One, Two, Three: Absolutely Elementary Mathematics [Hardcover]

David Berlinski's newest creation "One, Two, Three: Absolutely Elementary Mathematics" is the most provocative and charming account I have ever read of a great intellectual drama--that is the history of humankind formalizing its most basic intuitions about numbers and elementary mathematical operations. This is an immense and monumental subject, and moreover a relatively uncommon one (with none of the existing accounts commanding the same distinguished narrative structure and emotional impact as this book, making "One, Two, Three" completely novel), so in this light it is spectacular to see how Berlinski so deftly and even arrestingly navigates an area of thought we all generally take for granted. In this respect I could not be more opposed to the negative 1-star review it has received, and would advise any reader with a sense of curiosity, depth, and wit to obtain a copy immediately. I would most strongly recommend readers who are especially tilted toward an honest intellectual pursuit for its own sake, because this book is structured to develop a system of thought in a most rigorous and engaging narrative way--not strip it the bone with dryly chopped declarative sentences and remedial English (as so many other pop-science books do). I say this even though readers who are simply looking to master basic concepts will undoubtedly be satisfied too, though the method will be endearingly unusual. Berlinski treats the reader with respect and does not dumb down the subject matter, but rather speaks to the reader's intelligence by encasing concepts that are difficult in elegant, witty, and delightfully sprawling prose. The central theme may be summarized in a sentence Berlinski uses on p. 189 in describing the logical necessity of fractions and their subjugation to mathematical analysis, and that is

"[W]hat is at issue is not /whether/ this is known but /how/, and that is another matter entirely."

The book progresses from a state in which absolutely no conception of mathematics is assumed (the first chapter spends time justifying the existence of numbers and considering their attributes) to an ending point where the reader has been exposed to the mathematical justification for the four basic arithmetic operations, identity laws, equations, exponents, logarithms, set theory, mathematical recursion and induction, Peano arithmetic, etc. Any teacher seeking to gather creative and memorable quotes to communicate fundamental ideas will find them in excess in Berlinski's 200 pages. I personally love how Berlinski intersperses his direct communication to the reader with historical anecdotes of the life and times of intellectual giants, generally and humorously humanizing their various exploits. Irony is not lost. I especially enjoyed his accounts of Peter Aberlard, Leopold Kronecker, and Carl Jacobi. It almost seems that, in bringing these characters to life (as well as their powerful accomplishments and even their scandals), Berlinski instills in his reader a palpable desire to go off and join the mathematical academy, partly out of interest's sake and partly out of stylistic envy of the rock star personas he creates in his lucid accounts. This is remarkable.

I would love to give chapter-by-chapter summaries, but I fear that would spoil the book's uncommon approach of style. This book is a splash, a refreshment, a treat. You won't be sorry for reading it, expert or not. If you are looking for an intelligent, entertaining science read (or any read in general), this is the book for you.

Being one who is typically a "review reader", and not a "review writer", I felt the need to contradict the first reviers statments. Had I never read "A Tour of the Calculus" I may have turned away from picking up this book due to the inaccurate description given by the first reviewer of this work. I will have to say I am pleased with myself for following my instinct on this one. Berlinski has a way with making mathematics an enjoyable subject like no other author I have ever read. "One, Two, Three" was not only historically enlightening, but a pleasure to read from the first page to the last.

I am just a non-expert who came across this book shortly after its release. With little knowledge of the most basic origins of mathematics I chose to enlighten myself. The read was most pleasurable. Berlinski's wit and charm jump from every page, leaving the reader begging for more. If you're looking for a deeper understanding of mathematics, or simply have a taste for wittiness, I suggest this book to you.

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