Click to view The First 101 Interesting Numbers
How does a book like this come about? The answer is hardly elaborate. It got underway when a granddaughter of the first author was about to have birthday number six. Inasmuch as she had already displayed considerable interest in umbers and arithmetic, the proud grandparent had the idea that since six is, among other things, the first perfect number (the sum of its proper divisors 1, 2, and 3) as well as the product of 1, 2, and 3, maybe a listing of a good many of those and some other of its properties would be of interest to the young genius. The first draft of the entry for the number 6 herein was born. Next came a similar need for listing properties of the number 14. This short story became olonger as other birthdays arose, and eventually, the first draft of this book was developed somewhat as a hobby, and then with the help of valued colleaguse, it was born in its present form.
The title of the book is actually an inside joke. One way to define an “interesting” number is to require that it has some unique property. (To say that 17 is the 17th number doesn’t count.) To prove that every counting number is interesting it is sufficient to note that 0 and 1 are clearly interesting, so the set of interesting numbers is n9ot empty. Now suppose that some non-interesting numbers exist. Then the set of non=interesting numbers is not empty, hence there is a smallest non-interesting number. This is certainly a unique property. Contradiction. (Sorry about the non-constructive proof, Fred.
This is a joke, but it does hint that it is not interesting (every time, at least) that a number is the sum of four squares. I tend to want properties that are rare, if not unique.
We hope the reader enjoys the outcome.