The Mind of the Mathematician

Author: Michael Fitzgerald,Ioan James

Publisher: JHU Press

ISBN: 9780801885877

Category: Literary Criticism

Page: 181

View: 4664

Internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders.
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Emblems of the Mind

Author: Edward Rothstein

Publisher: Harper Perennial

ISBN: 9780380727476

Category: Mathematics

Page: 263

View: 3344

Unravels the mystery of the relationship between music and mathematics, discussing their differences and their surprising similarities--including their origins and historical links
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Infinity and the Mind

The Science and Philosophy of the Infinite

Author: Rudy Rucker

Publisher: Princeton University Press

ISBN: 1400849047

Category: Mathematics

Page: 368

View: 4418

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.
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Is God a Mathematician?

Author: Mario Livio

Publisher: Simon and Schuster

ISBN: 9781416594437

Category: Mathematics

Page: 320

View: 1378

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
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Shadows of the Mind

A Search for the Missing Science of Consciousness

Author: Roger Penrose

Publisher: Oxford University Press, USA

ISBN: 9780195106466

Category: Computers

Page: 457

View: 9686

Presenting a look at the human mind's capacity while criticizing artificial intelligence, the author makes suggestions about classical and quantum physics and the role of microtubules
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Birth of a Theorem

A Mathematical Adventure

Author: Cédric Villani

Publisher: Farrar, Straus and Giroux

ISBN: 0374710236

Category: Biography & Autobiography

Page: 272

View: 5844

In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of a Theorem is Villani's own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career. But you don't have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn't simplify or overexplain; rather, it invites readers into collaboration. Villani's diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to the dining-hall conversations at the world's greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker's whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.
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Adventures of a Mathematician

Author: S. M. Ulam

Publisher: Univ of California Press

ISBN: 9780520910553

Category: Mathematics

Page: 384

View: 1649

The autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his contributions to the research that resulted in the hydrogen bomb. Now Daniel Hirsch and William Mathews reveal the true story of Ulam's pivotal role in the making of the "Super," in their historical introduction to this behind-the-scenes look at the minds and ideas that ushered in the nuclear age. An epilogue by Fran oise Ulam and Jan Mycielski sheds new light on Ulam's character and mathematical originality.
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The Mathematician's Mind

The Psychology of Invention in the Mathematical Field

Author: Jacques Hadamard

Publisher: Princeton University Press

ISBN: 9780691029313

Category: Mathematics

Page: 143

View: 3771

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 L�vi-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.
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Cogwheels of the Mind

The Story of Venn Diagrams

Author: A. W. F. Edwards

Publisher: JHU Press

ISBN: 9780801874345

Category: Mathematics

Page: 110

View: 9565

Combining mathematical history and recreational mathematics, details the history behind Venn diagrams, the intersecting circles used to visually represent logical propositions.
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Great Circle of Mysteries

Mathematics, the World, the Mind

Author: Misha Gromov

Publisher: Birkhäuser

ISBN: 3319530496

Category: Mathematics

Page: 202

View: 8610

This visionary and engaging book provides a mathematical perspective on the fundamental ideas of numbers, space, life, evolution, the brain and the mind. The author suggests how a development of mathematical concepts in the spirit of category theory may lead to unravelling the mystery of the human mind and the design of universal learning algorithms. The book is divided into two parts, the first of which describes the ideas of great mathematicians and scientists, those who saw sparks of light in the dark sea of unknown. The second part, Memorandum Ergo, reflects on how mathematics can contribute to the understanding of the mystery of thought. It argues that the core of the human mind is a structurally elaborated object that needs a creation of a broad mathematical context for its understanding. Readers will discover the main properties of the expected mathematical objects within this context, called ERGO-SYSTEMS, and readers will see how these “systems” may serve as prototypes for design of universal learning computer programs. This is a work of great, poetical insight and is richly illustrated. It is a highly attractive read for all those who welcome a mathematical and scientific way of thinking about the world.
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A Mind for Numbers

How to Excel at Math and Science (even If You Flunked Algebra)

Author: Barbara A. Oakley

Publisher: TarcherPerigree

ISBN: 039916524X

Category: Business & Economics

Page: 316

View: 6863

An engineering professor who started out doing poorly in mathematical and technical subjects in school offers tools, tips and techniques to learning the creative and analytical thought processes that will lead to achievement in math and science. Original.
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Godel

A Life Of Logic, The Mind, And Mathematics

Author: John L. Casti,Werner DePauli,L Casti

Publisher: Basic Books

ISBN: 9780786747603

Category: Science

Page: 224

View: 6662

Kurt Gödel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Shattering hopes that logic would, in the end, allow us a complete understanding of the universe, Gödel's theorem also raised many provocative questions: What are the limits of rational thought? Can we ever fully understand the machines we build? Or the inner workings of our own minds? How should mathematicians proceed in the absence of complete certainty about their results? Equally legendary were Gödel's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first book for a general audience on this strange and brilliant thinker, John Casti and Werner DePauli bring the legend to life.
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The Girl with a Mind for Math

The Story of Raye Montague

Author: Julia Finley Mosca

Publisher: Amazing Scientists

ISBN: 9781943147427

Category: Juvenile Nonfiction

Page: 40

View: 1691

Meet Raye Montague--the hidden mastermind who made waves in the U.S. Navy! After touring a German submarine in the early 1940s, young Raye set her sights on becoming an engineer. Little did she know sexism and racial inequality would challenge that dream every step of the way, even keeping her greatest career accomplishment a secret for decades. Through it all, the gifted mathematician persisted--finally gaining her well-deserved title in history: a pioneer who changed the course of ship design forever. The Girl With a Mind for Math: The Story of Raye Montague is the third book in a riveting educational series about the inspiring lives of amazing scientists. In addition to the illustrated rhyming tale, you'll find a complete biography, fun facts, a colorful timeline of events, and even a note from Montague herself!
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The Number Sense: How the Mind Creates Mathematics

Author: Stanislas Dehaene

Publisher: Oxford University Press

ISBN: 0199881057

Category: Mathematics

Page: 288

View: 3329

The Number Sense is an enlightening exploration of the mathematical mind. Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.
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Emblems of Mind

The Inner Life of Music and Mathematics

Author: Edward Rothstein

Publisher: N.A

ISBN: 9780226729541

Category: Mathematics

Page: 263

View: 7120

From Kepler and the music of the spheres to Einstein and his violin, wherever we turn music and mathematics seem to bear a strong relationship. Through exploring music and math from the Greeks to the present, the chief music critic for The New York Times seeks to unravel this intriguing mystery.
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Wonders of Numbers

Adventures in Mathematics, Mind, and Meaning

Author: Clifford A. Pickover

Publisher: Oxford University Press

ISBN: 9780195348002

Category: Mathematics

Page: 417

View: 7051

Who were the five strangest mathematicians in history? What are the ten most interesting numbers? Jam-packed with thought-provoking mathematical mysteries, puzzles, and games, Wonders of Numbers will enchant even the most left-brained of readers. Hosted by the quirky Dr. Googol--who resides on a remote island and occasionally collaborates with Clifford Pickover--Wonders of Numbers focuses on creativity and the delight of discovery. Here is a potpourri of common and unusual number theory problems of varying difficulty--each presented in brief chapters that convey to readers the essence of the problem rather than its extraneous history. Peppered throughout with illustrations that clarify the problems, Wonders of Numbers also includes fascinating "math gossip." How would we use numbers to communicate with aliens? Check out Chapter 30. Did you know that there is a Numerical Obsessive-Compulsive Disorder? You'll find it in Chapter 45. From the beautiful formula of India's most famous mathematician to the Leviathan number so big it makes a trillion look small, Dr. Googol's witty and straightforward approach to numbers will entice students, educators, and scientists alike to pick up a pencil and work a problem.
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How Not to be Wrong

The Power of Mathematical Thinking

Author: Jordan Ellenberg

Publisher: Penguin

ISBN: 0143127535

Category: Business & Economics

Page: 480

View: 7582

"Using the mathematician's method of analyzing life and exposing the hard-won insights of the academic community to the layman, minus the jargon ... Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need"--
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Loving and Hating Mathematics

Challenging the Myths of Mathematical Life

Author: Reuben Hersh,Vera John-Steiner

Publisher: Princeton University Press

ISBN: 9781400836116

Category: Mathematics

Page: 432

View: 9915

Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment--as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.
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The Great Mathematical Problems

Author: Ian Stewart

Publisher: Profile Books

ISBN: 1847653510

Category: Mathematics

Page: 340

View: 5640

There are some mathematical problems whose significance goes beyond the ordinary - like Fermat's Last Theorem or Goldbach's Conjecture - they are the enigmas which define mathematics. The Great Mathematical Problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. It contains solved problems - like the Poincar Conjecture, cracked by the eccentric genius Grigori Perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the Riemann Hypothesis, remain baffling after centuries. Stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.
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Mathematicians

An Outer View of the Inner World

Author: Mariana Cook

Publisher: Princeton University Press

ISBN: 1400832888

Category: Mathematics

Page: 208

View: 2989

Mathematicians is a remarkable collection of ninety-two photographic portraits, featuring some of the most amazing mathematicians of our time. Acclaimed photographer Mariana Cook captures the exuberant and colorful personalities of these brilliant thinkers and the superb images are accompanied by brief autobiographical texts written by each mathematician. Together, the photographs and words illuminate a diverse group of men and women dedicated to the absorbing pursuit of mathematics. The compelling black-and-white portraits introduce readers to mathematicians who are young and old, fathers and daughters, and husbands and wives. They include Fields Medal winners, those at the beginning of major careers, and those who are long-established celebrities in the discipline. Their candid personal essays reveal unique and wide-ranging thoughts, opinions, and humor, as the mathematicians discuss how they became interested in mathematics, why they love the subject, how they remain motivated in the face of mathematical challenges, and how their greatest contributions have paved new directions for future generations. Mathematicians in the book include David Blackwell, Henri Cartan, John Conway, Pierre Deligne, Timothy Gowers, Frances Kirwan, Peter Lax, William Massey, John Milnor, Cathleen Morawetz, John Nash, Karen Uhlenbeck, and many others. Conveying the beauty and joy of mathematics to those both within and outside the field, this photographic collection is an inspirational tribute to mathematicians everywhere.
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