Foreword

Advances in Computational Mathematics -     

Foreword

Steve Smale set the agenda for FoCM in his call for the 1995 conference in Park City, Utah. No stranger he to ambitious agendas and extraordinary accomplishments. He is one of the dominant figures in the mathematics of the second half of the twentieth century. Smale’s theory of immersions, the generalized Poincare conjecture, and H-cobordism theorems with their far-reaching consequences are the bedrock of differential topology. His horseshoe is the hallmark of chaos, and his hyperbolic dynamics the rejuvenation of the geometric theory of dynamical systems. He is one of the pioneers in the introduction of infinite-dimensional manifolds for the study of nonlinear problems in the calculus of variations and partial differential equations. The list goes on: the systematic use of differential techniques in microeconomics, electrical circuit theory, chaos in predator–prey equations and, finally, for the twentieth century, the foundations of computational mathematics and complexity theory, and now, in the twenty-first century, the theory of learning. It has been our privilege to be among his collaborators and students in the broadest sense of the word. With these issues (Volume 5 Number 4 and Volume 6 Number 1, as well as an earlier article appearing in Volume 5 Number 2, are dedicated to Steve Smale’s 75th Birthday) we celebrate Steve’s 75th birthday and continuing vitality. He sets the bar high. We do our best.