Robert Bosch

Statement

There are two wolves inside me—a mathematician and an artist—and I feed them equally well. The mathematician wolf is fascinated by the various roles that constraints play in optimization: sometimes they make problems much harder to solve, and other times, much easier. The artist wolf is fascinated by the roles that constraints play in art: all artists deal with constraints that are forced upon them, but many also choose to impose their own constraints. The benefit of this was well expressed by Joseph Heller (while paraphrasing T.S. Eliot): "If one is forced to write within a certain framework, the imagination is taxed to its utmost and will produce its richest ideas."

Artworks

An open knight's tour of an 81x81 chessboard. This tour is a tour of tours, if you will, each one an open knight's tour of a 9x9 chessboard. If you get up close and follow the knight's path from its start (in the lower left corner) to its end (near the upper right corner), you will notice that the knight makes its way from 9x9 board to 9x9 board to 9x9 board in Peano-curve-like fashion. And if you step back and view the piece from a distance, you will see that the knight's tour resembles a 9x9 latin square—it is made of 9 different "motif" tours and has one copy of each in each row and one copy of each in each column.

An open knight's tour of an 81x81 chessboard. This tour is a tour of tours, if you will, each one an open knight's tour of a 9x9 chessboard. If you get up close and follow the knight's path from its start (in the lower left corner) to its end (near the upper right corner), you will notice that the knight makes its way from 9x9 board to 9x9 board to 9x9 board in Peano-curve-like fashion. And if you step back and view the piece from a distance, thinking of the 9x9 array of 9x9 subtours as a 3x3 array of two different types of motifs, you'll find that you can interpret the piece as a 3x3 magic square.