A presentation to the AAAS

Professor to outline dynamic history, uncertain future of mathematics

The practice and instruction of mathematics have changed over history, and more changes are in store, according to Brown Professor Joan L. Richards, who will join a discussion of "The Changing Environment of Science" from 3 to 6 p.m. Feb. 14 at the annual meeting of the American Association for the Advancement of Science.

PROVIDENCE, R.I. -- As the new millennium approaches, mathematics is struggling with an identity crisis that may change the way the subject is studied and taught, said Brown Professor of History Joan L. Richards.

Factors like the increasing use of computers and the growing need of universities to justify their investments in individual departments may influence mathematics instruction and study, Richards said. For example, in recent years some universities have begun to dissolve their math departments and integrate courses like statistics into other areas of the curriculum. Mathematics must now be defined by its ability to be flexible, Richards said.

Richards will talk about the "Changing Terms of Mathematical Demonstration: the Natural, the Rigorous and the Flexible," during a symposium on the changing environment of science from 3 to 6 p.m. Feb. 14 at the annual meeting of the American Association for the Advancement of Science.

Math "is a chameleon subject. It will change to fit the needs and society which it is in," Richards said. She pointed to the 18th century, when scholars were driven by the desire that their work have meaning. Mathematicians did not deal with negative or imaginary numbers because they wanted their work to have a connection to the natural world. They did not want to be identified with religious ideas about what was right or certain.

Early in the 19th century, mathematicians found a community of support in the professional association Ecole Polytechnique in France. Mathematicians were no longer worried about being attacked for doing something that may have been perceived as empty and meaningless, said Richards.

Soon math began to be defined by rigor - the idea that equations do not always need to have a numerical meaning. Letters were substituted for numbers, and rules were established on how to compute them. That notion has prevailed in mathematics throughout the 20th century, said Richards. It is viewed as allowing math to be pure and transcend the messiness of human interactions.

But after nearly two centuries of consistency in the study of mathematics, change is again likely. "People tend to assume math was a constant over time," said Richards. That idea is proven incorrect by its history.