For Our Mathematical Pleasure
Jim Henle, Editor
This is a column about the mathematical structures that
give us pleasure. Usefulness is irrelevant. Signiﬁcance,
depth, even truth are optional. If something appears in
this column, it’s because it’s intriguing, or lovely, or just
fun. Moreover, it is so intended.
Jim Henle, Department of Mathematics and Statistics,
Burton Hall, Smith College, Northampton,
MA 01063, USA
aymond Smullyan—logician, magician, mathemati
cian, puzzlist, and Taoist philosopher—passed away
last year at the age of 97. In each of his vocations, he
made serious contributions. But in his heart, and from his
head to his toes, he was an entertainer.
In gatherings large and small, among friends and among
strangers, Ray was ‘‘on.’’ If there was a piano, there would
be music. If there was a deck of cards, there would be
tricks. And if there was conversation, there would be sto-
ries, jokes, and paralyzing paradoxes.
Smullyan had important things to say about logic, about
knowledge, about mathematics, and about the meaning of
life. To bring his ideas to the public, he created libraries of
fantasies, puzzles, and conundrums. It’s my belief that
these were more than means to an end. They were really
his greatest joy. The professor professed—so the enter-
tainer could entertain.
Smullyan came to Smith College a number of times at
my invitation, but I can’t claim I really knew him. I base my
conclusions on his choice of careers, his books (especially
the memoirs), and on the recollections of others. In Four
Lives: A Celebration of Raymond Smullyan,
Claudia Schaer wrote:
I soon learned that he brings his deck of cards
everywhere and does magic tricks not just in restau-
rants, but at almost any opportunity, bringing a smile
to strangers who ﬁnd themselves in his proximity. He
just as gladly played at the piano.
One of his thesis students, Robert Cowen, wrote:
Whatever Ray does, be it in mathematics, puzzles,
music, or magic, is characterized by beauty and ele-
gance. Also, it is always very entertaining. In fact, Ray
is the ultimate entertainer; he will always have
something to delight you!
There were logic puzzles before Raymond Smullyan,
he raised the genre to the level of art. His ﬁrst puzzle book,
What Is the Name of This Book?
is pure pleasure. The
puzzles are populated by knights—who always tell the
truth, and by knaves—who always lie.
Here is one of Smullyan’s elegant puzzles:
I saw a pair on the island of knights and knaves. I
asked, ‘‘Is either of you a knight?’’ One fellow replied
and from his answer I knew what sort person he was
Jason Rosenhouse and Raymond Smullyan, Dover Books, 2014.
The history of the logic puzzle goes back at least 150 years to Lewis Carroll. Arguably, it is thousands of years old, and begins, perhaps, with the liar paradox of
This sort of logic puzzle appears in Maurice Kraitchik’s Mathematical Recreations (W.W. Norton, 1942). Kraitchik may have originated the form.
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