There's a book out called The Mental Calculator's Handbook by Jan van Koningsveld and Robert Fountain, which naturally piqued my interest just by the title.

How does this book compare to existing books on mental math? Check out this review and find out!

First, you'll probably want to know what kind of mental math expertise the authors have. Robert Fountain is a British calculating prodigy who was the first of only 3 current International Grandmasters of Mental Calculation.

German mental calculation champion Jan van Koningsveld has held several world records relating to mental calculation, including taking only 3 minutes and 6 seconds to solve 10 problems, each of which involved multiplying two 5-digit numbers. You can find several videos online of his performances, and even if you don't speak German, they're easy to follow due to the numbers and his results being displayed.

At first glance of the contents, The Mental Calculator's Handbook doesn't seem to be much different than, say Arthur Benjamin's The Secrets of Mental Math. The first few chapters cover addition, subtraction, multiplication, division, and fractions.

Once you delve into the chapters themselves, they do begin with basic techniques similar to other books. I was pleased to discover, however, that they do take even these basic techniques farther than most books. The exercises at the end of each section, and the detail given about the techniques is written very clearly, so it's easy to understand.

This early attention to detail and emphasizing the finer points really begins to pay off when you begin learning the techniques in the later chapters, which include working out classic feats such as finding roots, our old friend calendar calculation, and the rarely-discussed factoring of numbers into their prime components.

The section on prime factorization was an especially interesting eye-opener. I was familiar with the basic techniques from my own work on primes in mental math, but the techniques here went much farther. Testing for divisibility by 2, 3, 5, and 9 are simple enough, but when many primes provide a challenge for divisibility tests, such as 7, 11, 13, and 37. The authors turn these into almost trivial challenges by showing how working with much larger numbers, such as 999 and 1,001.

Regular Grey Matters readers won't be surprised to know that I enjoy reading about and working out calendar-related challenges, and even here I was surprised! Besides just the basics of working out the day of the week for any date, you learn how to handle questions such in which years between 2000 and 2099 will Halloween fall on a weekend, and in which months of 1961 the 29th fell on a Sunday.

The Mental Calculator's Handbook winds up with brief biographies of various past mental calculators and their performances. This section especially was a very enjoyable read, and gives you an idea of just what can happen when such feats are demonstrated, and learn the sometimes sad and often amazing ways in which these performer's lives were affected.

If you're not sure of your own interest in mental calculation, I suggest starting with a more basic book, such as The Secrets of Mental Math and see if it's something you'll enjoy. Once you're ready to pursue it further, then you're ready for The Mental Calculator's Handbook, and it's greater attention to detail and mastery of the field. As a matter of fact, this book is a great bridge between the simpler mental math books, and the far more advanced ones, such as Ronald W. Doerfler's Dead Reckoning: Calculating Without Instruments.

Overall, if you're interested in mental math, and want to go beyond the basics, The Mental Calculator's Handbook is an excellent resource to take you to those next steps.