“Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries?” So, stirringly, began David Hilbert at the beginning of the twentieth century. His wide-ranging list of twenty-three problems, heralded before the International Congress of Mathematicians in Paris, has inspired a stampede of research during this, the first of his future centuries. And the exciting news was that the third problem on his list concerned dissections!

It sounded wonderful, but there was a flip side: First, Hilbert proposed a negative result, challenging mathematicians to prove the impossibility of certain three dimensional dissections. Second, the problem was solved before the congress even got under way. Third, the problem has since been viewed as one motivated primarily by pedagogical concerns. So much for geometric dissection's brief membership in the vanguard of twentieth-century mathematics!