*Unexpected Links between Egyptian and Babylonian Mathematics,* Jöran Friberg, 2005. xii + 294 pp., $64.00 hardbound. ISBN 981-256-328-8. World Scientific Publishing Col, 5 Toh Tuck Link, Singapore 596224.

Teachers of mathematics and history of mathematics often use examples from ancient Egyptian and Babylonian sources to show the variety and sophistication of millennia-old mathematics. Although examples from these two cultures are often demonstrated in the same class, rarely does a teacher show connections between the two. Mainly, this is because scholars generally have thought there were few connections, if any.

However, Jöran Friberg, a noted scholar of ancient Babylonian mathematics who has also written about Babylonian roots of Greek mathematics, took a more careful look, especially at some cuneiform tablets from the ancient town of Mari. Mari was farther west than most Babylonian sites and closer to the trade routes to the Mediterranean (and hence to Egypt). He found variations in the numeration system, making it closer to Egypt’s base ten. But more significantly, he found problems that resembled some of the examples in Egyptian papyri, including some of the famous problems, such as the problem of the sum of powers of seven, noted as similar to the nursery rhyme about the man with seven wives on the road to St. Ives. He also found similarities in calculation techniques, linear algebra problems, and the well-known calculation of the volume of a truncated square pyramid. Notably, the connections appear at several different chronological periods, from early in the second millennium BCE up through the Egyptian-Greek-Roman work at the start of the Common Era.

Friberg concludes that there are many links that had previously not been noticed. This book is very technical (with detailed references to actual papyri and cuneiform texts) and could not be easily used in a class setting. However, the links he points out could be described to demonstrate that ancient mathematics was not just a collection of interesting examples, but a commerce of ideas that would later become the foundation of Western mathematics.

Lawrence Shirley, Professor of Mathematics, Towson University