Martin Gardner on Numbers

“Mathematicians apply the word 'number' to hundreds of strange abstract beasts that are far removed from counting.” –Martin Gardner

Not many writers can attract a readership so broad it encompasses scientists, students, artists, writers, housewives, postmen, magicians, skeptics, philosophers and ad men. Especially when they write about math. But Martin Gardner, who would have celebrated his 100th birthday in October this year, did just that—nearly every month—for 26 years via his “Mathematical Games” column in Scientific American magazine. His columns, which ran between 1957 and 1983, introduced more people to more math than perhaps any textbook, treatise or classical tome. According to Colm Mulcahy, a professor of mathematics at Spelman College in Atlanta, Georgia, “Gardner was the best friend mathematics ever had.”

Remarkably, Gardner was not a professional mathematician and had virtually no formal math training after high school. He did, however, possess an extraordinary intellect, along with extraordinarily diverse interests. He loved puzzles, which his father, a geologist, introduced to him as a teen, and he was fascinated by magic and its overlap with math. His first Scientific American article described hexaflexagons, flat, two-sided paper constructions (related to one-sided Mobius strips) that appear to conjure extra faces out of thin air when flipped in a certain way. And many of his columns presented popular puzzles or card tricks made less mystifying once explained in numbers.

In this eBook, Martin Gardner: The Magic and Mystery of Numbers, we strove to create a new “slice” through this wealth of material—because as any Gardner fan knows, his mathemagical tricks and games have been collected in many forms, including the six-book Scientific American series he edited himself. Regardless of the vehicle, he worked playful references and challenges into almost everything he ever wrote; and this sampling is no exception. Here, we focus on all flavors of number, from common integers and negative numbers to figurate numbers and the exotic random number, Omega, which can be described but not computed.

Some of these columns are less well known than, say, his writings about flexagons, but they are no less fun. In true Gardner fashion, they leap from magic and games—as well as art, music and literature—to flashes of deep mathematical insight. Lattice integers become a billiards challenge and surreal numbers spawn a host of related games. The “abracadabric number e,” quoting French entomologist Jean-Henri Fabre, leads to spiders’ webs and compounded interest. The binary Gray code inspires a poem and cracks the classic Chinese Rings puzzle. Negabinary numbers, used to perform calculations on a chessboard, unveil the etymology of such words as ‘Exchequer’ and ‘bank.’ And binary numbers unlock mind-reading tricks and the Tower of Hanoi.

In every case, what appears here are the original columns, more or less as they first appeared. Even so, they remain current and include several conundrums still unsolved—such as whether the sum of irrational numbers pi and e is itself irrational. Almost every column also offers up problems for readers to solve and test their understanding—along with the answers for anyone easily frustrated. We hope that they will prove as inspirational to readers now as they did to earlier audiences.

–Kristin Ozelli
Book Editor