Group theory began as a branch of pure mathematics. Mathematicians, through their study of the way numbers behave and how they may be treated, often discover theorems and relationships that may appear to have no immediate application to the physical world. On the other hand, physical scientists--chemists and physicists--attempt to understand how objects in the physical world behave, for instance how chemical molecules interact with each other in chemical reactions. They seek ways of visualizing these reactions and methods of predicting and calculating whether or how fast a reaction may be expected to occur. Since the days of Gallileo (1564-1642) and Isaac Newton (1642-1727), scientists have found that mathematics provides useful methods for scientists to accomplish this task. Group theory is one of a number of branches of mathematics that have proven useful to chemists and physicists in their work.

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