I was asked to comment on
Kevin Devlin -- _Mathematics, the New Golden Age_
Columbia U. Press (revised & enlarged edition, 2001)
and it seems appropriate to compare it to
Ivars Peterson -- _The Mathematical Tourist_
Owl Press (expanded edition, 1998)
Both books seem to be aimed at the same goal, namely
describing to the laity what has been going on in
mathematics over the last 50 years or so.
Executive summary: Both are fine books. _MT_ is
somewhat more glitzy and more introductory, while
_MNGA_ goes somewhat deeper. Both are engaging
and readable, much more so than you might have
expected given the subject matter. These are
*not* textbooks, but neither do they leave the
reader entirely on the outside looking in: I
actually learned some math that I was able to use
shortly afterward.
Both books are roughly at the /Scientific American/
level, but I would rate both of them as being more
readable than typical /SA/ articles, and also more
informative.
On the one hand I have to put "popular" in scare
quotes, because neither of these books is going to
knock Harry or Artemis off the kids'-best-sellers
lists. On the other hand, either of these books
is a good answer to the question of what prize to
give the kid who just won the math contest.
There is a lot of overlap in the subject matter
of the two books, but far less than 100% overlap,
and in any case the approaches are sufficiently
different that if you like one book you probably
will want to read the other book also. I'd suggest
reading _MT_ before _MNGA_ but it's not critical.
Devlin suggests in his subtitle that in the last
50 years we have seen a "golden age" in mathematics
... and then does a good job of making that point.
Consider the four-color map problem and Fermat's
last theorem: non-experts can easily understand
the question, yet the answer eluded experts for
a century or more. Both were knocked off in the
last 30 years.
Both books cover the topics you would expect:
-- finding huge primes, factoring huge numbers, crypto
-- undecidability, intractability, NP-completeness
-- fractals and chaos
-- four color theorem
-- Fermat's last theorem
-- topology and knots
I note in passing that some of these results
involved marrying computers to classical math
techniques --- but some of them didn't.
To caricature the difference between the books:
*) _MT_ spends several pages discussing Conway's
game of Life, while
*) _MNGA_ mentions Conway's capture of three
sporadic groups.
... and not vice versa.
Also: _MNGA_ is all black and white, while _MT_
has 16 gorgeous color plates of fractal ferns,
Julia sets, Penrose tilings, etc.
_MNGA_ (more so than _MT_) goes behind the results
to paint a picture of what it's like to be a
mathematician. Therefore I would particularly
recommend _MNGA_ to bright high-school students
who think they might want to grow up to be
mathematicians. (When I was in HS, people were
always asking me what I wanted to be when I grew
up, which was a ridiculous question since I had
never met a real mathematician or scientist, and
had no way of knowing what they did for a living.)
High-school geometry is based on idea that go back
2000+ years, and calculus goes back 300+ years.
IMHO it is important for folks to see that math
is still a living subject ... and also to see that
the recent results involve a lot of reeeally hard
work.
And you can always go to amazon.com and read the
reviews there.
===========
Amusing homework: Find a calculator good enough to
evaluate exp(pi*sqrt(163)) to an absolute accuracy of
+- .00000000001
and then again to an absolute accuracy of
+- .000000000000001
Hint: We're talking about a relative accuracy of parts
in 10^32 ... IEEE double-precision floating point isn't
going to get it done.