 It is notoriously difficult to convey the proper impression of the frontiers of mathematics to nonspecialists . Ultimately the difficulty stems from the fact that mathematics is an easier subject than the other sciences . Consequently , many of the important primary problems of the subject — ​ ​ that is , problems which can be understood by an intelligent outsider — ​ ​ have either been solved or carried to a point where an indirect approach is clearly required . The great bulk of pure mathematical research is concerned with secondary , tertiary , or higher @-@ order problem , the very statement of which can hardly be understood until one has mastered a great deal of technical mathematics . 
