This is a review of the current research in mathematics involving breadth of ideas. Research includes topics in number theory, classification of all finite simple groups, the representation of group aids in their application to the study of symmetry. (Author/SA)

Applies exponential growth and the speed of doubling times to the energy crises. Increases comprehension of this mathematical law and the significance of findings made through its use. Examines statements from authoritative sources on energy to illustrate the lack of understanding of arithmetic's relationship to the energy crisis. Suggests ways to…