The Pythagorean World

Why Mathematics Is Unreasonably Effective In Physics

Author: Jane McDonnell

Publisher: Springer

ISBN: 331940976X

Category: Mathematics

Page: 394

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This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.

The Best Writing on Mathematics 2012

Author: Mircea Pitici

Publisher: Princeton University Press

ISBN: 1400844673

Category: Mathematics

Page: 320

View: 8517

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This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

A Mathematical Medley

Fifty Easy Pieces on Mathematics

Author: George Szpiro

Publisher: American Mathematical Soc.

ISBN: 082184928X

Category: Mathematics

Page: 236

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Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. --Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. --Marcus du Sautoy, Oxford University, author of The Music of the Primes and Symmetry: A Journey into the Patterns of Nature Mathematics is thriving. Not only have long-standing problems, such as the Poincare conjecture, been solved, but mathematics is an important element of many modern conveniences, such as cell phones, CDs, and secure transactions over the Internet. For good or for bad, it is also the engine that drives modern investment strategies. Fortunately for the general public, mathematics and its modern applications can be intelligible to the non-specialist, as George Szpiro shows in A Mathematical Medley. In stories of a few pages each, Szpiro describes in layman's terms mathematical problems that have recently been solved (or thought to have been solved), research that was published in scientific journals, and mathematical observations about contemporary life. Anecdotal stories about the lives of mathematicians and stories about famous old problems are interspersed among other vignettes.


Plato's Podcasts

The Ancients' Guide to Modern Living

Author: Mark Vernon

Publisher: Oneworld Publications

ISBN: 1780744617

Category: Philosophy

Page: 240

View: 1780

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Do you ever get the feeling that something went wrong? What with credit crunches, the war on terror, and unemployment, it is natural to hark back to less complicated times. In this witty and inspiring book, Mark Vernon does just that. However, he doesn’t just look back to the 1980s – try 400BC! Filled with timeless insight into life, relationships, work and partying, Plato's Podcasts takes a sideways glance at modern living and presents the would-be thoughts of Ancient Philosophers on various topics central to our 21st century existence. With a zany cast of characters – from the Gymnosophists (the naked philosophers) to Diogenes, who lived in a barrel – this is a humorous but enlightening manual to living well today (and two thousand years ago). Mark Vernon is a writer, journalist, broadcaster, academic, and former priest. Author of numerous books including Wellbeing and What Not to Say, he is an Honorary Research Fellow at Birkbeck College, University of London, UK, and a frequent contributor for BBC radio and the BBC webportal.

To Explain the World

The Discovery of Modern Science

Author: Steven Weinberg

Publisher: Harper Collins

ISBN: 0062346679

Category: Science

Page: 432

View: 3152

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A masterful commentary on the history of science from the Greeks to modern times, by Nobel Prize-winning physicist Steven Weinberg—a thought-provoking and important book by one of the most distinguished scientists and intellectuals of our time. In this rich, irreverent, and compelling history, Nobel Prize-winning physicist Steven Weinberg takes us across centuries from ancient Miletus to medieval Baghdad and Oxford, from Plato’s Academy and the Museum of Alexandria to the cathedral school of Chartres and the Royal Society of London. He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world—they did not understand what there is to understand, or how to understand it. Yet over the centuries, through the struggle to solve such mysteries as the curious backward movement of the planets and the rise and fall of the tides, the modern discipline of science eventually emerged. Along the way, Weinberg examines historic clashes and collaborations between science and the competing spheres of religion, technology, poetry, mathematics, and philosophy. An illuminating exploration of the way we consider and analyze the world around us, To Explain the World is a sweeping, ambitious account of how difficult it was to discover the goals and methods of modern science, and the impact of this discovery on human knowledge and development.

THE EMERGENCE AND NATURE OF HUMAN HISTORY Volume One

Author: Joseph Miller

Publisher: Lulu.com

ISBN: 1300029323

Category: History

Page: 499

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This book attempts to define the issues that face us in trying to understand the often-overwhelming complexity of the human experience. It is intellectually challenging, broad in its scope, richly detailed, and densely argued. It is the first in a projected series of five volumes in which the author will seek to touch on every aspect of human historical reality and all the multitudinous variables that have shaped it.

Unser mathematisches Universum

Auf der Suche nach dem Wesen der Wirklichkeit

Author: Max Tegmark

Publisher: Ullstein eBooks

ISBN: 3843710783

Category: Mathematics

Page: 520

View: 1344

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„Max Tegmark, Prophet der Parallelwelten, flirtet mit der Unendlichkeit.“ ULF VON RAUCHHAUPT, FRANKFURTER ALLGEMEINE SONNTAGSZEITUNG WORUM GEHT ES? Max Tegmark entwickelt eine neue Theorie des Kosmos: Das Universum selbst ist reine Mathematik. In diesem Buch geht es um die physikalische Realität des Kosmos, um den Urknall und die „Zeit davor“ und um die Evolution des Weltalls. Welche Rollen spielen wir dabei – die Wesen, die klug genug sind, das alles verstehen zu wollen? Tegmark findet, dieses Terrain sollte nicht länger den Philosophen überlassen bleiben. Denn die Physiker von heute haben die besseren Antworten auf die ewigen Fragen. WAS IST BESONDERS? „Eine hinreißende Expedition, die jenseits des konventionellen Denkens nach der wahren Bedeutung von Realität sucht.“ BBC „Tegmark behandelt die großen Fragen der Kosmologie und der Teilchenphysik weitaus verständlicher als Stephen Hawking.“ THE TIMES WER LIEST? • Jeder, der das Universum verstehen will • Die Leser von Richard Dawkins und Markus Gabriel

Über die Hypothesen, welche der Geometrie zu Grunde liegen

Author: B. Riemann

Publisher: Springer

ISBN: N.A

Category: Mathematics

Page: 48

View: 6621

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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Is God a Mathematician?

Author: Mario Livio

Publisher: Simon and Schuster

ISBN: 9781416594437

Category: Mathematics

Page: 320

View: 8912

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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.


Alex im Wunderland der Zahlen

Eine Reise durch die aufregende Welt der Mathematik

Author: Alex Bellos

Publisher: eBook Berlin Verlag

ISBN: 3827078083

Category: Mathematics

Page: 480

View: 3434

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Erinnern wir uns nicht alle mit Schrecken an die ratlosen Momente vor der Tafel im Matheunterricht? Mit Kurvendiskussionen und Dreisatz dürften jedenfalls nur wenige Spaß und Spannung verbinden... Bis jetzt! Denn nun wagt sich Alex Bellos in den Kaninchenbau der Mathematik: in das Reich von Geometrie und Algebra, von Wahrscheinlichkeitsrechnung, Statistik und logischen Paradoxa. Auf der anderen Seite des Erdballs, am Amazonas, zählen die Mitglieder des Indianerstammes der Munduruku nur bis fünf und halten die Vorstellung, dass dies nicht genügen solle, für reichlich lächerlich. Bei uns in Deutschland dagegen finden jährlich die Meisterschaften der besten Kopfrechner der Welt statt - 2010 wurde in Magdeburg eine elfjährige Inderin zur Nummer eins unter den "Mathleten" gekürt. Die Mathe-Weltmeisterin unter den Tieren ist hingegen die Schimpansin Ai, die Alex Bellos im japanischen Inuyama aufspürt und über deren Rechenkünste er nur staunen kann. Auch wenn er von den bahnbrechenden Überlegungen Euklids erzählt oder erklärt, warum man in Japan seine Visitenkarten keinesfalls zu Dodekaedern falten sollte - Bellos führt uns durch das wahrhaft erstaunliche Reich der Zahlen und bringt uns eine komplexe Wissenschaft spielerisch nahe. Mit seiner Mischung aus spannender Reportage, Wissenschaftsgeschichte und mathematischen Kabinettstückchen erbringt er souverän den Beweis, dass die Gleichung Mathematik = Langeweile eindeutig nicht wahr ist. Quod erat demonstrandum.

Trick or Truth?

The Mysterious Connection Between Physics and Mathematics

Author: Anthony Aguirre,Brendan Foster,Zeeya Merali

Publisher: Springer

ISBN: 3319274953

Category: Science

Page: 250

View: 9953

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The prize-winning essays in this book address the fascinating but sometimes uncomfortable relationship between physics and mathematics. Is mathematics merely another natural science? Or is it the result of human creativity? Does physics simply wear mathematics like a costume, or is math the lifeblood of physical reality? The nineteen wide-ranging, highly imaginative and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition “Trick or Truth”, which attracted over 200 submissions. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.




Is mathematics inevitable?

a miscellany

Author: Underwood Dudley,Gerald L. Alexanderson,Nathan Altshiller-Court,John Aubry,Girolamo Cardano,Lewis Carroll,Patricia Cline Cohen,Jean Dieudonné,Leonard F. Klosinski,Joseph A. Gallian,Richard J. Gillings,Richard K. Guy,Arthur Edward Hallerberg,Paul Richard Halmos,David Hemenway,Morris Kline,Carl E. Linderholm,Robert L. McCabe,Edward Rothstein,Marlow Sholander,David Eugene Smith,John Lighton Synge,James Smith,Richard J. Trudeau,Steven Bradley Smith,Wong Ngai Ying

Publisher: The Mathematical Association of America

ISBN: 9780883855669

Category: Mathematics

Page: 325

View: 2708

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This is a collection of gems from the literature of mathematics that shine as brightly today as when they first appeared in print. They deserve to be seen and admired.The selections include two opposing views on the purpose of mathematics, The Strong Law of Small Numbers, the treatment of calculus in the 1771 Encyclopaedia Britannica, several proofs that the number of legs on a horse is infinite, a deserved refutation of the ridiculous Euler-Diderot anecdote, the real story of p and the Indiana Legislature, the reason why Theodorus stopped proving that square roots were irrational when he to the square root of 17, an excerpt from Mathematics Made Difficult, a glimpse into the mind of a calculating prodigy.There will be something of interest here for almost anyone interested in mathematics.Underwood Dudley is the bestselling author of several MAA books: Mathematical Cranks, Numerology, and the Trisectors. He has an Erdos number of 1.

Warum ist E = mc2?

Einsteins berühmte Formel verständlich erklärt

Author: Brian Cox,Jeff Forshaw

Publisher: Kosmos

ISBN: 3440152065

Category: Science

Page: 256

View: 4901

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E = mc2 ist die berühmteste Formel der Welt. Mit ihr brachte Einstein es auf den Punkt: Energie und Masse sind zwei Seiten derselben Medaille und die Lichtgeschwindigkeit c ist ihr Wechselkurs. Doch warum besteht dieses so einfache Verhältnis? Wie ist Albert Einstein zu diesem Schluss gekommen? Und welche Folgen für das Verständnis des Universums ergeben sich daraus? Brian Cox, Professor für Physik und in England durch seine Sendungen auf BBC sehr bekannt, hat sich zusammen mit seinem Kollegen Jeff Forshaw, Professor für theoretische Physik, die scheinbar einfache Einstein-Gleichung vorgenommen, um sie mit viel Energie ausführlich und verständlich zu erklären.


A Student's Guide to Natural Science

Author: Stephen M. Barr

Publisher: Intercollegiate Studies Institute

ISBN: 9781932236927

Category: Science

Page: 80

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Physicist Stephen M. Barr’s lucid Student’s Guide to Natural Science aims to give students an understanding, in broad outline, of the nature, history, and great ideas of natural science from ancient times to the present, with a primary focus on physics. Barr begins with the contributions of the ancient Greeks, in particular the two great ideas that reality can be understood by the systematic use of reason and that phenomena have natural explanations. He goes on to discuss, among other things, the medieval roots of the scientific revolution of the seventeenth century, the role played by religion in fostering the idea of a lawful natural order, and the major breakthroughs of modern physics, including how many newer “revolutionary” theories are in fact related to much older ones. Throughout this thoughtful guide, Barr draws his readers’ attention to the larger themes and trends of scientific history, including the increasing unification and “mathematization” of our view of the physical world that has resulted in the laws of nature appearing more and more as forming a single harmonious mathematical edifice.