What is the Hyperreal Dictionary of Mathematics?
You could read a whole essay about that question, here. To sum up, the Hyperreal Dictionary of Mathematics (HDM) is a virtual and at the same time immensely practical large-scale/long-term development project concerned with reengineering mathematics using computers.
Quick Links
Discussion
Directory and Overview
For a relatively current and complete account of what we have accomplished and where we are headed, please refer to the HDM Directory. For a depreciated but still potentially interesting decomposition into subject areas, see The important components of the HDM project. Here, briefly, is an overview of four high-level areas of inquiry, discussed in detail in the Directory, which seem to cover the technical portions of the project:
- Mathematics : This is what the project is "about". To target mathematical knowledge in the long run, we need to assemble some core (meta-)mathematical knowledge early on.
- Linguistics : We would like to find automated ways of "ripping" mathematical knowledge from existing texts, in order to save time and effort associated with typing data into the computer. Natural Language Processing is generally considered to be a Hard Problem(tm). Our ansatz is that it is at least somewhat easier where mathematical language is concerned.
- Artificial Intelligence : Here we are concerned with all of the myriad issues related to managing and utilizing a body of knowledge about mathematics.
- Human-Computer Interaction : This will be a relevant topic at all stages of the project (writing code, writing math, trying to access information stored in the computer, interacting with other project participants, etc.). We might say that this is the glue that holds this all together.
Related work
A project this broad is necessarily related to lots and lots of other research, both completed and on-going. Integrating results and work-effort from other efforts will be of fundamental importance to the HDM project. (Integrative thinking is important for the HDM product, too, of course!) Accordingly, here is a fairly prominent link to a page with HDM-related things to check out.
What will make HDM different from other computer-math systems?
This is a question we frequently hear. A quick answer is that HDM will be:
- Comprehensive;
- NL-compatible;
- Agential;
- Correct (wherever applicable); and,
- Free as in Freedom.
Further discussion: Things to think about & discuss elsewhere!
Projects