Alan Turing

Barry Cooper is Professor of Mathematical Logic at the University of Leeds. A graduate of the University of Oxford, his research follows that of Alan Turing in its focus on the nature of mental and physical computation. Author and editor of numerous books, including Computability Theory, New Computational Paradigms, and Computability in Context, he is a leading advocate of multidisciplinary research at the interface between what is known to be computable, and theoretical and practical incomputability. For more information, http://www1.maths.leeds.ac.uk/. Jan van Leeuwen is professor at the Department of Information and Computing Sciences at Utrecht University. He received a Ph.D. in mathematics in 1972 from the same institution. After having held several positions in computer science in the US, he returned to Utrecht as a faculty member in 1977. He was head of department from 1977 to 1983 and from 1991 to 1994, and served as dean from 1994 to 2009. His research interests extend to many branches of the theory and philosophy of computer science. He is a member of the Academia Europae, is the first recipient of a Distinguished Lorentz Fellowship Prize in the Netherlands, and holds an honorary doctorate from RWTH Aachen University. For more information, http://www.cs.uu.nl/staff/jan.html.

"The ‘tour de force’ is that it is quite possible, even recommended, to read the book not linearly but by selecting pieces randomly, just for fun…We…urge readers of this brief review to read the book. We are sure that they will definitely enjoy it. It is quite possible that they will also find there ideas or flashes of inspiration for their own research." --EMS Newsletter, June-2014"It is a rather remarkable achievement that the editors have managed to engage so many leading figures, 70 of them in all, and with such evident commitment…It is a fitting tribute to Turing's legacy…" --LMS Newsletter,October 1 2013"This thick volume is a collection of Turing’s most significant papers along with commentary by people that appreciated and furthered his ideas. What will astound even the people that know the work of Turing is the breadth of his interests and depth of his competence." --MAA.org, Jan 2 2014"There is a lot to be learned from his outlook and temperament, and Alan Turing: His Work and Impact can serve as both an instructional and an inspirational text." --Notices of the AMS, Sep 1 2014"The massive volume is a collection of Turing's key publications as well as commentaries about the papers. The volume is organized in four parts, with each section arranged by publication year of the papers…Given the number of minds involved in this undertaking, the editors must be congratulated…Summing Up: Highly recommended." --CHOICE Reviews Online, December 2013"The volume is an excellent introduction to many exciting topics that Turing greatly contributed to, and in some cases founded, from computability theory to programming languages, complexity theory, the philosophy of mind, artificial intelligence, and the emergence of structure in biology…Readers of almost any background and any level will find something fascinating, something to capture their imaginations, in this volume." --ComputingReviews.com, September 17, 2013"Introductions and commentaries are written by outstanding specialists in the given domains -- altogether by 70 contributors. They provide insight into the significance and contemporary impact of Turing's work…The book is published in a beautiful and careful way. It is a remarkable contribution to the celebration of the centenary of Alan Turing's birth. It is indispensable for all interested in Turing's work." --Zentralblatt MATH 1270-2013"…much of what’s presented is for specialists…But there’s still plenty even for a non-mathematician like me, some of it surprisingly moving…no matter how well you know the life and work of Turing, you’ll learn something from this book." --OECD Insights blog, August 26, 2013"This accessible book is an essential read for those interested in Turing’s work and provides a more contemporary perspective than anything else that is available." --CyberTalk, September 2013"This volume contains a mix of writings — some excerpts by Turing, but mostly writings about him and his work by those who understand his genius and his legacy. The writings include first person narratives of what he was like and what it was like to work with him, personal accounts of career-changing encounters with his thinking, and commentary on particular aspects of his work." --Reference and Research Book News, August 2013"The new testament of computer science has come, 101 years after the birth of founding prophet Alan Turing…How big is the incomputable universe? Can digital machines think? Do daisies emerge from pure chemistry? If your soul craves answers to such questions, this is your new bible."--Nature, June 19, 2013

• Part I: How Do We Compute? What Can We Prove?1.Alan Mathison Turing2.On Computable Numbers, with an Application to the Entscheidungsproblem3.On Computable Numbers, with an Application to the Entscheidungsproblem – correction4.Review of Turing 1936-75.Computability and λ-definability6.The p-function in λ-K-conversion7.Systems of Logic based on Ordinals8.A Formal Theorem in Church's Theory of Types9.The Use of Dots as Brackets in Church's System10.Practical Forms of Type Theory11.The Reform of Mathematical NotationPart II: Hiding and Unhiding Information: Cryptology, Complexity and Number Theory.1.On the Gaussian Error Function2.A Method for the Calculation of the Zeta-function3.Some Calculations of the Riemann Zeta-function4.On a Theorem of Littlewood5.The Word Problem in Semi-groups with Cancellation6.Solvable and Unsolvable Problems7.The Word Problem in Compact Groups8.On Permutation Groups9.Rounding-off Errors in Matrix Processes10.A Note on Normal Numbers11.Turing's treatise on the Enigma (Prof's Book); Report by Turing on U. S. Navy cryptanalytic work and their machinery, November 1942; Speech System 'Delilah' - report on progress, 6 June 1944; Checking a Large Routine; An early program proof by Alan Turing; Programmers' Handbook for the Manchester electronic computer; Local Programming Methods and ConventionsPart III: Building a Brain: Intelligent Machines, Practice and Theory.1.Lecture to the London Mathematical Society2.Intelligent Machinery3.Computing Machinery and Intelligence4.Chess; Solvable and Unsolvable Problems5.Intelligent Machinery: A heretical theory; Can digital computers think?; Can automatic calculating machines be said to think?6.Some Remarks on the Undecidability ResultsPart IV: The Mathematics of Emergence: The Mysteries of Morphogenesis.1.The Chemical Basis of Morphogenesis2.A Diffusion Reaction Theory of Morphogenesis in Plants3.Morphogen Theory of Phyllotaxis; Geometrical and Descriptive Phyllotaxis; Chemical Theory of Morphogenesis; A Solution of the Morphogenetical Equations for the Case of Spherical Symmetry4.Outline of the Development of the Daisy