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Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers (Englisch) Gebundene Ausgabe – 23. April 2014

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"Mazur gives readers the fascinating history behind the mathematical symbols we use, and completely take for granted, every day. . . . Mazur's lively and accessible writing makes what could otherwise be a dry, arcane history as entertaining as it is informative."--"Publishers Weekly"

"Mazur ("Euclid in the Rainforest") gives readers the fascinating history behind the mathematical symbols we use, and completely take for granted, every day. Mathematical notation turns numbers into sentences--or, to the uninitiated, a mysterious and impenetrable code. Mazur says the story of math symbols begins some 3,700 years ago, in ancient Babylon, where merchants incised tallies of goods on cuneiform tablets, along with the first place holder--a blank space. Many early cultures used letters for both numbers and an alphabet, but convenient objects like rods, fingers, and abacus beads, also proved popular. Mazur shows how our 'modern' system began in India, picking up the numeral 'zero' on its way to Europe, where it came into common use in the 16th century, thanks to travelers and merchants as well as mathematicians like Fibonacci. Signs for addition, subtraction, roots, and equivalence followed, but only became standardized through the influence of scientists and mathematicians like Rene Descartes and Gottfried Leibniz. Mazur's lively and accessible writing makes what could otherwise be a dry, arcane history as entertaining as it is informative."--"Publishers Weekly""

"[A] fascinating narrative. . . . This is a nuanced, intelligently framed chronicle packed with nuggets--such as the fact that Hindus, not Arabs, introduced Arabic numerals. In a word: enlightening."--George Szpiro, "Nature"

"Mazur begins by illustrating how the ancient Incas and Mayans managed to write specific, huge numbers. Then, for more than 200 pages, he traces the history of division signs, square roots, pi, exponents, graph axes and other symbols in the context of cognition, communication, and analysis."--"Washington Post"

"Mazur delivers a solid exposition of an element of mathematics that is fundamental to its history."--"Library Journal"

"Mazur treats only a subset of F. Cajori's monumental "A History of Mathematical Notation" (Dover, 1993 first edition 1922) and there is overlap with many other mathematical history books, but Mazur adds new findings and insights and it is so much more entertaining . . . and these features make it an interesting addition to the existing literature for anybody with only a slight interest in mathematics or its history."--"European Mathematical Society"

"Symbols like '+' and '=' are so ingrained that it's hard to conceive of math without them. But a new book, "Enlightening Symbols: A Short History of Mathematical Notation and its Hidden Power," offers a surprising reminder: Until the early 16th century, math contained no symbols at all."--Kevin Hartnett, "Boston Globe"

""Enlightening Symbols" retraces the winding road that has led to the way we now teach, study, and conceive mathematics. . . . Thanks to Mazur's playful approach to the subject, "Enlightening Symbols" offers an enjoyable read."--Gaia Donati, "Science"

"If you enjoy reading about history, languages and science, then you'll enjoy this book. . . . The best part is the writing is compelling enough that you don't have to be a mathematician to enjoy this informative book."--"Guardian.com's GrrlScientist blog"

"[I]nformative, highly readable and scholarly."--Brian Rotman, "Literary Review"

"[T]his insightful account of the historical development of a highly characteristic feature of the mathematical enterprise also represents a valuable contribution to our understanding of the nature of mathematics."--Eduard Glas, "Mathematical Reviews Clippings"

"Joseph Mazur's beautiful book "Enlightening Symbols" tells the story of human civilization through the development of mathematical notation. Surprises abound. . . . The book is visually exquisite, great care having been taken with illustrations and figures. Mazur's discussion of the emergence of particular symbols affords the reader an overview of the often difficult primary literature."--Donal O'Shea, "Sarasota Herald-Tribune"

"At whatever depth one chooses to read it, "Enlightening Symbols" has something for everyone. It is entertaining and eclectic, and Mazur's personal and easy style helps connect us with those who led the long and winding search for the best ways to quantify and analyze our world. Their success has liberated us from 'the shackles of our physical impressions of space'--and of the particular and the concrete--'enabling imagination to wander far beyond the tangible world we live in, and into the marvels of generality.'"--Robyn Arianrhod, "Notices of the AMS"

"Mazur introduces the reader to major characters, weaves in relevant aspects of wider culture and gives a feel for the breadth of mathematical history. It is a useful book for both student and interested layperson alike."--Mark McCartney, "London Mathematical Society"

"[T]his is a good book. It is well written by an experienced author and is full of interesting facts about how the symbols used in mathematics have arisen. It would certainly interest anyone who studies the history of mathematics."--Phil Dyke, "Leonardo"

"Mazur is a master story teller."--John Stillwell, "Bulletin of the American Mathematical Society"


"This book provides an insightful synthesis of the historical and mental revolutions that created humanity's most useful symbols--mathematical expressions."--Stanislas Dehaene, author of "Reading in the Brain"

"Mathematical symbols are much more than squiggles on paper--they serve as potent sources of insight into a wonderfully complex language. In this book, Joseph Mazur takes us on a fascinating journey into the origins of these symbols. You cannot ask for a better guide."--Mario Livio, astrophysicist and author of "Brilliant Blunders"

"Joseph Mazur teaches us that the history of mathematical notation is the history of human civilization."--Kenneth A. Ribet, University of California, Berkeley

"In this thoughtful, entertaining, and carefully researched book, Mazur lays out the development of the mathematical notations and symbols that we take for granted. He offers a fascinating look at the history of the conventions of writing mathematical ideas, and shows how important our choice of conventions has been for the growth of mathematical knowledge."--Emily R. Grosholz, author of "Representation and Productive Ambiguity in Mathematics and the Sciences"

"Worldwide, mathematicians speak a common symbolic language. Mazur traces how symbols developed and gradually took hold, uniting arithmetic, algebra, and geometry to give us metaphors as powerful as those of poems. A fascinating history!"--Philip Holmes, coauthor of "Celestial Encounters"

"A curiosity cabinet of mathematical gems, curated by Joseph Mazur's cosmopolitan good taste."--Siobhan Roberts, author of "Wind Wizard"

""Enlightening Symbols" explains the origins of symbols used in mathematics. But this fun book is so much more than this. Filled with interesting stories, captivating material, and delightful observations, it offers readers a better understanding of the nature of mathematics and a wonderful overview of mathematical history."--Dominic Klyve, Central Washington University

"An enjoyable and informative tour of mathematics history, "Enlightening Symbols" describes how our modern system of notation led to the abstraction we work with today. This is an important and interesting story."--Anna Pierrehumbert, Trinity School

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Format: Gebundene Ausgabe
Ich habe eine Standard-Eröffnungsrede, die ich gebe in allen Mathematik-Klassen, die ich unterrichte, und eine Komponente dieser Monolog ist die Rolle der Notation. Ich weise darauf hin, dass eines der Dinge, die Mathematik schwer verständlich zu machen, ist die Tatsache, dass die Symbole sind kompakte Darstellungen von Operationen. Ich auch darauf hinweisen, dass diese kompakte Darstellung ist vorbei, die jedes Problem als "Geschichte Problem", das Problem Formular, das am häufigsten von Studenten befürchten, zum Ausdruck zu bevorzugen.
Was ich fand, sehr aufschlußreich an diesem Buch ist die klare Schlussfolgerung, dass die mathematische Erziehung der Massen nicht möglich wäre, wenn die kompakte und effiziente Notation wurde nicht verwendet. Der Versuch, auch nach dem Lesen der Erläuterungen zu entziffern die rhetorischen Formen der Probleme war wirklich schwer. Darüber hinaus sind einige der Beispiele, in denen eine lange Textabsatz wird auf eine einfache Gleichheit übersetzt eine der dramatischsten Veränderungen man in der Mathematik zu finden. Auch wenn Sie für den besseren Verständnis der rhetorischen Form basierend auf umfangreichen Praxis zu ermöglichen, ist es schwer zu sehen, wie eine große Anzahl von Studenten konnten sie zu lösen. Schließlich ist es auch schwer vorstellbar, wie die Mathematik konnte so schnell voranzubringen, wie es nur mit rhetorischen Formen oder Nicht-Standard-Notation.
Dieses Buch befindet sich in bevorzugter Stil geschrieben, es gibt ein paar Gleichungen, aber nichts, was ein Leser mit einem Hintergrund in einfache Algebra nicht umgehen kann.
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Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)

Amazon.com: HASH(0x932260a8) von 5 Sternen 23 Rezensionen
23 von 23 Kunden fanden die folgende Rezension hilfreich
HASH(0x9322edc8) von 5 Sternen A Deeper Etymology, less scary symbols, and Works Well on Kindle too... 24. April 2014
Von Let's Compare Options Preptorial - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
We've all been disappointed when we got a Kindle title (or any e reader) and the MathML or LaTex was slaughtered. Since this book has numerous symbols but not a lot of complex formulas, Kindle is not a problem. Where there are "sentences" in math symbols, they are handled well.

That said, the hard cover is a treasure. This is a very well produced historical survey that should be in every library, including yours if you're into history, math or even language. I personally find that I understand the subtleties of (English) language better if I understand the etymology of a word. This is equally true albeit in a slightly different way with the fine treatment of symbolic evolution in this gem of a book.

Understanding how a summa symbol came to be won't tell you how to use it in combinatorics or a power series, or in double form in a logistic regression error term. However, the good news is we don't have to understand that to really enjoy this book. Flip side, if you ARE into math, you'll REALLY love this. I like books that don't just parrot formulas but give an idea of the "intuitive" meaning or reason for the formula, like "putting these numbers in a matrix makes it easier for a computer to change coordinate axes which is one reason we do it."

This text takes that a step further, and not only gives context, but HISTORICAL context in genuinely useful human endeavors-- the WHY and how of the underlying value as use evolved. This turns on a LOT of light bulbs if you're into math, and is still fun and a great "detective" read even if you're not. Which is my final point: don't get turned off due to the math side if you love history and detective (deductive) logic-- the writing is crisp, well paced and "leads" you quickly forward-- IOW NOT DULL or dry. And frankly, as I look at other math books, the symbols also seem a little more friendly and familiar, and less intimidating, knowing about the neighborhood in which they grew up. Would also make a great gift for a detail oriented picky person in your life!
29 von 31 Kunden fanden die folgende Rezension hilfreich
HASH(0x932fc81c) von 5 Sternen The Fascinating History of the Symbols Marking the Progress of Mathematics 6. April 2014
Von Donald Limuti - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
This is the highest rating, because this book sheds light on one of the toughest philosophical questions. The question is what accounts for the "Unreasonable Effectiveness of Mathematics in the Natural Sciences"? Mazur via his entertaining history that spans many places, times and cultures, explains that the mathematical symbols we commonly use did not come down from the mountain written on a tablet, but evolved with a lot of passion, genius, and serendipity. Our present mathematics have been pushed and cajoled into shape via symbols. This book may not be a complete explanation as to the effectiveness of mathematics, but it is an enlightening peek under the curtain. If you like history and have a mathematical bent (no need to be a mathematician, and mathematicians would like it) you would enjoy this book.
7 von 7 Kunden fanden die folgende Rezension hilfreich
HASH(0x932fc6fc) von 5 Sternen Wonderful source book for the development of mathematical thinking 27. Juni 2014
Von Arthur C Howard - Veröffentlicht auf Amazon.com
Format: Kindle Edition Verifizierter Kauf
This is an excellent source for not just the history of our common mathematical symbols -- which would have made it a great book to read -- but also the development of mathematical thinking, from purely geometric and rhetorical to abstract. I highly recommend it to anyone who teaches, or enjoys, mathematics.
5 von 5 Kunden fanden die folgende Rezension hilfreich
HASH(0x932fc7ec) von 5 Sternen So even a layman like me can tell you that one way to make ... 2. September 2014
Von William Cullerne Bown - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
There are thousands of books on the way words evolve. So even a layman like me can tell you that one way to make new words is through backslang ("boy to "yob" for example). Stephen Fry is on series 7 of his programmes on this topic on the BBC. And yet this seems to be the only book about how the words of mathematics, its symbols, evolve. It's incredble. Fortunately, this book is incredibly good.

The great power of this book is in showing us how wrong we are to assume that the basic mathematics we learn at school is obvious. As you follow the history of how the symbols evolved, you are given a very concrete history of how the world's thinking evolved. And it becomes clear that a thousand years of struggle has been poured into clarifying even the simplest mathematics for we who have come later.

We discover, for example, that in order to be able to do what my seven year old does at school, soldiers in the Chinese army were for centuries issued with a bag of sticks. Facts like this, as dumbfounding as they are awe-inspiring, spill out of the pages.
4 von 4 Kunden fanden die folgende Rezension hilfreich
HASH(0x932fc690) von 5 Sternen Mankind's Progress in Mathematics & Universal Notation 12. Juni 2014
Von Collage-nikov2010 - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
This book is a compendium of the progress mankind has made, by various cultures & each contribution to the science of Mathematics, Algebraic & other Advanced Numerical Notation & communication. It helps the reader some, if the reader is familiar with the field of math & some of the personalities & cultural backgrounds to early mathematics. The entire field of mathematics, calendars, & architectural math & development of Mayan, Incan & other significant contributions these early builders of ancient, magnificent temples, observatories, etc. is overlooked, bypassed, or ignored. Awesome book & well worth every penny that it cost! Easy to read, outstanding bibliography & research & an interesting invite into our human roots of mathematical progress!! Love it!!
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