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| pure mathematics alan turing: AS Pure Mathematics Rosemary Emanuel, John Wood, 2001-01 Providing your students with a thorough understanding of AS and A2 Pure Mathematics. Includes detailed worked examples, a wealth of practice, revision and examination exercises. Book 1 provides bridging material from GCSE with plenty of background algebra. Book 2 contains Advanced Extension material to stretch more able students and prepare them for the Advanced Extension Awards. Each chapter contains a range of graded exercises to build students knowledge and confidence and consolidate students learning. Regular revision exercises, Key points, Test yourself exercises and exam questions provide complete practice for AS and A2. |
| pure mathematics alan turing: Mathematical Logic R.O. Gandy, C.E.M. Yates, 2001-12-05 Mathematical Logic is a collection of the works of one of the leading figures in 20th-century science. This collection of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. His work in pure mathematics and mathematical logic extended considerably further; the work of his last years, on morphogenesis in plants, is also of the greatest originality and of permanent importance. This book is divided into three parts. The first part focuses on computability and ordinal logics and covers Turing's work between 1937 and 1938. The second part covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948. Finally, the third part focuses on enigmas, mysteries, and loose ends. This concluding section of the book discusses Turing's Treatise on the Enigma, with excerpts from the Enigma Paper. It also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript. This book will be of interest to mathematicians, logicians, and computer scientists. |
| pure mathematics alan turing: Alan Turing David E. Newton, 2003-07-08 Alan Turing ranks as one of the most brilliant of twentieth-century mathematicians. He is perhaps best known as one of the founding fathers of two fields of mathematics with enormous implications in the modern world: computer science and artificial intelligence. In addition, Turing’s work in decoding the German spy machine known as the Enigma was arguably one of the most important accomplishments in bringing World War II to a successful conclusion for the United States, Great Britain, and their Allies. |
| pure mathematics alan turing: Alan Turing: The Enigma Andrew Hodges, 2014-11-10 A NEW YORK TIMES BESTSELLER The official book behind the Academy Award-winning film The Imitation Game, starring Benedict Cumberbatch and Keira Knightley It is only a slight exaggeration to say that the British mathematician Alan Turing (1912–1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades—all before his suicide at age forty-one. This New York Times bestselling biography of the founder of computer science, with a new preface by the author that addresses Turing’s royal pardon in 2013, is the definitive account of an extraordinary mind and life. Capturing both the inner and outer drama of Turing’s life, Andrew Hodges tells how Turing’s revolutionary idea of 1936—the concept of a universal machine—laid the foundation for the modern computer and how Turing brought the idea to practical realization in 1945 with his electronic design. The book also tells how this work was directly related to Turing’s leading role in breaking the German Enigma ciphers during World War II, a scientific triumph that was critical to Allied victory in the Atlantic. At the same time, this is the tragic account of a man who, despite his wartime service, was eventually arrested, stripped of his security clearance, and forced to undergo a humiliating treatment program—all for trying to live honestly in a society that defined homosexuality as a crime. The inspiration for a major motion picture starring Benedict Cumberbatch and Keira Knightley, Alan Turing: The Enigma is a gripping story of mathematics, computers, cryptography, and homosexual persecution. |
| pure mathematics alan turing: Philosophical Explorations of the Legacy of Alan Turing Juliet Floyd, Alisa Bokulich, 2017-05-30 Chapters “Turing and Free Will: A New Take on an Old Debate” and “Turing and the History of Computer Music” are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com. |
| pure mathematics alan turing: Mechanical Intelligence Alan Mathison Turing, 1992 |
| pure mathematics alan turing: The Essential Turing Alan Mathison Turing, 2004-09-09 Lectures, scientific papers, top secret wartime material, correspondence, and broadcasts are introduced and set in context by Jack Copeland, Director of the Turing Archive for the History of Computing.--Jacket. |
| pure mathematics alan turing: Alan M. Turing Sara Turing, 2012-03-22 'In a short life he accomplished much, and to the roll of great names in the history of his particular studies added his own.' So is described one of the greatest figures of the twentieth century, yet Alan Turing's name was not widely recognised until his contribution to the breaking of the German Enigma code became public in the 1970s. The story of Turing's life fascinates and in the years since his suicide, Turing's reputation has only grown, as his contributions to logic, mathematics, computing, artificial intelligence and computational biology have become better appreciated. To commemorate the centenary of Turing's birth, this republication of his mother's biography is enriched by a new foreword by Martin Davis and a never-before-published memoir by Alan's older brother. The contrast between this memoir and the original biography reveals tensions and sheds new light on Turing's relationship with his family, and on the man himself. |
| pure mathematics alan turing: Turing’s Revolution Giovanni Sommaruga, Thomas Strahm, 2016-01-21 This book provides an overview of the confluence of ideas in Turing’s era and work and examines the impact of his work on mathematical logic and theoretical computer science. It combines contributions by well-known scientists on the history and philosophy of computability theory as well as on generalised Turing computability. By looking at the roots and at the philosophical and technical influence of Turing’s work, it is possible to gather new perspectives and new research topics which might be considered as a continuation of Turing’s working ideas well into the 21st century. The Stored-Program Universal Computer: Did Zuse Anticipate Turing and von Neumann?” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com |
| pure mathematics alan turing: Idea Makers Stephen Wolfram, 2016-07-07 This book of thoroughly engaging essays from one of today's most prodigious innovators provides a uniquely personal perspective on the lives and achievements of a selection of intriguing figures from the history of science and technology. Weaving together his immersive interest in people and history with insights gathered from his own experiences, Stephen Wolfram gives an ennobling look at some of the individuals whose ideas and creations have helped shape our world today. From his recollections about working with Richard Feynman to his insights about how Alan Turing's work has unleashed generations of innovation to the true role of Ada Lovelace in the history of computing, Wolfram takes the reader into the minds and lives of great thinkers and creators of the past few centuries—and shows how great achievements can arise from dramatically different personalities and life trajectories. |
| pure mathematics alan turing: The Annotated Turing Charles Petzold, 2008-06-16 Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be computable, creating the field of computability theory in the process, a foundation of present-day computer programming. The book expands Turing’s original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing’s statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others. Interwoven into the narrative are the highlights of Turing’s own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of gross indecency, and his early death by apparent suicide at the age of 41. |
| pure mathematics alan turing: Alan Turing Andrew Hodges, Douglas R. Hofstadter, 2012 It is only a slight exaggeration to say that the British mathematician Alan Turing (1912-1954) saved the Allies from the Nazis, invented the computer and artificial intelligence, and anticipated gay liberation by decades--all before his suicide at age forty-one. This New York Times?bestselling biography of the founder of computer science, with a new preface by the author that addresses Turing?s royal pardon in 2013, is the definitive account of an extraordinary mind and life.--Amazon.com. |
| pure mathematics alan turing: Alan Turing's Systems of Logic Alan Mathison Turing, 2014-11-16 A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that mathematical reasoning can be done, and should be done, in mechanizable formal logic. Turing's vision of constructive systems of logic for practical use has become reality: in the twenty-first century, automated formal methods are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science. |
| pure mathematics alan turing: Alan Turing's Manchester Jonathan Swinton, 2022-05-26 Alan Turing is a patron saint of Manchester, remembered as the Mancunian who won the war, invented the computer, and was all but put to death for being gay. Each myth is related to a historical story. This is not a book about the first of those stories, of Turing at Bletchley Park. But it is about the second two, which each unfolded here in Manchester, of Turing's involvement in the world's first computer and of his refusal to be cowed about his sexuality. Manchester can be proud of Turing, but can we be proud of the city he encountered? |
| pure mathematics alan turing: The Universal Computer Martin Davis, 2018-10-08 The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. Written by Martin Davis, respected logician and researcher in the theory of computation, The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and discoveries of seven remarkable mathematicians. It tells the stories of the unsung heroes of the computer age – the logicians. The story begins with Leibniz in the 17th century and then focuses on Boole, Frege, Cantor, Hilbert, and Gödel, before turning to Turing. Turing’s analysis of algorithmic processes led to a single, all-purpose machine that could be programmed to carry out such processes—the computer. Davis describes how this incredible group, with lives as extraordinary as their accomplishments, grappled with logical reasoning and its mechanization. By investigating their achievements and failures, he shows how these pioneers paved the way for modern computing. Bringing the material up to date, in this revised edition Davis discusses the success of the IBM Watson on Jeopardy, reorganizes the information on incompleteness, and adds information on Konrad Zuse. A distinguished prize-winning logician, Martin Davis has had a career of more than six decades devoted to the important interface between logic and computer science. His expertise, combined with his genuine love of the subject and excellent storytelling, make him the perfect person to tell this story. |
| pure mathematics alan turing: New Computational Paradigms S.B. Cooper, Benedikt Löwe, Andrea Sorbi, 2007-11-28 This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book. |
| pure mathematics alan turing: Thinking about Godel and Turing Gregory J. Chaitin, 2007 Dr Gregory Chaitin, one of the world's leading mathematicians, is best known for his discovery of the remarkable O number, a concrete example of irreducible complexity in pure mathematics which shows that mathematics is infinitely complex. In this volume, Chaitin discusses the evolution of these ideas, tracing them back to Leibniz and Borel as well as GAdel and Turing.This book contains 23 non-technical papers by Chaitin, his favorite tutorial and survey papers, including Chaitin's three Scientific American articles. These essays summarize a lifetime effort to use the notion of program-size complexity or algorithmic information content in order to shed further light on the fundamental work of GAdel and Turing on the limits of mathematical methods, both in logic and in computation. Chaitin argues here that his information-theoretic approach to metamathematics suggests a quasi-empirical view of mathematics that emphasizes the similarities rather than the differences between mathematics and physics. He also develops his own brand of digital philosophy, which views the entire universe as a giant computation, and speculates that perhaps everything is discrete software, everything is 0's and 1's.Chaitin's fundamental mathematical work will be of interest to philosophers concerned with the limits of knowledge and to physicists interested in the nature of complexity. |
| pure mathematics alan turing: Pure Mathematics Alan Mathison Turing, Irving John Good, 1992 The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today. |
| pure mathematics alan turing: Wittgenstein’s Annotations to Hardy’s Course of Pure Mathematics Juliet Floyd, Felix Mühlhölzer, 2020-08-31 This monograph examines the private annotations that Ludwig Wittgenstein made to his copy of G.H. Hardy’s classic textbook, A Course of Pure Mathematics. Complete with actual images of the annotations, it gives readers a more complete picture of Wittgenstein’s remarks on irrational numbers, which have only been published in an excerpted form and, as a result, have often been unjustly criticized. The authors first establish the context behind the annotations and discuss the historical role of Hardy’s textbook. They then go on to outline Wittgenstein’s non-extensionalist point of view on real numbers, assessing his manuscripts and published remarks and discussing attitudes in play in the philosophy of mathematics since Dedekind. Next, coverage focuses on the annotations themselves. The discussion encompasses irrational numbers, the law of excluded middle in mathematics and the notion of an “improper picture, the continuum of real numbers, and Wittgenstein’s attitude toward functions and limits. |
| pure mathematics alan turing: The Most Human Human Brian Christian, 2012-03-06 A playful, profound book that is not only a testament to one man's efforts to be deemed more human than a computer, but also a rollicking exploration of what it means to be human in the first place. “Terrific. ... Art and science meet an engaged mind and the friction produces real fire.” —The New Yorker Each year, the AI community convenes to administer the famous (and famously controversial) Turing test, pitting sophisticated software programs against humans to determine if a computer can “think.” The machine that most often fools the judges wins the Most Human Computer Award. But there is also a prize, strange and intriguing, for the “Most Human Human.” Brian Christian—a young poet with degrees in computer science and philosophy—was chosen to participate in a recent competition. This |
| pure mathematics alan turing: Mathematics for Computer Science Eric Lehman, F. Thomson Leighton, Albert R. Meyer, 2017-06-05 This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. The color images and text in this book have been converted to grayscale. |
| pure mathematics alan turing: Mathematics by Experiment Jonathan Borwein, David Bailey, 2008-10-27 This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, Recent Experiences, that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational P |
| pure mathematics alan turing: Alan Turing: Life and Legacy of a Great Thinker Christof Teuscher, 2013-06-29 Alan Turing's fundamental contributions to computing led to the development of modern computing technology, and his work continues to inspire researchers in computing science and beyond. This book is the definitive collection of commemorative essays, and the distinguished contributors have expertise in such diverse fields as artificial intelligence, natural computing, mathematics, physics, cryptology, cognitive studies, philosophy and anthropology. The volume spans the entire rich spectrum of Turing's life, research work and legacy. New light is shed on the future of computing science by visionary Ray Kurzweil. Notable contributions come from the philosopher Daniel Dennett, the Turing biographer Andrew Hodges, and the distinguished logician Martin Davis, who provides a first critical essay on an emerging and controversial field termed hypercomputation. A special feature of the book is the play by Valeria Patera which tackles the scandal surrounding the last apple, and presents as an enigma the life, death and destiny of the man who did so much to decipher the Enigma code during the Second World War. Other chapters are modern reappraisals of Turing's work on computability, and deal with the major philosophical questions raised by the Turing Test, while the book also contains essays addressing his less well-known ideas on Fibonacci phyllotaxis and connectionism. |
| pure mathematics alan turing: Computing with Quantum Cats John Gribbin, 2014-03-04 A mind-blowing glimpse into the near future, where quantum computing will have world-transforming effects. The quantum computer is no longer the stuff of science fiction. Pioneering physicists are on the brink of unlocking a new quantum universe which provides a better representation of reality than our everyday experiences and common sense ever could. The birth of quantum computers - which, like Schrödinger's famous dead and alive cat, rely on entities like electrons, photons, or atoms existing in two states at the same time - is set to turn the computing world on its head. In his fascinating study of this cutting-edge technology, John Gribbin updates his previous views on the nature of quantum reality, arguing for a universe of many parallel worlds where everything is real. Looking back to Alan Turing's work on the Enigma machine and the first electronic computer, Gribbin explains how quantum theory developed to make quantum computers work in practice as well as in principle. He takes us beyond the arena of theoretical physics to explore their practical applications - from machines which learn through intuition and trial and error to unhackable laptops and smartphones. And he investigates the potential for this extraordinary science to create a world where communication occurs faster than light and teleportation is possible. This is an exciting insider's look at the new frontier of computer science and its revolutionary implications. |
| pure mathematics alan turing: Pure Mathematics Alan Mathison Turing, Irving John Good, 1992 |
| pure mathematics alan turing: Natural Wonders Every Child Should Know Edwin Tenney Brewster, 1912 |
| pure mathematics alan turing: Frank Ramsey Cheryl Misak, 2020-02-13 When he died in 1930 aged 26, Frank Ramsey had already invented one branch of mathematics and two branches of economics, laying the foundations for decision theory and game theory. Keynes deferred to him; he was the only philosopher whom Wittgenstein treated as an equal. Had he lived he might have been recognized as the most brilliant thinker of the century. This amiable shambling bear of a man was an ardent socialist, a believer in free love, and an intimate of the Bloomsbury set. For the first time Cheryl Misak tells the full story of his extraordinary life. |
| pure mathematics alan turing: Science and Hypothesis Henri Poincare, 2016-03-31 Science and Hypothesis is a study written in 1902, by the French mathematician, Henri Poincaré. It was designed with non-specialist readers in mind, and contains information on mathematics, space, physics and biology. The main theme of this work is that the absolute truth of science is non-existent. It postulates that many scientific beliefs are closer to convenient conventions than valid explanations. The chapters of this book include: Number and Magnitude, On the Nature of Mathematical Reasoning, Mathematical Magnitude and Experiment, Space, Non-Euclidean Geometries, Space and Geometry, Experiment and Geometry, etcetera. Many vintage texts such as this are increasingly scarce and expensive, and it is with this in mind that we are republishing this book now, in an affordable, high-quality, modern edition. It comes complete with a specially commissioned biography of the author. |
| pure mathematics alan turing: Metamath: A Computer Language for Mathematical Proofs Norman Megill, David A. Wheeler, 2019 Metamath is a computer language and an associated computer program for archiving, verifying, and studying mathematical proofs. The Metamath language is simple and robust, with an almost total absence of hard-wired syntax, and we believe that it provides about the simplest possible framework that allows essentially all of mathematics to be expressed with absolute rigor. While simple, it is also powerful; the Metamath Proof Explorer (MPE) database has over 23,000 proven theorems and is one of the top systems in the Formalizing 100 Theorems challenge. This book explains the Metamath language and program, with specific emphasis on the fundamentals of the MPE database. |
| pure mathematics alan turing: Morphogenesis Alan Mathison Turing, 1992-11-26 The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today. |
| pure mathematics alan turing: A.M. Turing's ACE Report of 1946 and Other Papers B. E. Carpenter, R. W. Doran, 1986 Volume 10 in the Babbage Reprint Series contains two archival papers by Alan Turing-the ACE report (1945), a seminal paper detailing the design for an electronic universal machine called the Automatic Computing Engine (ACE), and Turing's Lecture to the London Mathematical Society (1947) amplifying the ideas outlined in the ACE report. Turing's report was the first time that the notion of artificial intelligence was discussed as a real possibility and Turing went on to devote the next decade to AI. Michael Woodger's paper, The History and Present Use of Digital Computers at the National Physical Laboratory (1958) gives a brief history of the construction of the pilot ACE, the first functional version of Turing's universal machine. |
| pure mathematics alan turing: Mechanical Intelligence D.C. Ince, 1992-02-13 The collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today. |
| pure mathematics alan turing: Homosexual Mathematician Who Rescued the World Still Died In Disgrace Manjunath.R, Alan Turing was a British mathematician and computer scientist who is widely regarded as one of the pioneers of modern computing. Born in 1912, Turing studied mathematics and logic at Cambridge University before beginning his groundbreaking work in the field of computer science. During World War II, Turing worked as a codebreaker at Bletchley Park, where he was instrumental in developing the machines and techniques that were used to crack German ciphers, including the Enigma machine. His work in cryptography is believed to have helped shorten the war and save countless lives. After the war, Turing continued his work in computing, and is credited with developing many of the fundamental concepts that are still used in modern computing today, including the Turing machine and the concept of artificial intelligence. He also made significant contributions to the field of mathematics, including his work on the foundations of computability and the theory of algorithms. Unfortunately, Turing's life was cut tragically short when he was convicted of homosexuality, which was then illegal in Britain. He was subjected to chemical castration and eventually took his own life in 1954 at the age of 41. Turing's contributions to computing and his tragic persecution have made him a symbol of both scientific innovation and the struggle for human rights. Homosexual Mathematician Who Rescued the World Still Died In Disgrace: The Brutal Life And Tragic Death Of Alan Turing is a book that provides an in-depth look at the life and legacy of the pioneering British mathematician and computer scientist, Alan Turing. This book explores Turing's groundbreaking contributions to mathematics, computer science, and cryptography, as well as his personal life and tragic death. The book covers Turing's early years, including his education and early work in mathematics and logic, as well as his groundbreaking contributions to computer science and artificial intelligence. It also delves into his work as a codebreaker during World War II, where his innovations in cryptography helped to crack the German Enigma machine and ultimately shorten the war. In addition to his professional accomplishments, the book also explores Turing's personal life, including his struggles with his sexuality in a time when homosexuality was illegal in Britain. It sheds light on the persecution he faced as a result of his sexuality, including his conviction for indecency and subsequent chemical castration, which many believe led to his tragic suicide at the age of 41. Overall, Homosexual Mathematician Who Rescued the World Still Died In Disgrace: The Brutal Life And Tragic Death Of Alan Turing is a fascinating and illuminating book that provides a comprehensive portrait of one of the most important figures in the history of computing and a tragic figure in the history of human rights. |
| pure mathematics alan turing: Machine Learning In Pure Mathematics And Theoretical Physics Yang-hui He, 2023-06-21 The juxtaposition of 'machine learning' and 'pure mathematics and theoretical physics' may first appear as contradictory in terms. The rigours of proofs and derivations in the latter seem to reside in a different world from the randomness of data and statistics in the former. Yet, an often under-appreciated component of mathematical discovery, typically not presented in a final draft, is experimentation: both with ideas and with mathematical data. Think of the teenage Gauss, who conjectured the Prime Number Theorem by plotting the prime-counting function, many decades before complex analysis was formalized to offer a proof.Can modern technology in part mimic Gauss's intuition? The past five years saw an explosion of activity in using AI to assist the human mind in uncovering new mathematics: finding patterns, accelerating computations, and raising conjectures via the machine learning of pure, noiseless data. The aim of this book, a first of its kind, is to collect research and survey articles from experts in this emerging dialogue between theoretical mathematics and machine learning. It does not dwell on the well-known multitude of mathematical techniques in deep learning, but focuses on the reverse relationship: how machine learning helps with mathematics. Taking a panoramic approach, the topics range from combinatorics to number theory, and from geometry to quantum field theory and string theory. Aimed at PhD students as well as seasoned researchers, each self-contained chapter offers a glimpse of an exciting future of this symbiosis. |
| pure mathematics alan turing: Mastering the History of Pure and Applied Mathematics Toke Knudsen, Jessica Carter, 2024-06-04 The present collection of essays are published in honor of the distinguished historian of mathematics Professor Emeritus Jesper Lützen. In a career that spans more than four decades, Professor Lützen's scholarly contributions have enhanced our understanding of the history, development, and organization of mathematics. The essays cover a broad range of areas connected to Professor Lützen's work. In addition to this noteworthy scholarship, Professor Lützen has always been an exemplary colleague, providing support to peers as well as new faculty and graduate students. We dedicate this Festschrift to Professor Lützen—as a scholarly role model, mentor, colleague, and friend. |
| pure mathematics alan turing: The Turing Guide Jack Copeland, Jonathan Bowen, Mark Sprevak, Robin Wilson, 2017-02-16 Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work. This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence. |
| pure mathematics alan turing: The Turing Test Stuart M. Shieber, 2004-06-18 Historical and contemporary papers on the philosophical issues raised by the Turing Test as a criterion for intelligence. The Turing Test is part of the vocabulary of popular culture—it has appeared in works ranging from the Broadway play Breaking the Code to the comic strip Robotman. The writings collected by Stuart Shieber for this book examine the profound philosophical issues surrounding the Turing Test as a criterion for intelligence. Alan Turing's idea, originally expressed in a 1950 paper titled Computing Machinery and Intelligence and published in the journal Mind, proposed an indistinguishability test that compared artifact and person. Following Descartes's dictum that it is the ability to speak that distinguishes human from beast, Turing proposed to test whether machine and person were indistinguishable in regard to verbal ability. He was not, as is often assumed, answering the question Can machines think? but proposing a more concrete way to ask it. Turing's proposed thought experiment encapsulates the issues that the writings in The Turing Test define and discuss. The first section of the book contains writings by philosophical precursors, including Descartes, who first proposed the idea of indistinguishablity tests. The second section contains all of Turing's writings on the Turing Test, including not only the Mind paper but also less familiar ephemeral material. The final section opens with responses to Turing's paper published in Mind soon after it first appeared. The bulk of this section, however, consists of papers from a broad spectrum of scholars in the field that directly address the issue of the Turing Test as a test for intelligence. Contributors John R. Searle, Ned Block, Daniel C. Dennett, and Noam Chomsky (in a previously unpublished paper). Each chapter is introduced by background material that can also be read as a self-contained essay on the Turing Test |
| pure mathematics alan turing: A Madman Dreams of Turing Machines Janna Levin, 2009-02-19 Kurt Gödel’s Incompleteness Theorems sent shivers through Vienna’s intellectual circles and directly challenged Ludwig Wittgenstein’s dominant philosophy. Alan Turing’s mathematical genius helped him break the Nazi Enigma Code during WWII. Though they never met, their lives strangely mirrored one another—both were brilliant, and both met with tragic ends. Here, a mysterious narrator intertwines these parallel lives into a double helix of genius and anguish, wonderfully capturing not only two radiant, fragile minds but also the zeitgeist of the era. |
| pure mathematics alan turing: The Origins of Digital Computers B. Randell, 2012-12-06 My interest in the history of digital computers became an active one when I had the fortune to come across the almost entirely forgotten work of PERCY LUDGATE, who designed a mechanical program-controlled computer in Ireland in the early I ':ICC's. I undertook an investigation of his life and work, during which I began to realise that a large number of early developments, which we can now see as culminating in the modern digital computer, had been most undeservedly forgotten. Hopefully, historians of science, some of whom are now taking up the subject of the development of the computer and accumulating valuable data, particularly about the more recent events from the people concerned, will before too long provide us with comprehensive analytical accounts of the invention of the computer. The present book merely aims to bring together some of the more important and interesting written source material for such a history of computers. (Where necessary, papers have been translated into English, but every attempt has been made to retain the flavour of the original, and to avoid possibly misleading use of modern computing terminology. |
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PURE | English meaning - Cambridge Dictionary
PURE definition: 1. not mixed with anything else: 2. A pure colour is not mixed with any other colour: 3. A pure…. Learn more.
PURE definition and meaning | Collins English Dictionary
Something that is pure is clean and does not contain any harmful substances. In remote regions, the air is pure and the crops are free of poisonous insecticides. ...demands for purer and …
pure adjective - Definition, pictures, pronunciation and usage …
Definition of pure adjective in Oxford Advanced American Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Pure - definition of pure by The Free Dictionary
1. not mixed with any extraneous or dissimilar materials, elements, etc: pure nitrogen. 2. free from tainting or polluting matter; clean; wholesome: pure water. 3. free from moral taint or …
pure, adj., adv., & n. meanings, etymology and more | Oxford …
What does the word pure mean? There are 36 meanings listed in OED's entry for the word pure, 11 of which are labelled obsolete. See ‘Meaning & use’ for definitions, usage, and quotation …
Pure - Definition, Meaning & Synonyms | Vocabulary.com
The adjective pure describes something that's made of only one substance and is not mixed with anything else. For example, your favorite soft, warm winter scarf might be made from pure …
pure - WordReference.com Dictionary of English
pure (pyŏŏr), adj., pur•er, pur•est. free from anything of a different, inferior, or contaminating kind; free from extraneous matter: pure gold; pure water. unmodified by an admixture; simple or …
PURE Definition & Meaning - Merriam-Webster
The meaning of PURE is unmixed with any other matter. How to use pure in a sentence. Synonym Discussion of Pure.
High Net Worth Insurance | PURE Insurance
At PURE, insurance is about more than just the things we protect. It's about our members. It's about making them smarter about risk, helping them reduce their chances of experiencing a …
PURE Definition & Meaning | Dictionary.com
Pure definition: free from anything of a different, inferior, or contaminating kind; free from extraneous matter.. See examples of PURE used in a sentence.
PURE | English meaning - Cambridge Dictionary
PURE definition: 1. not mixed with anything else: 2. A pure colour is not mixed with any other colour: 3. A pure…. Learn more.
PURE definition and meaning | Collins English Dictionary
Something that is pure is clean and does not contain any harmful substances. In remote regions, the air is pure and the crops are free of poisonous insecticides. ...demands for purer and …
pure adjective - Definition, pictures, pronunciation and usage …
Definition of pure adjective in Oxford Advanced American Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
Pure - definition of pure by The Free Dictionary
1. not mixed with any extraneous or dissimilar materials, elements, etc: pure nitrogen. 2. free from tainting or polluting matter; clean; wholesome: pure water. 3. free from moral taint or …
pure, adj., adv., & n. meanings, etymology and more | Oxford …
What does the word pure mean? There are 36 meanings listed in OED's entry for the word pure, 11 of which are labelled obsolete. See ‘Meaning & use’ for definitions, usage, and quotation …
Pure - Definition, Meaning & Synonyms | Vocabulary.com
The adjective pure describes something that's made of only one substance and is not mixed with anything else. For example, your favorite soft, warm winter scarf might be made from pure …
pure - WordReference.com Dictionary of English
pure (pyŏŏr), adj., pur•er, pur•est. free from anything of a different, inferior, or contaminating kind; free from extraneous matter: pure gold; pure water. unmodified by an admixture; simple or …
