Let's restrict our attention to
creative theory formation in ⊗4mathematics⊗*: 
how to propose interesting new concepts  and plausible
hypotheses connecting them.
Although many great minds have introspected on this problem
[Poincare', Hadamard, Polya], we in AI all know the gulf that
separates smooth prose from smooth code.

The experimental  vehicle of my research
is   a    computer   program   called   ⊗2AM⊗* (for   ⊗2↓_A_↓⊗*utomated
⊗2↓_M_↓⊗*athematician),   which carries out some of the activities involved
in mathematical research: noticing simple relationships in empirical data,
formulating  new  definitions  out  of  existing  ones,  proposing some
plausible conjectures (and, less importantly, sometimes  proving them),
and evaluating the aesthetic "interestingness" of new concepts.

(1) What are these heuristics? Where do they come from, what is their
justification, their power?

(2) What is the AM program like? What is its control structure, its
representation for a concept? How do the heuristics fit in?

(3) How does the AM program work? What does it start with, what does it
do from there? How and why?

(4) What can we all learn from AM? Abstracted out, what are the new ideas,
the traps that were fallen into?