Many authors wince at the stock-image covers that emerge after their books are handed off to their publishers. But I was lucky with Tetraktys.

The cover artist, Melissa Lucar, produced a graphic that I find beautiful. And I also enjoy it because its images are rooted in the story.

The deep blue field shows a manuscript called the Archimedes Palimpsest. It contains a tenth-century fragment of the Stomachion, a treatise by Archimedes (the ancient Greek mathematician of bathtub-and-“Eureka!” fame).

The Stomachion is a puzzle in which a square is carved into fourteen pieces according to a standard pattern—much like a tangram. To create the puzzle, the pieces are jumbled. The challenge is to reassemble them into a square. Here’s a picture of the Stomachion:

A puzzle may be a frivolous thing. But Archimedes, it seems, had a gift for spinning frivolity into insight. Some scholars believe that in the Stomachion, he invented a previously unknown field of mathematics: Combinatorics.

Today, combinatorics lies at the heart of computer science. It’s the branch of mathematics concerned with counting combinations of objects. How many ways are there to route a message over a network? How many ways are there to reassemble the fragments of a file? These are combinatorial problems. So Archimedes may deserve fresh laurels as a pioneer of computer science. In a nod to this accomplishment, his Stomachion flashes across the storyline of Tetraktys.

(The first Maytruscan brainteaser on this site, Puzzle #1: “Animals”, is a combinatorial puzzle.)