The first page contains small thumbnail photographs of 17 living mathematicians who are interested in the Reimann hypothesis. This is the first book that I have seen that focuses on people who are alive and doing leading edge mathematics. I love it!

I do not recognize even one name on the page. I am a little surprised to see that most of them appear to be past 40.

What appears to be missing is a whole series of mathematics books, written by mathematicians, that clearly describes a field of study in terms of the basic ideas and theorems, as well as the current difficulties, in a manner that is more conceptual than textbook. Current textbooks appear to focus on drill and practice as one "learns" the techniques, but it is difficult to see why the techniques are important or where it is leading. And most of the techniques are low level algorithmic procedures rather than meta-level problem solving approaches.

Even this book fails to mention the use of technology (e.g. Mathematica) to help pursue the ideas related to prime numbers although many of the images in the book were generated by some form of computer graphics software.

There are a few important ideas that underly much of mathematics: the concept of function and limit and that of types of number. Much of calculus is actually about types of number as one plays with functions and limits that push the boundaries of our understanding of number. Calculus is about limits and continuity and either very large numbers or very small numbers. And so is much of number theory.

How can one construct a map that shows either (or both):

• the connections among mathematicians (dead or alive)
• the connections among ideas ?

Many of the books I have purchased in the last few years are about one number (pi, e, golden ratio, Euler's ratio, infinity). This has the merit of being a mind-sized chunk.

At the moment I have no clear idea of what the major areas of interest are for mathematicians. It should be possible to identify these in terms that are understandable to the non-mathematician. And mathematicians need to improve their communication skills. One component of this would be a collection of mind maps that show how various people are conceptualizing their field and how they map their strategies. We need to get these strategies out in the open, explicit, so they can be scrutinized.

The prologue mentions a book called "The Joy of Sets". I must try to track this down. Set theory is one way to conceptualize number and this may be an interesting introduction to the topic.

I have spent a very enjoyable half-hour in amazon.com . There are many superb books out there on mathematics. I was surprised to see that The Joy of Sets was written by Keith Devlin. It does look good. Another author worth keying on is George Simmons. I will pursue this when I return to Lethbridge.

Now to have a look at the Riemann book....

Why stop with only one bivariate taxonomy? What other ways are there to categorize whole numbers:

• odd, even
• modulo n (what happens as n approaches infinity?)
• rectangular, triangular, square, hexagonal, ...

Do any of these categories have interesting properties?