The Art of the Infinite: The Pleasures of Mathematics by Robert Kaplan (PDF)

Description

The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Robert and Ellen Kaplan guide us through the “Republic of Numbers,” where we meet both its upstanding citizens and its more shadowy dwellers; and transport us across the plane of geometry into the unlikely realm where parallel lines meet. The journey is enriched by deft character studies of great mathematicians (and equally colorful lesser ones). And as we go deeper into infinity, we explore the most profound mystery of mathematics: Are its principles eternal truths that we discover? Or ones that we invent?

User’s Reviews

Editorial Reviews: About the Author Ellen Kaplan has taught mathematics to people from six to sixty, at leading independent schools and most recently at Harvard University. With her husband, Robert, she wrote The Art of the Infinite. Ellen is also co-author of Chances Are: Adventures in Probability and Bozo Sapiens: Why to Err is Human, co-written with her son, Michael Kaplan.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐“The essence of mathematics lies entirely on its freedom”, said Georg Cantor. THE man who figured out that there are countable and uncountable infinities. Wow. Infinite freedom? Well, at least freedom within a playground nested with infinities (Hilbert’s paradise), as you are about to learn in this book. Hey, Robert and Ellen managed to make number theory palatable for the layperson with an entire chapter on Cantor’s work. An infinite gold mine as a chapter. And there is much more. The whole thing is a vivid narrative about mathematical beauty everywhere; playful, with subtle humor and deep erudition. That is, history + geometry + philosophy + poetry + … = infinite entertainment.

⭐This book covers some very fine topics in math. It attempts to balance mathematical rigor with analogies and interesting historical points. The attempt however is not totally sucessful because the language used is too obscure. The mathematical topics discussed are complex enough by themselves and the additional obscure language makes them that much harder to understand. I would have vastly preferred the use of stright forward English for the discussion. The analogies and historical facts could have been presented separately alongside the main discussion. Nevertheless I enjoyed reading it and will recommend it to others as long as they have a good command of English and are willing to go along with the less than ideal presentation.

⭐This is an excellent tome… entertaining. Written with whit and charm, it gives one pause for thought and contains a lovely subtle humor… which is too bad for the authors as this dooms the book to wide rejection from those who are still in need of redrafting their sixth grade expositions on ‘Where The Red Fern Grows’… too bad, too bad. Now, will those of you who are playing in the match this afternoon move your clothes down onto the lower peg immediately after lunch, before you write your letter home, if you’re not getting your hair cut, unless you’ve got a younger brother who is going out this weekend as the guest of another boy, in which case, collect his note before lunch, put it in your letter after you’ve had your hair cut, and make sure he moves your clothes down onto the lower peg for you… ok?

⭐I’m not a math expert. I completed a high school-equivalent math education as an adult, and this book was part of my education. Its figures are literally illustrative. Its writing is obtusely poetic.Dots on a page, arranged in a square, show something about quantities that other mathematical symbols cannot. Those illustrations are obvious and educational. Words such as, “Armies of Unalterable Law”, written above or below, cypher intentions of non-random connections in-between.This book is exactly that. It’s as if it had two authors: one obviously instructional, the other obsessively imaginative. This book does have two authors, of course, but I mean so figuratively.

⭐Gives insights into how mathematical concepts developed, beyond what one usually gets in math classes (which only show the results). Not the easiest reading, but accessible to a general audience if you’re willing to take the time to think through the concepts as they are presented, and engaging in the way it brings out connections to other disciplines such as music, art, literature, as well as what you might expect (e.g. physics).

⭐If you are young and have not read a lot you will not appreciate this book. 🙂 This book is for literate folks who want to learn about some important math ideas.

⭐You can follow most of the math discussion without be a degreed mathematician, and there are some very surprising discoveries. A good book by professors with a wonderful writing style.

⭐It is an amazon book. Worthwhile reading.

⭐One of the best Maths books I have read.

⭐Formidável. Leitura fluida, com bons exemplos. Recomendo.

⭐

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