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.