List of ContributorsIntroductionPart I How Do We Compute What Can We Prove 1955 Alan Matbison Turing by Max Newman（Bibliographic Memoirs of the Fellows of the Royal Society， 1 （Nov．），253-263）Andrew Hodges contributes——A Comment on Newman's Biographical MemoirBiographical Memoir1936-7 On Computable Numbers， with an Application to the Entscheidungsproblem（Proc． Lond． Math． Soc． （2）42， 230-265）1937 - A Correction （ibid： 43， 544-546）Christos Papadimitriou on ——Alan and ITuring textsStephen Wolfram on ——The Importance of Universal ComputationMartin Davis illuminates ——Three Proofs of the Unsolvability of the EntscheidungsproblemSamson Abramsky detects ——Two Puzzles About ComputationPaul Vitanyi illustrates the importance of Turing Machines and Understanding Computational ComplexityGregory Chaitin traces the path ——From the Halting Problem to the Halting ProbabilityRobert Irving Soare expands on ——Turing and the Art of Classical ComputabilityRainer Glaschick takes us on a trip back toTuring Machines in MunsterFrom K． Vela Velupillai ——Reflections on Wittgenstein's Debates with Turing during his Lectures on the Foundations of MathematicsJan van Leeuwen and Jiri Wiedermann on ——The Computational Power of Turing's Non-Terminating Circular a-MachinesMeurig Beynon puts an empirical slant on ——Turing's Approach to Modelling States of MindHenk Barendregt and Antonio Raffone explore ——Conscious Cognition as a Discrete， Deterministic and Universal Turing Machine ProcessAaron Sloman develops a distinctive view of——Virtual Machinery and Evolution of Mind （Part 1）Artur Ekert on the physical reality of ——NOTCristian Calude， Ludwig Staiger and Michael Stay on ——Halting and Non-Halting Turing ComputationsPhilip Welch leads us——Toward the Unknown Region： On Computing Infinite Numbers1937 On Computable Numbers， with an Application to the Entscheidungsproblem by A． M． Turing - Review by：Alonzo Church（J．Symb．Log．2，42）Andrew Hodges finds significance in ——Church's Review of Computable Numbers1937 Computability and λ-Definability（J． Symb． Log． 2， 153-63）Henk Barendregt， Giulio Manzonetto and Rinus Plasmeijertrace through to today ——The Imperative and Functional Programming ParadigmTuring text1937 The p-Function in λ-K Conversion（J．Symb．Log．2，164）Henk Barendregt and Giulio Manzonetto point out the subtleties of——Turing's Contributions to Lambda CalculusTuring textPart Ⅱ Hiding and Unhiding Information： Cryptoloty，Complexity and Unmber TheoryPart Ⅲ Building a Brain： Intelligent Machines，Practice and TheoryPart Ⅳ The Mathematics of Emergence： The Mysteries of MorphogenesisAfterwordBibliographyIndex