The Moment of Proof: Mathematical Epiphanies

Rating:
Summary: Delivers on the promise of the title
Review: A good mathematical proof can be better than sex.

My definition of the joy of mathematics:

You have a few facts, awkwardly arrayed. You have some idea of a new fact you think might be a logical consequence of those facts. You start finding ways of stating them more interestingly. This may lead you to defining new composite concepts. You play around with them for a while. Sometimes you have to throw them out and start over. Often if you are brilliant, once in a great while if you are me, things start falling into place rather elegantly. Then you finally discover a snappy way of articulating all the pieces of a problem and the proof pops out.

And it feels amazing.

This book allows people like me, who wish they could have these moments more often, to live them vicariously through the great selection of theorems and demonstrations Donald Benson has put together. I didn't find this book particularly hard to read. In fact, I often read it while walking -- wishing I had a chalkboard, admittedly. It is written for laypersons who are not afraid to spend quite a bit of time on a page: all the knowledge you need is there, but seeing how it fits together to produce a given result can take some effort. The proofs are all some combination of elegant, surprising, and subtle, and always cause a few minutes of ecstasy.

Rating:
Summary: Very few epiphanies make for a disappointment
Review: I found this book to be a disappointment. In the introduction, the author talks about proofs that occur due to a sudden burst of insight, a phenomena he calls a mathematical epiphany. The next point is that he hopes to share instances of mathematical epiphany with the readership. However, the material of the book is largely routine mathematics that has appeared in many other popular works. The promised aha! moments are practically nonexistent. There are no mathematical epiphanies to be found in the mathematics of secret codes, the finding of large primes, the development of the negative numbers and the fundamentals of a proof by contradiction or infinite descent.
That aside, the book is well written, as Benson explains things in great detail. Anyone interested in popular mathematics will find interesting topics, my point is that there are no points of revelation. Perhaps I have been spoiled by the material in "Aha! Insight", that wonderful book by Martin Gardner, where apparently difficult problems are suddenly solved by looking at them a different way.

Rating:
Summary: Fun exercises of medium to hard difficulty
Review: I specifically commend the very broad coverage of the subject of Mathematics for readers who may even be struggling to recall some elementary algebra. Even most educated people do not realize that Mathematics includes such things as Probability Theory, Game Theory, Finding Optimal Strategies, The Study of Prime Numbers, Map Coloring with no more than four colors and designing and deciphering Secret Messages.

I specifically appreciated the many excellent comments in marginal boxes and the frequent marginal notations of a "Dangerous curve" in many key areas. I also appreciated the comment near the end of having "finished the main course, and even the dessert, of our mathematical banquet" and the comment on page 298 about there being no Nobel Prize in Mathematics.

Rating:
Summary: Good for Laymen
Review: This book has been written for laymen, but unlike most such books manages to convey the flavor of mathematics. It also contains a fair bit of elementary combinatorics and number theory. It can take its place alongside Courant and Robbins' "What is Mathematics", and Hilbert and Cohn-Vossen's "Geometry and the Imagination." It could be read with profit and enjoyment by college freshmen intending to specialise in mathematics, and used in enrichment programs in high schools.My only cavil is that the book is too short (330 pages).

Rating:
Summary: An excellent summary of the BROAD Field of Mathemetics
Review: This is an EXCELLENT book on the broad subject of Mathematics - not just related to those topics that the general public understands as being Mathematics.

I specifically commend the very broad coverage of the subject of Mathematics for readers who may even be struggling to recall some elementary algebra.

Even most educated people do not realize that Mathematics includes such things as Probability Theory, Game Theory, Finding Optimal Strategies, The Study of Prime Numbers, Map Coloring with no more than four colors and designing and deciphering Secret Messages.

I specifically appreciated the many excellent comments in marginal boxes and the frequent marginal notations of a "Dangerous curve" in many key areas that may not be obvious to the general reader.

I also appreciated the comment near the end of the book of having "finished the main course, and even the dessert, of our mathematical banquet" and the comment on page 298 about there being no Nobel Prize in Mathematics.

Clearly a book to remember and one to make you think!

Rating:
Summary: Too serious
Review: This is not a college textbook, and, I think, it meant to be fun to read. Like most textbooks, the size of the book is too big - you need to sit down and hold a pencil to read it. All the fun will be gone if reading books this way. After all, we are not reading this book to make a living. Make the book smaller, easier to read. Get rid of the big margins. Most of the math in the book is elementary, who really needs the big margins?