Mathematics for the Million

• Publisher:   W.W. Norton & Co.
• Number Of Pages:   656
• Publication Date:   1993-09-17
• ISBN-10 / ASIN:   039331071X
• ISBN-13 / EAN:   9780393310719

"It makes alive the contents of the elements of mathematics."—Albert Einstein Taking only the most elementary knowledge for granted, Lancelot Hogben leads readers of this famous book through the whole course from simple arithmetic to calculus. His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy. .

This history of mathematics spares no equation in the presentation of the order in which mathematical ideas arose. It begins before the beginning, when there was no such thing as formal mathematics. The title of the first chapter is "Mathematics in Remote Antiquity" and is a description of the mathematics used in the ancient civilizations of Egypt, Iraq, Pakistan, China and the Americas. Some of this is of course informed speculation, as in many cases the record is incomplete.
Formal mathematics in the western world began with what we call the Greek civilization, although it should more accurately be called the Eastern Mediterranean civilization. Euclid well forever go down is history as one of the greatest organizers in history, we are fortunate that his interests were in mathematics. The rules and proofs that he set down have been improved, but that has been an expansion of his ideas and not a refutation. Chapter 3 is an extensive coverage of the role of Euclid in the development of formal mathematics.
The remaining chapters are: *) Number lore in antiquity
*) The rise and decline of Alexandrian civilization
*) The dawn of nothing
*) Mathematics for the mariner
*) The geometry of motion
*) Logarithms and the search for series
*) The calculus of Newton and Liebnitz
*) The algebra of the chessboard
*) The algebra of choice and chance This book is an excellent choice for a text in a history of math course for junior or senior level math majors. The coverage is extensive; exercises appear at the end of each chapter and solutions to some are included in the appendix.

I bought a used copy of this book 3 years ago (it was published in 1944). To think that it was written for ordinary people 60 or more years ago is astonishing. One can learn all the math that 99% of people need during their lives. If todays high school students would take the time to learn what is so excellently explained in this book, they would score 650 - 800 on the math SAT exam. One example is: there is a chapter where the author walks you through all the calculations and probabilities needed to set up your own life insurance company! This beats calculating the probability of drawing 3 green balls out of an urn filled with green and red balls. Buy It.

I was sold by the back cover quotes from Einstein and H.G. Wells and by the idea of the author leading me from arithmetic to calculus. It's ostensibly a book written so that everyone can understand mathematics. However, the book is not an easy read. Like one of my students said after I explained to her why I didn't like the book: "the author is multi-tasking." He tries to explain math concepts and show us the history of math at the same time. The result is halfway explained math which the reader has to spend a lot of effort on in order to grasp. This is good mental exercise but as you get deeper and deeper into the book you realize that the author has made it unnecessarily harder by being verbose. A good number of his sentences are wordy, for example: "It does little credit to contestants of either camp, and the outcome was highly detrimental to the progress of mathematics in the land of Newton's birth." In the land of Newton's birth? Why not just England? Here's another one: "Laplace, the renowned French astronomer-mathematician who told Napoleon that God is an unnecessary hypothesis, recognized forty years before Babbage, an Englishman, designed the first computing machine, that the number 2 (in our Hindu-Arabic notation) has an immense advantage in terms of the number of different operations we need to perform to carry out a computation such as some our parents had to learn (e.g. finding /4235) the hard way." Not only is this sentence wordy but why did he have to add that Laplace told Napoleon that God was an unnecessary hypothesis or that Babbage was an Englishman and designed the first computing machine? He also sprinkles his book with gratuitous thoughts and opinions like: "Before discussing this, it may protect the author from unnecessary correspondence to state the truth about one of those historical tags on all fours with the ludicrous assertion that a document called Magna Carta which a circus of half-literate Baronial gangsters forced an English monarch to sign is the Keystone of British and/or United States democracy." This becomes annoying to the reader that has already struggled enough with Mr. Bogden's math explanations to have to worry about whether what he is saying next is something relevant or just him enjoying hearing himself speak.

This book, jointly with Bertrand Russell's "Story of the Western Philosophy", aim to show that Mathematics and Philosophy, the most abstract of our intellectual creations, are driven by cultural, political and historical forces, too.
Happily, both authors have succeeded with their works.
Hogben describes the historical forces behind mathematical inventions, from early antiquity to the calculus era. And in doing so, he gives to the reader the mathematical ideas and techniques necessary to the "citizenship kit" of our technological society.

Mathematics is no more black and scary magic, while we go through this book, which was written long ago, but seems to fit right-oh in our life as if perscribed just yesterday. I've read it some 30 years ago and never forgot the quantum leap it gave me to win over the threat of mathematics.

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