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Outline for Dissertation

Title: Automated Theory Formation in Mathematics

Committee: E. Feigenbaum, C. Green, B. Buchanan, D. Knuth


Chapter 1: 
Overview
A self-contained summary of the entire project.

Chapter 2: 
Model of Mathematical Research
Give special attention to the summary of this chapter

Chapter 3: 
Analysis of Scientific Discovery
Examples drawn from several domains, not just no. thy

Chapter 4: 
Synthesis of Scientific Discovery
Again, several examples, corr. to those in the earlier chapter

Chapter 5: 
Details of Representation
Show how consideration of the problem led to to the evolution of the reprs
for concepts, for heuristics, etc.

Chapter 6: 
Details of the Flow of Control
Again motivated by the problem and/or model. Job-list agenda, reasons.

Chapter 7:
Initial Concepts
What they were, why.

Chapter 8:
Guiding Heuristics
How elicited, what they were, justifications, classified by generality.

Chapter 9:
Some Experimental Forays
Simple examples of AM in action, presented on several levels.

Chapter 10:
Some Detailed/Advanced Examples

Chapter 11:
Discussion of Results
What behaviors would indicate "successful" performance? Measuring performance.
Things AM did/didn't do but could/ probably couldn't do.
Numerical data: time, space.
Human engineering in such a system  (and in AM in particular).
Importance of various heurs. and kinds of heurs., various starting concepts, etc.

Chapter 12:
Conclusions
The kinds  of discoveries that AM could probably never make.
Uses for AM: most valuable as a co-researcher (not always master, nor servant).
Implications for math education.

Chapter 13:
Directions for Future Research
Parts of the grand plan still not realized in AM.
New ideas for future work on AM.
Extending AM to other domains in math and other fields.
Factoring out all the hack sci. discoveries.

Appendix 1:
The Theory of Maximally-Divisible Numbers

Appendix 2:
Introduction to BEINGs representation scheme

Appendix 3:
Some traces of AM in action

Appendix 4:
Some sample Concepts and Heuristics

Appendix 5:
Bibliography, Documentation

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Technical details of presentation

The thesis will be organized on 3 levels, for those wishing a 
cursory/detailed/complete look at the project.
For the former, the overview chapter alone must be a self-contained
introduction. For the medium, each chapter will have a 2-3 page
summary. For the latter, there is of course the entire document.