory"" contemplates the four great mathematicians who developed index theory - Sir Michael Atiyah, Raoul Bott, Friedrich Hirzebruch, and I.M. Singer - through the eyes of their students, collaborators and colleagues, their friends and family members, and themselves. In addition to their own essays and correspondence - of historical importance - this volume presents a variety of material of a decidedly personal as well as compelling mathematical nature, written by some of their most notable students and long-time collaborators, including such leading current figures in mathematics and physics as Simon Donaldson, Edward Witten, and S.T. Yau. In these writings, one perceives the expansive influence of their work across various fields of mathematics and into theoretical physics. At a time when the long and illustrious careers of Atiyah, ...