The Harley Quin stories (this collection, plus two later stories) are amongst the most peculiar mysteries ever written. (They certainly are Dame Agatha's most peculiar. They were also her personal favorites.)

The broad outline is always the same. One Mr. Satterthwaite, elderly and independently wealthy, finds himself embroiled in an old mystery or a soon to happen tragedy. Out of nowhere, Mr. Quin, or some surprise signal from him, pops up, and by the most innocent and nonleading of questions, Mr. Satterthwaite finds himself unraveling the mystery. He doesn't actually solve it, so to speak, but just finds that the relevant facts are suddenly apparent.

The stories are best read in order (in particular, the collection does not have a table of contents, no doubt to discourage random access), as the sense of strangeness grows from story to story. One finds oneself embroiled in the metamystery of who or what is this Harley Quin.

In "The Bird With the Broken Wing", Mr. Satterthwaite finds himself called to house Laidell by Quin via a round of "table turning" (a forerunner of the Ouija board). By this time in the stories, Mr. Satterthwaite knows that a call from Quin is always important, and he leaves for Laidell immediately.

The owner turns out to be "a most brilliant mathematician", who had authored a book "totally incomprehensible to ninety-nine hundredths of humanity". And like the impact his professional work had on ordinary people, so too went his personality. He was essentially one with the furniture, whom servants and guests equally had trouble noticing. And then something happens....

Shares a theme with the Father Brown story, "The Invisible Man." The use of math here plays on biases against certain academic types.