Discussion Groups / English Usage / November 2006

Lancelot Hogben's "Mathematics For The Million" is excellent. Also
"Mathematician's Delight" by WW Sawyer which is an easier read but
doesn't cover the range of topics.

Math for millions by Hobgen (mentioned in the other posting) takes
historical perspective and scratches various math topics, however it has
nothing about current/modern math at all (as in 19th/20th century).

I don't think there's a laymen's book about math (covering most/all of
the subjects, such a book doesn't exists for professionals either
there's simply too much material), so most (popular science math) books
will focus on particular aspects/topics.

Martin Gardner is a generally recommendable author.

A very interesting book about math (without requiring too much math
knowledge) is:

Davis/Hersh: Descartes' Dream

It examines how math influences society.

Partially accessible to laymen as well are the  real (and ever growing)
math encyclopedias on the web:

http://en.wikipedia.org/wiki/Portal:Mathematics
http://mathworld.wolfram.com/

and somewhat lesser accessible
http://eom.springer.de/
http://planetmath.org/

Here's one:
http://www.amazon.com/CRC-Concise-Encyclopedia-Mathematics-Second/dp/1584883472
(Read the reviews.)

And there are several online encycs, e.g.:
http://mathworld.wolfram.com/
(See above.)
http://planetmath.org/encyclopedia
http://www.math.niu.edu/~rusin/known-math/index/dict.html
http://www.mathacademy.com/pr/prime/

Adrian

...

You might look into "The World of Mathematics" edited b James R Newman.
It's been published many times, last by Microsoft Press:

http://www.amazon.com/World-Mathematics-James-Roy-Newman/dp/1556151489

 - A

Go to amazon.com
search: mathematics encyclopedia
get some answers...

 CRC Concise Encyclopedia of Mathematics, Second Edition  
 Van Nostrand Reinhold Concise Encyclopedia of Mathematics  
 Prentice-Hall Encyclopedia of Mathematics
 Encyclopedia Of Mathematics (Science Encyclopedia)

A good place to ask would be in sci.math.

David Ames

The question is where to stop.  By the time you're looking up
"forcing" or "cohomology of groups" ayou aren't really a layman
any more, but any encylopaedia would have to say something about
those if it were not to be seriously misleading about what modern
mathematics is.

There is a survey about the size you want from a Japanese institute,
which was available in the 1990s - I can't find this on Google.  It
wasn't elementary and it wasn't cheap.  There is a much larger (and
very expensive) one from Springer and Kluwer.

Mathematics is one subject where you are better getting a bunch of
surveys of specific areas.  Some subjects are fairly well covered at
an accessible level, like logic and differential geometry.  But for
even something as basic to much of the maths of the last century as
measure theory, there is no way in except by getting a real honest-
to-god textbook, and for currently hot topics like quantum algebra,
forget it.

Wikipedia is usually pretty hopeless.  There are some useful and
extended essays, but mostly you get a tangle of links with only
trivial information at each node.

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Jack Campin:  11 Third St, Newtongrange EH22 4PU, Scotland | tel 0131 660 4760
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The trouble I ran into was symbology.  I began to compile a list of symbols
in a statistics class I was taking, then, I tried to use those same symbols
in an economics class later.  That worked for about 2 chapters.  Different
disciplines use different symbology.  Likewise, I'm sure different
mathematicians would also in the various areas of research.  I'd guess some
even invent their own symbology.

I think the problem comparing mathematical disciplines is like trying to
compare Latin to Chinese.  The greater human concepts are the same, however,
the apparatus and means to express them are totally differently.

Wesstein, Eric W., _CRC Concise Encyclopedia of Mathematics_ (2 Ed,
2002) 3252pp., about $125

Tanton, James Stuart, _Encyclopedia Of Mathematics_ (2005) 568pp, about $75

S. Gottwald, _Van Nostrand Reinhold Concise Encyclopedia of Mathematics_
(Springer, 1990), about $90

Although a bit out of date, I would suggest the Gottwald.