Mr. Brandenburg's Math and Science  Related Books You Can Read
Mr. Brandenburg compiled a list of about 80 mathrelated books, mostly recent, for his geometry students to choose from, read, and do a report on, using recommendations from others and his own reading as well. Following is the assignment he gave to his students and also the list with links to Amazon.com.
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"You are lucky to be alive during a real boom in good, popular math and
science writing. You will need to read and report on two of these books
during the next 3 months. Some of these books are very recent, which
means that they may or may not be in public libraries yet. I have provided a review. If the review is in quotes, then I did not write the review myself but found it on one of the following sites: Daedalus Books, Hamilton Books, Mathematical Association of America (MAA), Barnes and Noble or Amazon. In addition to the review, a publisher, the number of pages, and a copyright date are also given on most selections. Remember that some books, especially popular ones, change publishers and go through several different editions over the years. I have read less than half of these books myself. They are in alphabetical order by author."
Mr. Brandenburg
 1. Edwin A. Abbott
Flatland: A Romance of Many Dimensions
 "Flatland is one of the very few novels about math and philosophy that can appeal to almost any lay person. Published in 1880, this short fantasy takes us to a completely flat world of two physical dimensions where all the
inhabitants are geometric shapes, and who think the planar world of
length and width that they know is all there is. But one inhabitant
discovers the existence of a third physical dimension, enabling him to
finally grasp the concept of a fourth dimension." (A review) (Dover, 128
pp, reprint)
 2. Amir D. Aczel
The Mystery of the Aleph: Mathematics, the Kabbalah, and the Human Mind
 "Aczel tells of mathematicians struggling with
absolute infinity and some of its mindbending ramifications. The crown
jewel of this struggle was conceived more than a century ago by Georg
Cantor and remains an enigma to mathematicians. Cantor spent his life
going back and forth between trying to prove and disprove his continuum
hypothesis. In the Kabbalah, the aleph "represents the infinite nature,
and the oneness, of God." Cantor deliberately picked this symbol for use
in his equations: to him, trying to understand the absolute infinite was
like trying to touch the face of God." (4 Walls 8 Windows, 258 pp, 2000)
 3. Donald J. Albers and G. L. Alexanderson, editors
Mathematical
People: Profiles and Interviews
 This book is a collection of profiles
and interviews with twentyfive prominent mathematicians. (NTC, 392 pp,
1986)
 4. Donald J. Albers, Gerald L. Alexanderson, and Constance Reid
More
Mathematical People
 Probably a continuation of the previous item.
(Academic Press, 375 pp, 1990)
 5. Arthur Benjamin and Michael Shermer
Mathemagics: How to Look like a Genius Without Really Trying
 Teaches you how to calculate in your head
faster than you can with a calculator. (Lowell, 218 pp, 1993)
 6. David Blatner
The Joy of Pi
 This is an easy book to read. It has
many different parts: breezy narratives of the history of pi, and quirky
stories of those obsessed with it. There are piinspired cartoons,
poems, limericks, and jokes. Also has the firs one million digits of
pi. (Walker, 129 pp, 1997)
 7. Mary Blocksma
Reading the Numbers: A Survival Guide to the Measurements, Numbers, and Sizes Encountered in Everyday Life
 This is
a reference book, but it gives details on all sorts of things, like what
the ISBN is, what those last 4 new digits on the Zip Code mean, what all
those letters and numbers on automobile tires mean, and so on. (Penguin,
224 pp, 1989)
 8. Colin Bruce
Conned Again, Watson!: Cautionary Tales of Logic, Math, and Probability
 "Some people who think they hate math are lucky to
learn that they actually just can't abide its often dry, abstract
presentation. Physicist Colin Bruce turns math teaching on its head by
using conflict, drama, and familiar characters to bring probability and
game theory to vivid life in Conned Again, Watson! Cautionary Tales of
Logic, Math, and Probability. Using short stories crafted in the style
of Sir Arthur Conan Doyle, he lets Sherlock Holmes guide Watson and his
clients through elementary mathematical reasoning." (A review) (Perseus,
320 pp, 2002)
 9. Dionys Burger
Sphereland: A Fantasy About Curved Spaces and an Expanding Universe
 "Sphereland, the sequel to Flatland, is a great book
to help one expand one's mind. This book is a satire, a geometry lesson,
and a good exercise for the mind. Sphereland is also useful for helping
one to think outside of the box, and the universe for that matter. This
book stretches the confines of your mind and imagination." (A review)
(International, 1982)
 10. John L. Casti
Five Golden Rules: Great Theories of 20thCentury Mathematicsand Why They Matter
 "Books on mathematics
with such beauty, breadth, and insight are rare. Five Golden Rules is
replete with intriguing information  not only for curious lay people but
also for seasoned mathematicians and scientists. Casti has produced a
truly stunning survey of mathematics' manifold consequences." (Review by
Clifford Pickover) (Wiley & Sons, 235 pp, 1996)
 11. John L. Casti
Mathematical Mountaintops: The Five Most Famous Problems of All Time
 "The recent boom in mathematics bestsellers has
contributed a great deal towards raising the public profile of the
subject. But such books ignore a significant section of potential
readers, namely those who have more of a mathematical background that
the general reader but who are not professional mathematicians. Such
mathematical enthusiasts have no doubt enjoyed some of the popular
books, but would really prefer a more technical treatment. This is
exactly what John Casti provides in Mathematical Mountaintops. It is
nether a textbook nor a pop math book, rather it is a serious indepth
look at the great problems of mathematics." (Oxford, 196 pp, 2001)
 12. Calvin C. Clawson
Mathematical Mysteries: The Beauty and Magic of Numbers
 "Many of the dazzling beauties of higher mathematics are just
as accessible to an ordinary untrained spectator as are similar wonders
of great literature, visual art, and music. This wellkept secret is
finally blown wide open in Calvin Clawson's latest book." (A review) Has
equations, but explains them well.. (Perseus, 313 pp, 1996)
 13. Calvin C. Clawson
Mathematical Sorcery: Revealing the Secrets of Numbers
 "Few mathematicians today have the ability to write about math
more entertainingly, with greater enthusiasm and clarity, than Calvin
Clawson. A splendid introduction to the great ideas of mathematics,
their powerful magic, and their intricate, mysterious beauty." (Review
by Martin Gardner.) ISBN 073820496X. (Perseus, 234 pp, 1999)
 14. Donald Cohen
Calculus by and for Young People (Ages 7, Yes 7 and Up)
 A description of how young people, Don and some mathematicians,
solved problems which involve infinite series, infinite sequences,
functions, graphs, algebra, +,  important mathematical ideas. Also
available, the Worksheets (some say all you need)... (1989)
 15. John Horton Conway and Richard K. Guy
The Book of Numbers
 "A fascinating review of numbers: from Egyptian fractions to surreal
numbers; prime numbers, Fibonacci numbers, Catalan numbers, Fermat
numbers; from numbers so large they cannot be imagined (and barely be
named) to rulerandcompass." (Copernicus/SpringerVerlag, 310 pp, 1996)
 16. Philip J. Davis and Reuben Hersh
The Mathematical Experience
 "A brilliant and engrossing view of the development of
mathematics...wonderful at communicating its beauty and excitement to
the general reader." This is the classic introduction for the educated
lay reader to the richly diverse world of mathematics: its history,
philosophy, principles, and personalities. Winner of an American Book
Award (HoughtonMifflin, 411 pp, 1998)
 17. Keith Devlin
Life by the Numbers
 "Most of us think mathematics is
about numbers and counting. That's just the basics, though, and Keith
Devlin's companion book to the PBS series "Life by the Numbers" gives
examples of the versatility of math as a tool for understanding just
about everything. Devlin loves mathhe calls it 'one of the greatest
creations of mankind' in a chapter entitled 'It's an M World'and he
wants everyone to love it." (A review) (Wiley, 224 pp, 1999)
 18. Keith Devlin
The Math Gene: How Mathematical Thinking Evolved and Why Numbers are Like Gossip
 "Keith Devlin's book was a revelation to
me. For a long time I suspected that there was some connection between
our ability to do math and our possession of language. Now, that
connection is made dazzlingly clear in a language that even a
mathematical ignoramus like myself can understand. A mustread for
anyone who has ever wondered what makes us human." (A review) (Basic
Books, 328 pp, 2000)
 19. Keith Devlin
Mathematics: The New Golden Age
 "Why a 'new golden age?' According to Keith Devlin, we are currently witnessing an astronomical amount of mathematical research. Charting the most
significant developments that have taken place in mathematics since
1960, Devlin expertly describes these advances for the interested
lay person and adroitly summarizes their significance as he leads the
reader into the heart of the most interesting mathematical perplexities
 from the biggest known prime number to the ShimuraTaniyama conjecture
for Fermat's Last Theorem." (Columbia, 2001)
 20. Douglas Downing
Algebra the Easy Way
 "An algebra text in the form
of a fantasy novel, with the story's characters solving problems by
using algebra." (Barron's, 329 pp, 1996)
 21. Douglas Downing
Trigonometry the Easy Way
 "Here's a complete, easytograsp course in trigonometry that takes the form of a fantasy novel. The King of Carmorra and his subjects have many practical problems to solve, and their answers can be found by applying principles of trigonometry. Readers follow along and learn to solve many different problems that can be reduced to triangular diagrams. They learn the laws of sine and cosine, trigonometric functions and inverse functions,
waves, conic sections, polynomial approximation, and much more. The book
is filled with instructive exercises and their solutions, plus
illustrative drawings, graphs, and diagrams. This new edition contains
updated coverage on using graphing calculators and computer spreadsheets
for solving trigonometric problems." (Barron's, 326 pp, 2001)
 22. Apostolos Doxiadis
Uncle Petros and Goldbach's Conjecture
 "A novel of mathematical obsession. It is fascinating thus far (80 pages in). Received it as a late holiday gift from close friends. I think it
appeared in Greek in '92 and in English just last year. I'd love to hear
what others thought of it and to recommend it to those who like
literature and mathematics with some history thrown in. A mathematical
conjecture unsolved for two centuries; a mathematical genius uncle
driven mad trying to solve it; an ambiguous relation with a
mathematicallyminded nephew; and acute human observation all come
together in Uncle Petros to make a very funny, tender, charming and, to
my mind, irresistible novel. In the tradition of Fermat's Last Theorem
and Einstein's Dreams, a novel about mathematical obsession." (A
review) (Bloomsbury, 224 pp, 2001)
 23. Underwood Dudley
Mathematical Cranks
 "On the one hand, mathematics is the great leveler of the sciences. Anyone can do mathematical research, with no equipment but pencil and paper. On the other hand, mathematics is the only science where something can be proven,
irrefutably and for all time, to be impossible. These two ingredients
make mathematics one of the most fertile grounds for inspiring crankery.
This book is not only entertaining, the broadness of its examples
provides a fascinating insight into the mind of cranks. I couldn't put
it down." (MAA, 384 pp, 1992.
 24. William Dunham
Journey Through Genius: The Great Theorems of Mathematics
 "Strikes an extraordinary balance between the historical
and technical. He devotes each chapter to a principal result of
mathematics, such as the solution of the cubic series and the divergence
of the harmonic series. Not only does this book tell the stories of the
people behind the math, but it also includes discussions and rigorous
proofs of the relevant mathematical results". (Penguin,1990)
 25. William W. Dunham
The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems and Personalities
 "Contains
a wealth of amusing stories and little known facts from the annals of
math. All proofs and equations are introduced through easytofollow,
stepbystep explanations. Discusses some of the most intriguing
mysteries such as Russell's Paradox. Features brief biographies of many
great mathematicians including Isaac Newton, Bertrand Russell and
Hypatia of Alexandria." (Wiley, 314 pp, 1997)
 26. Hans Magnus Enzensberger
The Number Devil: A Mathematical Adventure
 "In 12 dreams, a 12yearold boy who hates math discovers the
amazing world of numbers: infinite numbers, prime numbers, Fibonacci
numbers, numbers that magically appear in triangles, and numbers that
expand without end." (Holt, 262 pp, 2000)
 27. Clifton Fadiman (ed)
Fantasia Mathematica: Being a Set of Stories, Together With a Group of Oddments and Diversions, All Drawn from the Universe of Mathematics
 "What a relief to open the pages of this book. I approach mathematics as a subject necessary, but always painful, to learn. Dare I say I love this book? Some of the short
stories are humorous, some are endearing, some have common characters.
All deal with mathematics in one way or another. Fadiman's book
succeeded where so many others failedit interested me.his book closely
tied math with imagination and fantasya connection never clearly drawn
in my public education. I think, though, that it's very important to
present mathematics as the language for interpreting the world that it
is...rather than as a cold and mostly irrelevant subject to get C
minuses in! IT MADE MATH EXCITING. Yikes, did I say that? It is another
way to know why your baseball is going to break the window, how to build
a spaceship in your back yard, and how to teleport to Argentina in 0
seconds flat. A real tangible benefit to reading this book was learning
the derivation of Pythagoras' Theorem. Not to sound like an idiot, but I
think most of us went through high school geometry having no clue where
a2 + b2 = c2 came from. In two pages, this book explained it so clearly
to me that I laughed out loud. IF ONLY THEY USED THIS TO TEACH ME
INSTEAD OF A BRUTAL MATH BOOK!" (Copernicus, 298 pp, 1997)
 28. Sarah Flannery
In Code: A Mathematical Journey
 "British bestseller
by and about the 16yearold who stunned the world by inventing a way of
making publickey encryption much more efficient; an engaging, almost
playful, book in which the reader is encouraged to spend lots of time
working out mathematical puzzles." (Workman, 341 pp, 2001)
 29. George Gamow
One Two Three...Infinity: Facts and Speculations of Science
 "This book changed lives around the world. Many of us began our journey
into science and mathematics with this book. The reviews at the other
book site show how many of us were changed in our young lives by this
book. Buy it for every child you know." (A review) This book has been in
print for over 50 years, because it's GOOD. (Dover, 335 pp, reprint)
 30. Martin Gardner
Knotted Doughnuts and Other Mathematical Entertainments
 One of his many collections of his columns from the
Scientific Americans, and contains an entirely new set of problems,
paradoxes, teasers and tricks. Investigates mathematical games such as
Sim, Chomp, and Race Track; also investigates coincidences that seem to
violate the laws of probability. (Freeman, 278 pp, 1986)
 31. Martin Gardner
 any book he wrote on math and science is good!
 32. James Gleick
Chaos: Making a New Science
 This new science offers a way of seeing order and pattern
where formerly only the random, the erratic, the unpredictablein
short, the chaotichad been observed. Chaos is a history of discovery.
It chronicles, in the words of the scientists themselves, their
conflicts and frustrations, their emotions and moments of
revelation. After reading Chaos, you will never look at the world in
quite the same way again. (Viking Penguin, 317pp., 1988)
 33. Larry Gonick
The Cartoon Guide to Statistics
 "You'll find lucid
explanations of probability, distributions, error functions, hypothesis
testing, and other basic tools of statistics." And, best of all, it's
written in the form of cartoons. (HarperCollins, 223 pp, 1993)
 34. Denis Guedj
Numbers: the Universal Language
 "Numbers, like letter forms, have a rich and complex history. Who first invented the? How old are they, and how were they developed? How did they come to represent a world of abstract ideas and universal concepts? How do they differ throughout the world today?" (From the cover.) (Abrams, 175 pp, 1996,
1997)
 35. Jan Gullberg
Mathematics: From the Birth of Numbers
 "If a family
is to have only one mathematics book on the reference shelf, then this
is the one... " Not really something you would read from cover to cover,
but more like an encyclopedia. Very well written. (Norton, 1120 pp,
1996)
 36. Nina Hall, editor
Exploring Chaos: A guide to the New Science of Disorder
 In the past few years, a new line of scientific inquiry called
"chaos theory" has caught the popular imagination. Young people, in
particular, have taken to the complex computergenerated patterns that
seem to teeter precariously between order and randomness. A dazzling
mathematical object, the Mandelbrot set, now decorates posters, record
sleeves, and pop videos (as well as the back cover of this book jacket).
Chaos theory, it turns out, has a deeper meaning for our understanding
of nature. All sorts of phenomena  from dripping faucets to swinging
pendulums, from the unpredictability of the weather to the majestic
parade of the planets, from heart rhythms to gold futures  are best
perceived through the mathematical prism of chaos theory. In this
collection of incisive, frontline reports, ably edited by Nina Hall for
New Scientist magazine, internationally recognized experts such as Ian
Stewart, Robert May, and Benoit Mandelbrot draw on the latest research
to explain the roots of chaos in modern science and mathematics. (W.W.
Norton, 223 pp, 1991)
 37. G. H. Hardy
A Mathematician's Apology
 'This is a profoundly sad book, the memoir of a man who has reached the end of his ambition, who can no longer effectively practice the art that has consumed him since he was a boy. But at the same time, it is a joyful celebration of the subjectand a stern lecture to those who would sully it by dilettantism or attempts to make it merely useful. "The mathematician's patterns," G.H. Hardy declares, "like the painter's or the poet's, must be
beautiful; the ideas, like the colours or the words, must fit together
in a harmonious way. Beauty is the first test: there is no permanent
place in the world for ugly mathematics." '(Cambridge, 142 pp, reprint 1940.
 38. Douglas Hofstadter
Goedel, Escher, Bach: An Eternal Golden Braid
 "Twenty years after it topped the bestseller charts, Douglas R.
Hofstadter's Goedel, Escher, Bach: An Eternal Golden Braid is still
something of a marvel. Besides being a profound and entertaining
meditation on human thought and creativity, this book looks at the
surprising points of contact between the music of Bach, the artwork of
Escher, and the mathematics of Goedel. It also looks at the prospects for
computers and artificial intelligence (AI) for mimicking human thought.
For the general reader and the computer techie alike, this book still
sets a standard for thinking about the future of computers and their
relation to the way we think." (A review) (Basic, 777pp, 1979/1999)
 39. Douglas R. Hofstadter
Metamagical Themas: Questing for the Essence of Mind and Pattern
 "When I was in high school I discovered the joys of
reading Martin Gardner's "Mathematical Games" column in Scientific
American. After a few years of pleasure he was replaced by someone else
who (among other things) wrote on the joys of Rubik's cube and I found
myself wasting weeks of time and filling notebooks with my quest to
explore and solve the cube. That columnist was Douglas Hofstadter, who
brought the same skill at sharing his enthusiasm for his topic that
created the amazing, mind shattering 'Goedel, Escher, Bach'. His column,
that occupied the same place as "Mathematical Games", was called
"Metamagical Themas" (looking closely at those two names will tell you a
lot about Douglas Hofstadter) and lasted for 13 issues. This book is a
compilation of those columns, each with a new endnote by Hofstadter and
some letters received by the magazine and his reply." (Basic, 880 pages,
1985)
 40. Lancelot Hogben
Mathematics for the Million/How to Master the Magic of Numbers
 "The best elementary
math book ( for algebra, geometry ,trig, and spherical trig) Like the
Thompson book ,it has been in continuous print since the 1930's! There
is also lots of history in it. The same author has a history of math
book, with wonderful illustrations, that I often give to children and
arts friends. It really inspired me as a kid." Albert Einstein wrote:
"It makes alive the contents of the elements of mathematics." (numerous
versions available.)
 41. Wendy Isdell
A Gebra Named Al: A Novel
 "Julie hates algebrauntil
she meets a gebra named Al, and the Periodic horses journey through the
Land of Mathematics, where the Orders of Operations are real places and
fruits that look like Bohr models grow on chemistrees." (Free Spirit,
128 pp, 1993)
 42. Norman Juster
The Dot and the Line: A Romance in Lower Mathematics
 "My geometry teacher read this story to my class and it is the sweetest
story I've ever heard. It may be a tale of a dot and a line, but it
means so much more. It says the age is from 48 but I think people of
all ages will enjoy the story of the dot and the line. Five stars, try
six stars. It's great!" (Random, orig. 1963)
 43. Robert Kaplan
The Nothing That Is: A Natural History of Zero
 "It
is hard to imagine that an entertaining, informative book could be
written about nothing, but Robert Kaplan has done it brilliantly.
Starting with the great invention of zero as a place holder, Kaplan
takes you through the use of zero in algebra, and in calculus, through
the importance of the null set. His book closes with that unthinkable
question, 'Why is there something rather than nothing?' about which one
cannot long meditate without fear of going mad." (Review by Martin
Gardner) (Oxford, 225 pp, 2000)
 44. Peggy Kaye
Afterwards; Folk and Fairy Tales With Mathematical Ever Afters
 "I enjoyed this book. My students
enjoyed the moral lessons that it taught. The stories had a set of
mathematical problems at the end for the students to work. Many of the
problems could be changed to different grade levels." (reading level: ages 912) (Cuisenaire, 128 pp, 1997)
 45. Margaret Kenda and Phyllis S. Williams
Math Wizardry for Kids
 Over
200 math puzzles, games and designs for kids, also available as a kit
with a protractor, various triangles, a ruler, compass, and other
essential tools (Ages 8 to 12) (Barron's, 336 pp, 1995)
 46. Donald Knuth
Surreal Numbers: How Two ExStudents Turned on to Pure Mathematics and Found Total Happiness: A Mathematical Novelette
 "An astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the
air, then reaches into almost nothing and pulls out an infinitely rich
tapestry of numbers that form a real and closed field. Every real number
is surrounded by a host of new numbers that lie closer to it than any
other "real" value does. The system is truly 'surreal.'" (Addison
Wesley, 128 pp, 1982, reprinted many times)
 47. Serge Lang
The Beauty of Doing Mathematics: Three Public Dialogues
 This is another book from the famous Yale math professor, Serge Lang.
However, this isn't a textbook  it's a collection of 3 dialogues Lang
gave in Paris in the 80s. Certainly the discussions are very
interesting. The interactions between Lang and the audience, comprising
mostly 'ordinary' people but also highschool and college students, set
this book apart from a textbook. Lang does a fairly good job at covering
the material (relating to primes, Diophantine equations, and a bit of
geometry/topology) and explaining it to the nonmathematicallyinclined.
Of course, with this come problems  Lang only skims over the material
and much of what he says is not supported by proof. (SpringerVerlag,
124 pp, 1985)
 48. Lawrence S. Leff
Geometry the Easy Way
 "This book will supplement
any High School Geometry textbook. The problems in the book range from
easy to challenging (some just tedious) that will help and prepare
students for tests and other standardized exams. What I really like about
this book is that it lays down all of the concepts in a very clear way
without using too many words. The book should be used more as a
supplement, a reminder, and a guide to help you solve problems. It's not
the most colorful and fun book to read, but it is worth all your money
if you are looking for a good outlined approach to the subject."
(Barron's, 375 pp, 1997)
 49. Eli Maor
e: The Story of a Number
 "Until about 1975, logarithms
were every scientist's best friend. They were the basis of the slide
rule that was the totemic wand of the trade, listed in
huge books consulted in every library. Then handheld calculators
arrived, and within a few years slide rules were museum pieces. But e
remains, the center of the natural logarithmic function and of calculus.
Eli Maor's book is the only more or less popular account of the history
of this universal constant." (Princeton, 232 pp, 1998)
 50. Eli Maor
Trigonometric Delights
 "Maor writes Trigonometric
Delights from an historical perspective, but it is not a history book.
It contains many theorems and results of trigonometry, but it is not a
textbook. Rather, Maor achieves a satisfying blend of mathematics and
history, creating a work that informs, teaches, and stimulates thought,
while underscoring that mathematics is a human endeavor, not a stale
collection of facts that exist in a vacuum. His book is the labor of a
missionary whose aim is to deepen our appreciation of ideas and the
people who developed them, ideas about which we have heard, but have not
fully enjoyed. It is evident throughout that Maor is devoted to his
subject. His love for trigonometry is contagious. He writes
enthusiastically and engagingly." (Princeton, 239 pp, 1998)
 51. Leonard Mlodinow
Euclid's Window; The Story of Geometry from Parallel Lines to Hyperspace
 "Mlodinow reveals how geometry's first
revolution began with a 'little' scheme hatched by Pythagoras: the
invention of a system of abstract rules that could model the universe.
That modest idea was the basis of scientific civilization. But further
advance was halted when the Western mind nodded off into the Dark Ages.
Finally in the fourteenth century an obscure bishop in France invented
the graph and heralded the next revolution: the marriage of geometry and
number ·" "The story of 5 revolutions in geometry." (Free Press, 306 pp,
2001.)
 52. Paul J. Nahin
An Imaginary Tale
 "This tells the 2000yearold history of one of mathematics' most elusive numbers, the square root of minus one, also known as i, recreating the baffling mathematical problems that conjured it up and the colorful characters
who tried to solve them. Addressing readers with both a general and
scholarly interest in mathematics, Nahin weaves into this narrative
entertaining historical facts, mathematical discussions, and the
application of complex numbers and functions to important problems."
(Princeton, 258 pp, 1998)
 53. Paul Nahin
Duelling Idiots and Other Probability Puzzlers
 "What are your chances of dying on your next flight, being called for jury
duty, or winning the lottery? We all encounter probability problems in
our everyday lives. In this collection of twentyone puzzles, Paul Nahin
challenges us to think creatively about the laws of probability as they
apply in playful, sometimes deceptive, ways to a fascinating array of
speculative situations". (Princeton, 256 pp, 2000)
 54. Theoni Pappas
The Adventures of Penrose the Mathematical Cat
 "Penrose, a cat with a knack for math, takes children on an adventurous
tour of mathematical concepts from fractals to infinity. When the
fractal dragon jumps off the computer screen and threatens to grow
larger than the room itself, Penrose must find out if fractal patterns
can work in reverse, getting smaller instead of larger." (ages 912)
(World Wide, 132 pp, 1997)
 55. Theoni Pappas
The Joy of Mathematics
 "Part of the joy of mathematics is that it is everywhere: in soap bubbles, electricity, da Vinci's masterpieces, even in an ocean wave. Written by the wellknown mathematics teacher consultant, this two volume collection of over 500 clearly illustrated mathematical ideas, concepts, puzzles, and games
shows where they turn up in the 'real' world. You'll find out what a
googol is, visit hotel infinity, read a thorny logic problem that was
stumping them back in the 8th century." (World Wide, 237 pp, 1989)
 56. Theoni Pappas
More Joy of Mathematics: Exploring Mathematics All Around You
 "Part of the joy of mathematics is that it is everywhere in
soap bubbles, electricity, da Vinci's masterpieces, even in an ocean
wave. Written by the wellknown mathematics teacher consultant, this two
volume collection of over 500 clearly illustrated mathematical ideas,
concepts, puzzles, and games shows where they turn up in the 'real'
world. (World Wide, 304 pp, 1991)
 57. John Allen Paulos
A Mathematician Reads the Newspaper
 In my opinion
a bit easier to read than his "Innumeracy". Has contents of his numerous
articles that are published online and in various periodicals, where he
investigates the numbers that make the news in economics and politics,
health issues, sports, spindoctoring, recipes, celebrity features, and
more. ISBN 0465043623 (Basic, 212 pp, 1995)
 58. Ivars Peterson
The Mathematical Tourist: Snapshots of Modern Mathematics
 "The only popular book on mathematics that covers many of
the really new developments in the field. Ivars is accurate yet
accessible, a delicate combination in this subject, particularly."
(Freeman, 240 pp, 1988; newer versions are available.)
 59. Clifford A. Pickover
Keys to Infinity
 "A treasure trove of
recreational problems." (Martin Gardner) "What could be more appropriate
to the subject of infinity than a book like this one, so dense with
wonderful puzzles, anecdotes, images, and computer programs that you
could pore over it forever?" (Wiley, 332 pp, 1995)
 60. George Polya
How to Solve It
 "This perennial best seller was
written by an eminent mathematician, but it is a book for the general
reader on how to think straight in any field. In lucid and appealing
prose, it shows how the mathematical method of demonstrating a proof or
finding an unknown can be of help in attacking any problem that can be
"reasoned" out from building a bridge to winning a game of anagrams.
Generations of readers have relished G. Polya's deftindeed,
brilliantinstructions on stripping away irrelevancies and going
straight to the heart of the problem." (1971; there are many editions)
 61. Hans Rademacher and Otto Toeplitz
The Enjoyment of Math
 "What is
so special about the number 30? How many colors are needed to color a
map? Do the prime numbers go on forever? Are there more whole numbers
than even numbers? These and other mathematical puzzles are explored in
this delightful book by two eminent mathematicians. Requiring no more
background than plane geometry and elementary algebra, this book leads
the reader into some of the most fundamental ideas of mathematics, the
ideas that make the subject exciting and interesting. Explaining clearly
how each problem has arisen and, in some cases, resolved, Hans
Rademacher and Otto Toeplitz's deep curiosity for the subject and their
outstanding pedagogical talents shine through." (Dover, 216 pp,
1966/1990)
 62. Constance Reid
From Zero to Infinity : What Makes Numbers Interesting
 "A classic of popular mathematical literature (since 1955)
that combines the mathematics and the history of number theory with
descriptions of the mystique that has, on occasion, surrounded the
numbers even among great mathematicians." (MAA, 4th edition)
 63. Constance Reid
The Search for E. T. Bell
 An account of one of the
century's most colorful mathematicians. Bell's Men of Mathematics (1937)
presented mathematics and mathematicians in a way that had never been
done before, fascinating many of his colleagues, irritating others, and
inspiring young people to become mathematicians. Bell was also widely
known as the science fiction writer John Taine. As a result of
biographer Reid's discoveries about his early life, almost every
statement now in print about Bell's family background and early life
will have to be revised, and a new look taken at his extensive
mathematical work and his science fiction. (MAA, 384pp, 1993)
 64. Rudy Rucker
Infinity and the Mind
 "By far the best
choice for an educated lay person is this jazzy book which is an
excellent introduction to all aspects of the infinite. Rucker does a
good job balancing accessibility and sophistication  though the book
covers some very sophisticated math, even a highschool student should
be able to comprehend most of it. It's a good deal at roughly $13 and,
moreover, widely available  Borders, Barnes and Noble, etc usually have
a copy in their math section. Run out and buy a copy  your horizons
will be infinitely expanded! also contains one of the best expositions
of Goedel's incompleteness theorem." (Princeton, 342 pp, 1995)
 65. Rudy Rucker
The Fourth Dimension: Toward a Geometry of Higher Reality
 "Superb! It will hurt your brain if you don't know what you're
getting into. On the other hand, if you know what to expect from Science
Fact based text then you should be extremely pleased. The Plato's cave
story is exceptional, and the tale of Flatland and the contemplation of
a 2D creature seeing/fathoming a 3D creature is thought provoking.
MUST READ." (Houghton Mifflin, 228 pp, 1984)
 66. Rudy Rucker
Mind Tools: The Five Levels of Mathematical Reality
 "This is an amazing book for teaching the concepts of mathematical
logic, fractals, number theory, and information theory. I have never
seen these concepts introduced in such an easytounderstand fashion. I
recommend it highly to anyone with an interest in these concepts. Near
the end of the book, it does go a little overboard with the information
theory and becomes hard to follow."
 67. David Salsburg
The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
 "In The Lady Tasting Tea, David Salsburg tells the fascinating story of how statistics has revolutionized science in the twentieth century. Leading the reader through a maze of randomness and probability, the author clearly
explains the nature of statistical models, where they came from, how
they are applied to scientific problems, and whether they are true
descriptions of reality. Salsburg also discusses the flaws inherent in a
statistical model and the serious problems they've created for
scientists as we enter the twentyfirst century." (Holt, 340 pp, 2001)
 68. Bruce Schechter
My Brain is Open: The Mathematical Journeys of Paul Erdos
 "Physicist and science writer Bruce Schechter's biography of
legendary Hungarian mathematician Paul Erdos is an engaging portrait,
warm and intimate, bringing this strange, happy man to life. Schechter's
focus is quite a bit tighter, and more traditionally biographical, than
Paul Hoffman's in The Man Who Loved Only Numbers. Here, we get to see
Erdos's brief childhood transform quickly into a carefree adolescence of
solving difficult math problems with his circle of brilliant
friendsuniquely encouraged by a country that valued the contributions
of mathematics in a way that has never been equaled." (Touchstone, 224
pages, 2000)
 69. David M. Schwartz
On Beyond a Million: An Amazing Math Journey
 "Amazing facts about millions, trillions, and much bigger numbers are
explained in picturebook cartoon scenarios, contributed by Paul Meisel,
that show kids in the classroom, at the seashore, in the rain forest,
and all over the place, learning how to count by powers of 10. The
design is busy, with sidebars and balloon comments. Each doublepage
spread is clearly meant to be talked about, and the discussions aren't
overwhelming. The sheer numbers are astounding, though, whether they
refer to the population of the U.S. or the number of stars in the Milky
Way; and the explanation of exponents gives kids a way to count what
seems unimaginable." (Ages 912) (Bantam, 1999)
 70. Dennis Shasha
The Puzzling Adventures of Dr. Ecco
 "This is an
extremely entertaining book written in a lively style. The problems and
puzzles are unique and exciting. Dr. Ecco's Holmesian character is
insightful and engaging. What is so delightful here is that the problems
presented, in addition to being challenging, open up readers to
significant and important areas of mathematics and their applications."
(Freeman, 181 pp, 1988)
 71. Simon Singh
The Code Book; The evolution of secrecy from Mary, Queen of Scots to Quantum Cryptography
 Codes have decided the fates of
empires, countries, and monarchies throughout recorded history.
Combining a superb storyteller's sense of drama and a scientist's
appreciation for technical perfection, Singh traces the evolution of
secret writing from ancient Greek military espionage to the frontiers of
computer science. (Doubleday, 402 pp, 1999)
 72. Simon Singh
Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem
 This is the story of the proof of
Fermat's Last Theorem by Andrew Wiles, who wrote, "Perhaps I could best
describe my experience of doing mathematics in terms of entering a dark
mansion. One goes into the first room and it's dark, really dark, and
one stumbles around bumping into the furniture. Gradually you learn
where each piece of furniture is, and finally, after six months or so,
you find the light switch and suddenly it's all illuminated and you can
see exactly where you are." (Walker, 315 pp, 1997)
 73. Michael Smith
The Emperor's Codes: The breaking of Japan's Secret Ciphers
 More of a history book than a math book, it shows how important
it was in World War 2 for the USA to break the Japanese codes. Gives
some details on how it was done. (Arcade,336 pp, 2000)
 74. Sherman Stein
How The Other Half Thinks: Adventures in Mathematical Reasoning
 "Occasionally, in some difficult musical compositions there
are beautiful, but easy, parts  so simple a beginner could play them.
So it is with mathematics as well. There are some discoveries in
advanced mathematics that do not depend on specialized knowledge, not
even on algebra, geometry, or trigonometry. Instead, they may involve,
at most, a little arithmetic, such as 'the sum of two odd numbers is
even,' and common sense. As I wrote, I kept in mind two types of
readers: those who enjoyed until they were turned off by an unpleasant
episode, usually around fifth grade; and mathematics aficionados, who
will find much that is new throughout the book." (McGrawHill, 177 pp,
2001)
 75. Ian Stewart
Does God Play Dice? The New Mathematics of Chaos
 "The
science of chaos is forcing scientists to rethink Einstein's fundamental
assumptions regarding the way the universe behaves. Chaos theory has
already shown that simple systems, obeying precise laws, can
nevertheless act in a random manner. Perhaps God plays dice within a
cosmic game of complete law and order. Does God Play Dice? reveals a
strange universe in which nothing may be as it seems. Familiar
geometrical shapes such as circles and ellipses give way to infinitely
complex structures known as fractals, the fluttering of a butterfly's
wings can change the weather, and the gravitational attraction of a
creature in a distant galaxy can change the fate of the solar system."
(Blackwell, 416 pp, 2002)
 76. Ian Stewart
Nature's Numbers: The Unreal Reality of Mathematics
 "Firstrate popular mathematics writing...Stewart achieves what other
popular mathematics writers merely strive for: an accurate, informative
portrayal of contemporary mathematics without a single equation in
sight...[If] someone you know wants to know what mathematics really is,
buy them a copy of Nature's Numbers." (Basic, 176 pp, 1997)
 77. Malba Tahan
The Man Who Counted: A Collection of Mathematical Adventures
 "The Arabian adventures of a man with remarkable
mathematical skills, which he uses to settle conflict and give wise
advice." (Norton, 244 pp, 1993)
 78. James Tanton
Solve This: Math Activities for Students and Clubs
 "Jim teaches in the Boston area Math
Circle. He is fabulous. The book has plenty of illustrations and lots of
engaging problems, some of which would be suitable for bright 8th and
9th graders. Jim has contributed articles to Math Horizons which may be
accessible online. This is a wonderful book for students and teachers
alike. Sophisticated mathematics is made accessible to everyone. Written
with humor, thoughtfulness and a real sense of where people have
difficulties and how to get around them, Tanton puts his finger on the
pleasures and promises of each problem. Not to be missed, no matter how
experienced or inexperienced you are." (MAA, 240 pp, 2001)
 79. Carol Vonderman
How Math Works: 100 Ways Parents and Kids Can Share the Wonders of Mathematics
 "Fascinating explanations, activities,
profiles of history's most noted mathematical thinkers, and experiments
introduce young readers to the world of mathematics." (Putnam, 192 pp,
1999) (Ages 12 +)
 80. Norbert Wiener
ExProdigy: My Childhood and Youth or I am a Mathematician or Cybernetics or The Human Use of Human Beings: Cybernetics and Society
 Norbert Wiener was one of the greatest applied
mathematicians of this century, and had a great impact on the invention
and uses of robots and computers. His writing is clear and elegant. The
last book mentioned does not have a single equation. Anything by him
that you can find in a library would be good, if you can understand it.
 81. Robert Wright
Nonzero: The Logic of Human Destiny
 "In defiance of the recent scorn heaped on speculations positing progressive or directional laws of history, Robert Wright believes that game theory offers the framework for interpreting such seemingly disparate phenomena
as the invention of writing, DNA, and the World Trade Organization as
parts of an overarching pattern. The "logic of human destiny" Wright
refers to in his subtitle is the logic of nonzero  that nonzerosum
games inherently provide more fitness for survival than zerosum games
in the long run, and that nonzeroness breeds more nonzeroness by
opening up new and more elaborate ways to profit and thrive." (Vintage,
448 pp, 2001)
