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The Mathematician's Mind

The Mathematician's Mind PDF Author: Jacques Hadamard
Publisher: Princeton University Press
ISBN: 0691212902
Category : Mathematics
Languages : en
Pages : 98

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Book Description
Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field, remains an important tool for exploring the increasingly complex problem of mental life. The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought.

The Mathematician's Mind

The Mathematician's Mind PDF Author: Jacques Hadamard
Publisher: Princeton University Press
ISBN: 0691212902
Category : Mathematics
Languages : en
Pages : 98

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Book Description
Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field, remains an important tool for exploring the increasingly complex problem of mental life. The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought.

The Mind of the Mathematician

The Mind of the Mathematician PDF Author: Michael Fitzgerald
Publisher: JHU Press
ISBN: 0801885876
Category : Literary Criticism
Languages : en
Pages : 181

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The Mathematician's Brain

The Mathematician's Brain PDF Author: David Ruelle
Publisher: Princeton University Press
ISBN: 0691190305
Category : Mathematics
Languages : en
Pages :

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Book Description
The Mathematician's Brain poses a provocative question about the world's most brilliant yet eccentric mathematical minds: were they brilliant because of their eccentricities or in spite of them? In this thought-provoking and entertaining book, David Ruelle, the well-known mathematical physicist who helped create chaos theory, gives us a rare insider's account of the celebrated mathematicians he has known-their quirks, oddities, personal tragedies, bad behavior, descents into madness, tragic ends, and the sublime, inexpressible beauty of their most breathtaking mathematical discoveries. Consider the case of British mathematician Alan Turing. Credited with cracking the German Enigma code during World War II and conceiving of the modern computer, he was convicted of "gross indecency" for a homosexual affair and died in 1954 after eating a cyanide-laced apple--his death was ruled a suicide, though rumors of assassination still linger. Ruelle holds nothing back in his revealing and deeply personal reflections on Turing and other fellow mathematicians, including Alexander Grothendieck, René Thom, Bernhard Riemann, and Felix Klein. But this book is more than a mathematical tell-all. Each chapter examines an important mathematical idea and the visionary minds behind it. Ruelle meaningfully explores the philosophical issues raised by each, offering insights into the truly unique and creative ways mathematicians think and showing how the mathematical setting is most favorable for asking philosophical questions about meaning, beauty, and the nature of reality. The Mathematician's Brain takes you inside the world--and heads--of mathematicians. It's a journey you won't soon forget.

Mathematics and Mind

Mathematics and Mind PDF Author: Alexander George
Publisher: Oxford University Press on Demand
ISBN: 0195079299
Category : History
Languages : en
Pages : 204

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Book Description
The essays in this volume investigate the conceptual foundations of mathematics illuminating the powers of the mind. Contributors include Alexander George, Michael Dummett, George Boolos, W.W. Tait, Wilfried Sieg, Daniel Isaacson, Charles Parsons, and Michael Hallett.

Relation Philosophy of Mathematics, Science, and Mind

Relation Philosophy of Mathematics, Science, and Mind PDF Author: Helier J. Robinson
Publisher: Lulu.com
ISBN: 0978363515
Category : Mathematics
Languages : en
Pages : 246

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How the Mind Works

How the Mind Works PDF Author: Steven Pinker
Publisher: W. W. Norton & Company
ISBN: 9780393069730
Category : Science
Languages : en
Pages : 672

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Book Description
"A model of scientific writing: erudite, witty, and clear." —New York Review of Books In this Pulitzer Prize finalist and national bestseller, one of the world's leading cognitive scientists tackles the workings of the human mind. What makes us rational—and why are we so often irrational? How do we see in three dimensions? What makes us happy, afraid, angry, disgusted, or sexually aroused? Why do we fall in love? And how do we grapple with the imponderables of morality, religion, and consciousness? How the Mind Works synthesizes the most satisfying explanations of our mental life from cognitive science, evolutionary biology, and other fields to explain what the mind is, how it evolved, and how it allows us to see, think, feel, laugh, interact, enjoy the arts, and contemplate the mysteries of life. This edition of Pinker's bold and buoyant classic is updated with a new foreword by the author.

Creative Minds, Charmed Lives

Creative Minds, Charmed Lives PDF Author: Yu Kiang Leong
Publisher: World Scientific
ISBN: 9814317586
Category : Mathematics
Languages : en
Pages : 333

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Book Description
This book features interviews of 38 eminent mathematicians and mathematical scientists who were invited to participate in the programs of the Institute for Mathematical Sciences, National University of Singapore. Originally published in its newsletter Imprints from 2003 to 2009, these interviews give a fascinating and insightful glimpse into the passion driving some of the most creative minds in modern research in pure mathematics, applied mathematics, statistics, economics and engineering. The reader is drawn into a panorama of the past and present development of some of the ideas that have revolutionized modern science and mathematics. This book should be relevant to those who are interested in the history and psychology of ideas. It should provide motivation, inspiration and guidance to students who aspire to do research and to beginning researchers who are looking for career niches. For those who wish to be broadly educated, it is informative without delving into excessive technical details and is, at the same time, thought provoking enough to arouse their curiosity to learn more about the world around them.

Fractals of Brain, Fractals of Mind

Fractals of Brain, Fractals of Mind PDF Author: Earl Mac Cormac
Publisher: John Benjamins Publishing
ISBN: 902728489X
Category : Psychology
Languages : en
Pages : 359

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Book Description
This collective volume is the first to discuss systematically what are the possibilities to model different aspects of brain and mind functioning with the formal means of fractal geometry and deterministic chaos. At stake here is not an approximation to the way of actual performance, but the possibility of brain and mind to implement nonlinear dynamic patterns in their functioning. The contributions discuss the following topics (among others): the edge-of-chaos dynamics in recursively organized neural systems and in intersensory interaction, the fractal timing of the neural functioning on different scales of brain networking, aspects of fractal neurodynamics and quantum chaos in novel biophysics, the fractal maximum-power evolution of brain and mind, the chaotic dynamics in the development of consciousness, etc. It is suggested that the ‘margins’ of our capacity for phenomenal experience, are ‘fractal-limit phenomena’. Here the possibilities to prove the plausibility of fractal modeling with appropriate experimentation and rational reconstruction are also discussed. A conjecture is made that the brain vs. mind differentiation becomes possible, most probably, only with the imposition of appropriate symmetry groups implementing a flowing interface of features of local vs. global brain dynamics. (Series B)

Philosophical Letters of David K. Lewis

Philosophical Letters of David K. Lewis PDF Author: David K. Lewis
Publisher: Oxford University Press
ISBN: 0192597612
Category : Philosophy
Languages : en
Pages : 480

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Book Description
David Kellogg Lewis (1941-2001) was one of the most influential philosophers of the twentieth century. He made significant contributions to almost every area of analytic philosophy including metaphysics, philosophy of language, philosophy of mind, and philosophy of science, and set the agenda for various debates in these areas which carry on to this day. In several respects he remains a contemporary figure, yet enough time has now passed for historians of philosophy to begin to study his place in twentieth century thought. His philosophy was constructed and refined not just through his published writing, but also crucially through his life-long correspondence with fellow philosophers, including leading figures such as D.M. Armstrong, Saul Kripke, W.V. Quine, J.J.C. Smart, and Peter van Inwagen. His letters formed the undercurrent of his published work and became the medium through which he proposed many of his well-known theories and discussed a range of philosophical topics in depth. A selection of his vast correspondence over a 40-year period is presented here across two volumes. As metaphysics is arguably where Lewis made his greatest contribution, this forms the focus of Volume 1. Arranged under the broad areas of Causation, Modality, and Ontology, the letters offer an organic story of the origins, development, breadth, and depth of his metaphysics in its historical context, as well as a glimpse into the influence of his many interlocutors. This volume will be an indispensable resource for contemporary metaphysics and for those interested in the Lewisian perspective.

LAST FRONTIERS OF THE MIND

LAST FRONTIERS OF THE MIND PDF Author: MOHANDAS MOSES
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120328515
Category : Philosophy
Languages : en
Pages : 440

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Book Description
In this original and brilliantly written book, Mohandas Moses has embarked on a daring theme-the challenge of artificial intelligence to the human mind and human creativity. The mind, he says, is the greatest invention in the universe; it has created the greatest works of art and science: its dimensions and potential are yet to be fathomed. But now the marvellous human mind stands challenged by the machine. To illustrate the central theme of his book, the author has brought together the views of a galaxy of eminent philosophers, cognitive scientists and neuroscientists who have explored the phenomenon and evolution of the human mind and consciousness, and the growth of Artificial Intelligence. The author describes the contribution made by the 'Artificial Intelligentsia', the human-computer interaction, and emphasizes the formidable power of the machine mind to usurp the grandeur of the human mind. He has described the manner in which memory, language, creativity, mathematics, teaching-learning and chess-playing could be altered by the digital culture. He says that 'the question we need to ask ourselves as thinking men is-would we like to sense sensations, experience experiences and think thoughts with under-standing as human beings should or are our personas to be blue matched to the template of the machine mind?' With erudition and wry humour the author takes the reader on a fascinating journey of exploration. Written with brilliance and clarity, there is freshness in his perspective and a lucid presentation of ideas. This book will be of great interest as much to academics, experts on artificial intelligence, as to the general reader who wishes to know about the challenges to the human intellect and creativity in the digital age.