This collection of thirteen papers takes the reader on a journey through many important mathematical developments over the past half century. Among the authors and topics are: J. Milnor on curvature and fundamental group; M. F. Atiyah on equivariant K-theory; Gheorghe Lusztig on Novikov's higher signature and families of elliptic operators; Edward Witten on super-symmetry and Morse theory; Kefeng Liu on modular invariance and rigidity theorems; and M. J. Hopkins and I. M. Singer on quadratic functions in geometry, topology, and M-theory. With a foreword by Shing-Tung Yau, and a preface by Simon Donaldson.