2023 Bridges Conference Art Exhibition

# David Richeson

## Artists

## Statement

In my mathematical career, I endeavor to bring the beauty, logic, applicability, and wonder of mathematics to a general audience. I do this through my teaching, research, writing, and speaking. I have always been interested in using mathematics to create and describe artistic objects, but it was not until those first stressful months of the COVID-19 pandemic that I saw that mathematical art could have therapeutic value. I realized that this interest of mine was an untapped way for me to share my love of mathematics with wider audiences.

## Artworks

A Latin square is an nxn grid in which every row and column contains all values 1 to n. A Graeco-Latin square is obtained by combining two Latin squares so each entry is an ordered pair of values—one from each Latin square—and no cells contain the same pair. Euler conjectured there are no examples when n is an odd multiple of 2. He was correct about 2 and 6 (the “36 officers problem”) but was wrong otherwise. A 10x10 example, presented as pairs of colors instead of numbers, graced the cover of Scientific American in 1959.
My 10x10 Graeco-Latin square is made from colored Truchet tiles. To obtain the design I numbered the squares top to bottom and bottom to top and rotated by 90° the 50 squares that are prime in one of the numberings.