Dear Professor Levy,

I imagine that Professor Amarel (or Bruce  Buchanan) has told you who
I am,  what my interests are, etc.   Professor Amarel has informed me
that Friday, Feb. 20, would  be a good day for  me to give a talk  at
Rutgers about my thesis research.  That is fine with me. He indicated
that you would coordinate the final plans for my visit.

I  am mailing  to him  a nicely-printed  title and abstract  for that
talk.   A somewhat garbled  version is  appended to  the end of  this
note.

I will try to call you  tomorrow (Monday, Feb.  9) around 1pm and 5pm
your time, and again Tuesday at those  times.  I will be at the  A.I.
Lab (415-497-4971)  off and on  those days.   Of course you  can also
reach me via the Arpanet (DBL@SU-AI).

If you attend the ACM conference in Anaheim next week, perhaps we can
meet there. If not, I'll see you at Rutgers.

Sincerely, 
Doug Lenat

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Automating the Discovery of Mathematical Concepts


We often face the difficult task of formulating new research problems
which must be soluble and yet  nontrivial.  Can such "originality" be
mechanized? Well, how about ⊗4partially⊗* mechanized?

This   talk  describes  one  approach  to  partially  automating  the
development of new mathematical concepts.  First, we  consider how to
⊗4explain⊗*  a discovery,  by  systematically analyzing  it  until it
seems obvious. Inverting this reduction procedure, we obtain a simple
scheme for ⊗4generating⊗* new discoveries.   Many heuristic rules are
needed  for guidance, to combat  the combinatorially explosive nature
of this process.

An experimental interactive  LISP program  has been developed,  which
carries out  some of the  activities involved in  simple mathematical
research:   noticing   obvious  relationships   in   empirical  data,
formulating new  definitions  out of  existing  ones, proposing  some
plausible conjectures, and estimating the potential worth of each new
concept.

After explaining the workings  of this program,  we can discuss  such
	issues as:
(i) Choice of task  domain: Why mathematics?  Suitability  of various
	other sciences.
(ii) Experiments one  can perform on this program: What do we hope to
	learn?
(iii) The role of the human user: spectator ⊗4vs⊗* co-researcher.
(iv) How can  one judge the performance  of a concept-proposer  which
	has no fixed goal?
(v) What kinds of discoveries are most difficult to mechanize?
(vi) Can the reasons for ⊗4considering⊗* X aid in ⊗4proving⊗* X?