The mystery of the prime numbers: a review

The Mystery of the Prime Numbers: Secrets of Creation v. 1, Matthew Watkins (Author), Matt Tweed (Illustrator). Inamorata Press, 2010.

The author and illustrator describe some of the mysteries of the distribution of primes, ending with Riemann's harmonic decomposition of the distribution. (If you don't understand what all that means, you will if you read the book and concentrate a lot). It is the first part of a trilogy which the author promises will culminate in a connection with quantum theory.  I can't wait.

The most remarkable thing about this book is the presentation.  You do not have to understand symbolic math.  The ideas are communicated using many, many pictures and metaphors. For example, you have a number of apples and you can't arrange them into a rectangle (a row doesn't count as a rectangle) then the number is a prime. Technical terminology is avoided, especially when the terminology consists of ordinary English words with new meanings.  So a prime factorization of a number is a "cluster" — and of course it really is since the order the primes occur in is irrelevant. On other occasions he will use the technical term (for example "distribution of primes" but warn you against your understanding being contaminated by the everyday meaning such as "distribute two pencils to each student").

The author is not afraid of saying the same thing several times, using different metaphors and rewording.  He will notice that some ideas will make you uncomfortable, such as the prime number theorem which "ought" to tell you the exact number of primes less than a number instead of merely estimate it.  (How many of your teachers ever admitted that an idea may make you uncomfortable and this is why it does…)  His explanation of functions and graphs is pictorial (using the endograph — arrows from one place to another on the real line) and kinetic (a ball rising from the x axis, hitting the graph, and being knocked horizontally to the y axis).

This makes me believe a reader who finds algebraic equations hard to understand and the nomenclature baffling can still get a reasonable mental picture of what primes are and what the Prime Number Theorem and Riemann's theorem on the distribution are actually saying.  It won't be easy: such a reader will have to concentrate and stop and think a lot (and I hope doodle pictures) and at times it will be slow going.  But this book makes it possible for someone who has no self-confidence in their ability to understand math to understand some deep stuff that many mathematicians find as astonishing as anything in math.

If we had a hundred authors writing books like this about different parts of math we would (in the long run) have fewer people who hate math or claim it all sounds like gibberish.

The long time reader of Gyre & Gimble will note that I have been saying for years that math should be explained like this.  So naturally I am pleased to recommend this book.  (Even so, all the times I taught primes I never thought of defining a prime number by saying you can't arrange your trinkets into a rectangle.  Oh, the chagrin…)


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