For Our Mathematical Pleasure
Jim Henle, Editor
Meaning to Please
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
ometimes mathematical structures are designed to
please. They are brought into this world not to serve
but to charm. They live not only because they are
true but also because they intrigue. They demand attention
because they excite wonder and delight.
Mathematics that is pleasurable is not new. But I think
that something has changed in the last hundred years or so.
Mathematics created speciﬁcally to please gets more
attention today. And there seem to be more mathematicians
(and others) whose private and public joy has been the
pleasure of their mathematical creations. It is this phe-
nomenon—the compelling mathematical structures, the
people who found them, and the society that appreciates
them—that is the focus of this column.
I’ll set the stage today by talking a little about mathe-
matical structures, about mathematical pleasure, and about
intention. Then I’ll show you something unexpected.
To the world, mathematical expertise is special. Still more
special is the capacity to appreciate mathematical beauty.
And most special of all is the intelligence and sensitivity to
create beautiful mathematical structures. But special, it turns
out, is not rare. I taught a course last year that was speciﬁcally
for students with no required mathematical background. I
asked the students to create structures. I gave them some
background and schooled them in some mathematical aes-
thetics. They came up with some gems.
When the preliminaries are over, I’ll show you three examples:
THE MATHEMATICAL INTELLIGENCER Ó 2018 Springer Science+Business Media, LLC, part of Springer Nature