This Sumerian clay tablet from ancient southern Mesopotamia shows a tally of sheep and goats using incised cuneiform characters.

Denise Schmandt-Besserat made the great discovery that the origins of writing are actually found in counting. This discovery began as most ground-breaking work does, with an unrelated pursuit. The University of Texas at Austin professor began her academic career in the 1960s. At that time, the main concern was not where writing came from but little bits of clay and their role in ancient Middle Eastern life. At nearly every Middle Eastern archaeological site, researchers found these perplexing little pieces of fired clay.

Though it was sure that these bits of clay played an important role in ancient civilization, for years no one knew what they were. Then along came Denise Schmandt-Besserat. The French-born graduate student, through a number of fellowships and grants, began what...