From Here to InfinityScienceBookGuide HOME FEATURES Size Scales Time Scales Books By Author Books By Theme Reader Ratings Requests Forum APPROACHES Overviews Polemics Essays Biographies Memoirs Histories Metascience Everyday Life FIELDS Physical Sciences Life Sciences Social Sciences Symbolic Sciences Tech and Engineering SISTER SITES MysteryGuide.com Troutworks Games ABOUT US FAQ Contribute! Privacy E-mail us From Here to Infinity A Guide to Today's Mathematics by Ian Stewart REVIEW There's an inherent problem with trying to popularize higher mathematics, which is that genuine understanding isn't that different from real expertise. If a geologist tells me that the Earth's core is made of iron, I can appreciate the fact without in the least understanding how you might design experiments and models that would lead you to that conclusion. In mathematics, though, understanding is the coin of the realm --- sure, there's a difference between being able to follow proofs and being able to create them, but all of the people who really understand Wiles' proof of Fermat's Last Theorem, for example, are themselves professional mathematicians. This difficulty is just one of the reasons why it's such a pleasure to see math's best popularizer at work --- Stewart uses every trick in the book, including sheer clarity of writing, to communicate the flavor of the real problems mathematicians confront, while taking care to gloss over exactly the parts that are either least essential or most impenetrable. He is intent on showing that mathematics is a living, breathing discipline, and so he is not content to explain problems that were squared away two centuries ago; instead he follows some fields right up through current perplexities, and the third edition he updates the reader with some of the startling changes in those fast-moving fields in the eight years since the first edition. Through it all Stewart writes with style, humor, and unbridled enthusiasm. The book is divided up into mostly self-contained essays, and I think I owe the reader a list of the topics: factoring and primality testing, Fermat's Last Theorem, the history of non-Euclidean geometries, the Continuum Hypothesis, infinitesimals and non-standard analysis, applications of group theory, the Four Color Problem, the theory of knots, the origins of complex analysis, dissection and the Banach-Tarski paradox, modern probability and measure theory, Newtonian mechanics and the solar system, turbulence and chaos, fractal models, and the theory of computability. If that's all Greek to you, be brave: you can trust Ian to lead you through it. If instead you are familiar with all the topics above, don't assume there's nothing here for you; each essay takes the topic just as a starting point, with lots of interesting digressions, and although I've had training in a couple of the subjects mentioned I still found amusement and enlightenment in Stewart's treatments of them. Reviewer: TC Cool factoid I learned from this book You can't tie a knot in four dimensions --- every 4-dimensional embedding of a loop of string is equivalent to the "unknot". Summary information Year published: 2000 Number of pages: 297 Difficulty: 8/10 General areas: Symbolic Sciences Specific fields: Mathematics Approaches: Overview By the same author Life's Other Secret by Ian Stewart An enthusiastic argument for the role of mathematics in the biology of form and development. What did YOU think? Have you read this book? If so, let us know what you thought of it. Just click one of the five rating buttons below and your vote will be recorded. Something on your mind that doesn't fit into a 1 through 5? Let us all in on it, and post a comment to the ScienceBookGuide forum Reader Ratings Ratings so far for this book: RatingNumber 5 - Superb3 4 - Very good1 3 - Good1 1 - Poor1 See how other books have done at the Reader Ratings page. © 1999 Troutworks, Inc. All rights reserved.