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Outline for Dissertation

Title: Automating the Discovery of Mathematical Concepts

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
	Final set of starting concepts; initial info. (incl. heuristics) about each.

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 by AM?
	c) Numerical data: time, space.
	d) Human engineering in such a system  (and in AM in particular).
	e) Experiments on AM
		 Importance of various heurs.,
		 Importance of kinds of heurs., 
		 Vary the starting concepts, etc.

Chapter 7:
Conclusions
	a) What gives AM it's power? Identifying the crucial ideas.
	b) Ultimately, what kinds of things could AM-lik systems (never) do?
	c) Uses for AM-like systems: 
		Synergy: AM most valuable as a co-researcher 
	d) Implications for math education.
	e) 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:
History of the "BEINGs" representation scheme

Appendix 3:
Some sample Concepts and Heuristics, as coded in LISP

Appendix 4:
Some traces of AM in action

Appendix 5:
Bibliography, Documentation, Acknowledgements