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C00002 00002	Outline for Dissertation
C00006 00003	Outline for Dissertation
C00011 00004	Technical details of presentation
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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



Outline for Dissertation

Title: Automated Theory Formation in Mathematics

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

Reading Committee: E. Feigenbaum, D. Knuth, A. Newell

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

Chapter 2: 
A Model for Creative Discovery in Science
	a) Scientific discovery as heuristic search
	b) Validating that simple model
		i) Analyzing a given discovery
		ii) Character of interdisciplinary research
	c) Questioning that model
		i) Second-order corrections to the model
		ii) Misleading character of polished results
		iii) Primary vs Secondary creativity

Chapter 3: 
Designing a Math Theorizer
	a) Choice of task domain to test out the model
		i) Why math?
		ii) What else could it be/ not be?
	b) Detailed model of math research
	c) Implications for an automated mathematician

Chapter 4: 
Implementing this System
	Gradual development of the representation and control structure
	

Chapter 5:
Some Experimental Forays
	Simple examples of AM in action, presented on several levels.
	Some Detailed/Advanced Examples

Chapter 6:
Discussion of Results
	a) Measuring performance.
	b) What was (not done? could (not) be done (with slight changes) by AM?
	c) Numerical data: time, space.
	d) Human engineering in such a system  (and in AM in particular).
	e) Expts on AM
		 Importance of various heurs.,
		 Importance of kinds of heurs., 
		 Vary the starting concepts, etc.

Chapter 7:
Conclusions
	a) Ultimately, what kinds of things could AM-lik systems do?
	b) Uses for AM-like systems: 
		most valuable as a co-researcher 
	c) Implications for math education.
	d) Directions for Future Research
		i) Parts of the grand plan still not realized in AM.
		ii) New ideas for future work on AM.
		iii) Extending AM to other domains in math and other fields.
		iv) 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

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.