One, Two, Three: Absolutely Elementary Mathematics Hardcover – May 10 2011
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"Berlinski here discusses the ‘commons’ of mathematics: natural numbers, zero, negative numbers, and fractions…. The seamless integration of broader contextual ideas brings his writing to life." —Library Journal
“[A] tour de force by a mathematician who wants the intellectually curious and logically minded . . . to understand the foundations and beauty of one of the major branches of mathematics.”
“With broad culture and wry humor, Berlinski takes a look at some basic concepts in math and the people who worried about them. A treat!”
—Gregory Chaitin, author of Meta Math!
“With wit and philosophy, with the clash of symbols and history, Berlinski displays the inner soul of simple arithmetic.”
—Philip J. Davis, professor emeritus of applied mathematics, Brown University
About the Author
David Berlinski received a B.A. from Columbia University and a Ph.D. from Princeton University. He has taught mathematics and philosophy at universities in the United States and France, and currently lives in Paris.See all Product Description
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Most Helpful Customer Reviews on Amazon.com (beta)
I found this book through a long series of events. First I found Berlinski from a guest spot he did on Ben Stein's movie 'Expelled: No Intelligence Allowed.' Then as my personal research in the sciences continued I found him in various guest spots and interviews including an interview on his position of dissent on Darwinian Evolution. It was an interview about his book 'The Devil's Delusion.' I had seen countless videos and speeches by Berlinkski. I admire his vast knowledge, vocabulary, word choice, and understanding. He has a true passion for his subjects and a desire for all his readers to take it with them. I am far from passionate about mathematics but I am passionate about truth.
Berlinksi is a brilliant teacher unlike most of our high school math teachers in this way; he not only is brilliant enough to understand his own subject within himself but to be able to present it in the most basic way possible to the least naturally intellectually gifted (Me). He is an intellectual that is able to present himself as an everyman. I cannot stress this point enough. How many books have you read the back of when the subject matter alone makes you cringe? It is not that you aren't interested in the subject matter. This is generally because we tend to feel that we will be inadequate to understand not necessarily the material presented, but how it is presented and by whom. Berlinski has the amazing ability to hold your hand as you walk through what seemed before to be dangerous ground.
I recommend not only this book but Berlinski as a man. He is a powerful mind that I am glad to have encountered in this life.
I've had the pleasure of interviewing David on the radio and it was a real treat.
Review by Jerry Bowyer.
Berlinski anticipates, and voices, the reader's (or at least this reader's) questions and objections along the way. Yes, I learned the number line. But why is there a number line? And, if it comes to that, why read about it? Because it's an amazing invention, DB made me see, and like a truly top notch teacher, he related it to counting, which has forever taken on a sort of golden glow for this reader, and showed how it can even handle the negative numbers, themselves an amazing invention. That would have been enough, but there's more. And it's even more elementary or primal. "The calculations and concepts of absolutely elementary mathematics are controlled by the single act of counting by one." You're kidding! I'm hooked, and that's only page five.
There aren't many of the long, lyrical portraits that seem drawn from forgotten novels that are so prevalent in "Calculus", although they start sprouting in the second half of the book. But there are some terse bits in the history of mathematics that tie everything together. It's even possible to "do some forgetting" and see these discoveries afresh, and feel their attendant excitement. But also, revisiting the classroom scenes, Berlinski asks the questions students form but don't put, and shows how to get to the answers teachers might not give. It's truly exciting to see the relations between the various operations of addition, subtraction, multiplication and division, and the various proofs that work for some of these and not others, with Berlinski explaining and showing why this would be the case. Moreso, how this led to things before I only knew the names of: sets, and rings, and succession, and fields, and, in the tantalizing realm of physics, Planck's length.
I knew of the mysterious properties of zero from reading about binary, heretofore the most interesting and fruitful mathematical idea I had encountered, but Berlinski's discussion of zero opens onto endless vistas. He brings up base 10 and the decimal system, but not in a discussion of bases (binary doesn't figure in anywhere). rather, of exponents and logarithms. This last always seemed to me to be entirely arbitrary, but his brief once over clears it right up, and he doesn't even delve into sines and cosines. That's how absolutely elementary this mathematics is. Which makes for absolutely engaging reading.