Historic Conjectures: More Sequence Mysteries

Among notable recent achievements in mathematics are the resolutions of some celebrated long-standing conjectures: the proof by Deligne of the Weil conjectures; by de Branges of the Bieberbach conjecture; and by Faltings of the Mordell conjecture. On the other hand, the Fermat problem,* the Riemann hypothesis, and the socalled Poincaré conjecture remain unresolved, though for brief periods it was claimed that they too had been settled. In any case, it seems timely to present some scattered facts about the origins of some of these problems. For most of what follows in this section, aside from the next paragraph, I am indebted to Professor M. R. Choudhury of the University of Dhaka, Bangladesh.