Unsolved Problems in Number Theory

Mathematics often owes more to those who ask questions than to those who answer them. The solu tion of a problem may stifte interest in the area around it. But "Fermat's Last Theorem", because it is not yet a theorem, has generated a great deal of "good" mathematics, whether goodness is judged by beauty, by depth or byapplicability. To pose good unsolved problems is a difficult art. The balance between triviality and hopeless unsolvability is delicate. There are many simply stated problems which experts tell us are unlikely to be solved in the next generation. But we have seen the Four Color Conjecture settled, even ifwe don't live long enough to leam the status of the Riemann and Goldbach hypotheses, of twin primes or Mersenne primes, or of odd perfeet numbers. On the other hand, "unsolved" problems may not be unsolved at all, or may be much more tractable than was at first thought.