Burton H. Camp

Suggested Problems for Mathematical Research

The following list of problems is suggested as the result of a letter sent out to about three hundred members of the Association, all of whom had exhibited recent interest in research, principally of the socalled practical type. The letter suggested that the practical worker had problems which the mathematician ought to be working at and that mathematicians would be glad to work on them if they might be told what they were. Mathematicians were constantly being accused of being out of touch with things that really mattered, but if that was true, it was not because they preferred to be. Some of the suggestions that members were good enough to send do not appear on this list. Many of them have had their forms altered more or less, in some cases perhaps so as to become unrecognizable to those who sent them. This has been necessary in order to present what seemed to be the underlying mathematical problems that were really holding up progress, although they may not have been put initially in such concrete forms. The author has made some progress on almost all of these problems himself, i.e., in each case he has pushed the analysis far enough to be confident that the problem will not simply fade out when looked at closely. In none of the cases presented here, however, does he now have a complete and satisfactory solution. Occasionally a solution developed after a little study; in such a case the solution was sent back to the sender and the problem does not appear here. It is quite likely that solutions of some of the others have actually been published, for the original list comprised such a wide variety of fields that it was not possible to search the literature carefully in all cases.