Capturing the Content of Mathematics for Collaborative Computer-Supported Document Development

Michael Kohlhase (School of Engineering and Science, International University Bremen)

In this talk I will survey the new opportunities for the development and dissemination of mathematical knowledge opening up by the Internet. It is plausible to assume that the way we publish mathematics will change radically in the next five years, and more generally that the way we do (conceive, develop, and verify) math. Of course, this development is not restricted to mathematics itself, but will also affect other well-conceptualized and highly structured areas like physics or engineering.

The trend towards high-quality Internet accessible math. is initiated by the availability of XML-based representation standards for mathematical formulae (MathML and OpenMath) together with corresponding browsers that allow to present formulae in LaTeX-quality, while retaining the flexibility of html.

The next step will inevitably follow: to represent the meaning of formulae, so that they can be transmitted to mathematical software systems like computer algebra systems, automated theorem provers, or proof presentation systems. The possibility of universal exchange of mathematical objects will radically change and de-centralize the way we work in mathematics, engineering and sciences.

In this talk, I want to discuss the infrastructure that is needed to conveniently and efficiently manipulate, visualize, and distribute mathematical knowledge on the basis of the OMDoc format (an extension of the OpenMath standard for the communication of mathematical objects). I will concentrate on the implications the trend towards content-oriented approaches to mathematics has on collaboration in the knowledge management process.

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