Consider a set of n points such that every line through any two of them also passes through a third point in the set. Must all n points be collinear?
Sylvester believed that the answer was no in the complex projective plane, but he had no idea what the answer was in the Euclidean plane. The problem lay dormant and unsolved for forty years.
In 1933, the Hungarian mathematician Paul Erdös (1913–1996), unaware of Sylvester's question, encountered the same problem but could not solve it.
His compatriot and friend Tibor Gallai (1912–1992) first provided him with a solution using projective geometry. Then, in 1943, Erdös posed the problem again in the American Mathematical Monthly.
