The purpose of this research is to investigate computer technology in support of the representation and manipulation of mathematical knowledge. The long-term goal is to produce a consistent and constructive representation of mathematics, driven by the needs of significant applications. Key issues to be examined include the use of object-oriented multiple representations, the encoding of dependencies, and techniques for incorporating ambitious data bases of formulas of various types. These applications might include o The development of modern interactive systems for general mathematics. o Integrated applications which involve access to large data- bases of mathematical or physical knowledge, approximation techniques, and "expert" systems; areas of interest include computational fluid dynamics, robot planning, and computer- aided design of solids. o Publication of hypertext-like technical reference texts or educational material which would include not only mathematics as typeset material but mathematics as representations and executable algorithms. o Interactive manipulation of scientific software (program text, libraries) for program generation, (human) comprehension, improvement, and validation.
