If You Would Know the Number

For those whose appreciation of recreational mathematics dates back no earlier than Martin Gardner’s “Mathematical Games” articles in Scientific American, it may be a bit startling to find that mathematics writing for a “general audience” has been around for centuries.

The book A Wealth of Numbers: An Anthology of 500 Years of Popular Mathematics Writing, edited by historian and writer Benjamin Wardhaugh (Princeton University Press), is an eye-opening collection of fascinating mathematical tidbits, aimed at “ordinary people.”

The 100 or so extracts included in the book add up to a history of mathematics that “shows the subject through the eyes of the interested and the curious from the sixteenth century to the present,” Wardhaugh notes.

The extracts also offer telling glimpses of different styles of mathematical exposition and how they may have been influenced by different mathematical audiences, different social contexts, and different senses of the use of mathematics, he adds.

Wardhaugh’s first example goes back to 1564 and a book titled The Welspring of Sciences, written by London teacher and writer Humfrey Baker.

The final section of Baker’s book includes a selection of mathematical amusements. Perhaps you’ll recognize the following number trick:

If you would know the number that any man doth think or imagine in his mind, as though you could divine . . .

Bid him triple the number. Then, if the result must be even, let him take half of it; if it be odd, let him take the “greater half” (that is, the next whole number above half of it). Then bid him triple again the said half. Next, tell him to cast out, if he can, 36, 27, 18, or 9 from the result: that is, ask him to subtract 9 as many times as possible, and keep the number of times in mind. And when he cannot take away 9 any more, tell him to take away 3, 2, or 1, if he can, so as to find out if there is anything left besides the nines.

This done, ask how many times he subtracted 9. Multiply this by 2. And if he had any thing remaining beside the nines, add 1.

Baker then provides two worked examples showing how you would come up with the initial secret number.

I find it fascinating to ponder the social context in which Baker worked and produced his book. Queen Elizabeth of England was early in her reign at that time; William Shakespeare was born in 1564. There was no Royal Society (founded in 1660).

Who were Baker’s readers? What sorts of students did he have?

Baker’s writing was undoubtedly popular, and this book, later titled Baker’s Arithmetick, went through numerous editions down to 1670.—Ivars Peterson

What is Math Comm

MAA Mathematical Communication (mathcomm.org) is a developing collection of resources for engaging students in writing and speaking about mathematics. The site originated in the MIT Department of Mathematics and was expanded through support from an NSF grant.