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Arithmetic Hardcover – August 21, 2017
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“What an exuberant, exciting invitation to take joy in the wonderful human activity of counting, and to think deeply about its many origins. Marvelously personal, quite surprising at times, and fun to read.”―Barry Mazur, Gerhard Gade University Professor at Harvard University, coauthor of Prime Numbers and the Riemann Hypothesis
“Once I started reading, the text proved mind-blowing. Some of the most ingrained and fundamental assumptions about the way we count and understand numbers are here deconstructed and shown to be arbitrary…For the mathematical layman, this book will be a very pleasant surprise…I am delighted to say that Lockhart is a fabulously entertaining writer, and that his light-hearted approach managed to keep me cheerfully engaged even when his discussions were most abstract…It’s in equal measures entertaining and educational, and a pleasant surprise on more levels than one.”―Andrea Tallarita, PopMatters
“Arithmetic is inspiring and informative, and deserves to be widely read.”―Jane Gleeson-White, Wall Street Journal
“Beginning with counting and moving through topics such as multiplication and fractions, Arithmetic provides a nuanced understanding of working with numbers, gently connecting procedures that we once learned by rote with intuitions long since muddled by education…Lockhart presents arithmetic as a pleasurable pastime, and describes it as a craft like knitting. Manipulating calculi on a tabula, you can see what he means.”―Jonathon Keats, New Scientist
“More than just an informative survey of the fundamentals of basic arithmetic, this fun book offers a philosophical take on number systems and revels in the beauty of math.”―Science News
About the Author
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In this book the author takes the reader on a journey through the history of numbers as well as showing the "properties" of those numbers. We look at the numbers themselves and the way they have been represented through time - after all a "3" is just the current way in the Hindu-Arabic numbering system that we represent "threeness" - and could just as easily have some other notation which, in a different society, would represent the same "threeness".
We are taken through the Roman numerals, and their counting Tabula, as well as the Japanese Soroban (a type of abacus), and are exposed to the way the ancient Egyptians wrote their numbers (as well as the fairly cool (my description) of the way they notated fractions). Through all of this we start to see the numbers as entities in their own right, and not as the particular symbol we assign to them in our Hindu-Arabic numbering system.
The author starts us off slowly with addition, then moves into subtraction, then multiplication, then division, and eventually into such "odd ball" concepts as negative numbers. He almost makes it into "set theory", but stops just short.
The author also imparts a bit of advice along the way, for example on page 134 he notes "don't bother being more accurate than your data." Something one has to remember when doing calculations based on real world observations.
To understand where the author is "coming from" take note of what he says on page 98 "That's kind of the whole math thing: working hard to find ways to get out of working hard."
So, if you enjoy numbers and their patterns, then you will probably find this book enjoyable - but, if when someone mentions math you are the first to run screaming from the room --- then not so much.
First, a reply to some who found it too simple. Yes, this is elementary. Maybe you did learn this when you were in school. But I am a product of the local public school and a teacher of 10 years, some of those years in a top 3 ranked school in South Carolina (which was a private school. And in South Carolina, none-the-less. But our SAT/ACT and AP Scores were ranked alongside the public schools as well). I think I have some room to say that most if not all students are NOT taught or reinforced with this understanding and relationship with the subject. I taught as a Learning Specialist. That is, I helped students who wanted it to become better students at learning. I helped students at whatever subject troubled them. Algebra and Geometry were regulars for me all the years. And from my experience with them, what Paul Lockhart explains here was not in their books nor reinforced in the classroom. I did my best to bring it to them.
If you have read his earlier book, then you are familiar with his style of writing, which I enjoyed. Other than that, Paul Lockhart has the understand and experience to help the reader gain a personal understand of Arithmetic that isn't confined to the Industrial Age manipulation we live with today. This includes the understanding that this is not confined to some utilitarian value.
HERE IS THE BIG DIFFERENCE I see between Utilitarian Public School and Lockhart's understanding of Arithmetic: Public Schools help students understand and known and the already discovered process for getting to the already known answer in terms of systems and rules. Lockhart sees it in terms of options and tools discovered and created on the way to understanding the character of entities and ways to arrange it 'for ease of communication and comparison'.
I like how he provides clear examples, and also how he injects a small amount of humor into his writing. There is no reason at all that a book about mathematics should be boring, should it?
I would recommend Paul's book to anyone who wants to know about counting systems and/or mathematical operations.