The year 2019 saw the 70th anniversary of Alan Turing’s paper “Checking a Large Routine”, and the 50th anniversary of Tony Hoare’s paper, “An Axiomatic Basis for Compuer Programming”. In that paper, Hoare stated: “When the correctness of a program, its compiler, and the hardware of the computer have all been established with mathematical certainty, it will be possible to place great reliance on the results of the program, and predict their properties with a confidence limited only by the reliability of the electronics.”

In this talk, I will review the 70+-year history of this vision, describing the obstacles, the controversies, and progress milestones. I will conclude with the description of both impressive progress and dramatic failures exhibited over the past few years.