Mathematical Knowledge Management

INTRODUCTION Mathematical knowledge is significantly different from other kinds of knowledge. It is abstract, universal, highly structured, extraordinarily interconnected, and of immense size. Managing it is difficult and requires special techniques and tools. Mathematicians have developed (over the last two or three millennia) many techniques for managing mathematical knowledge. For example, there is a large collection of techniques based on the use of special symbols and notations. Although these techniques are quite effective and have greatly advanced mathematical practice, they are primitive in the sense that the only tools they require are pencil and paper, typesetting machines, and printing presses. Today mathematics is in a state of transition. Mathematicians are using the Internet in new ways to find information and to share results. Engineers and scientists are producing new kinds of mathematical knowledge that is oriented much more to practical concerns than to theoretical interests. This is particularly true in the field of software development where software specifications and code are forms of mathematical knowledge. Computers are being pushed to perform more sophisticated computations and to mechanize mathematical reasoning. Mathematical knowledge , as a result, is being produced and applied at an unprecedented rate. It is becoming increasingly difficult to effectively disseminate mathematical knowledge, and to ascertain what mathematical results are known and how they are related to each other. Traditional ways of managing mathematical knowledge are no longer adequate, and current computer and communication technology do not offer an immediate solution. Since mathematical knowledge 2977 Mathematical Knowledge Management is vital to science and technology, and science and technology is vital to our society, new ways of managing mathematical knowledge based on new technology and new theory are needed. This article introduces the main issues of managing mathematical knowledge. It is organized as follows. The Background section describes mathematics as a process of creating, exploring, and connecting mathematical models. The special characteristics of mathematical knowledge and the four main activities that constitute the management of mathematical knowledge are discussed in the Main Focus of the Article. The Future Trends section introduces Mathematical Knowledge Management (MKM), a new field of research, and discusses some of the challenges it faces. The article ends with a conclusion, references , and a list of key terms. The management of mathematical knowledge is an emerging field of research. Researchers are just starting to build a foundation for it. This article focuses on the core concerns …