COMMENT ⊗   VALID 00003 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	.DEVICE XGP
C00004 00003	5↓_Overview_↓*
C00014 ENDMK
C⊗;
.DEVICE XGP

.FONT 1 "BASL30"
.FONT 2 "BASB30"
.FONT 4  "BASI30"
.FONT 5  "BDR40"
.FONT 6  "NGR25"
.FONT 7  "NGR20"
.TURN ON "↑α↓_π[]{"
.TURN ON "⊗" FOR "%"
.PAGE FRAME 54 HIGH 80 WIDE
.AREA TEXT LINES 4 TO 53
.COUNT PAGE PRINTING "1"
.TABBREAK
.ODDLEFTBORDER←EVENLEFTBORDER←1000
.AT "ffi" ⊂ IF THISFONT ≤ 4 THEN "≠"  ELSE "fαfαi" ⊃;
.AT "ffl" ⊂ IF THISFONT ≤ 4 THEN "α∞" ELSE "fαfαl" ⊃;
.AT "ff"  ⊂ IF THISFONT ≤ 4 THEN "≥"  ELSE "fαf" ⊃;
.AT "fi"  ⊂ IF THISFONT ≤ 4 THEN "α≡" ELSE "fαi" ⊃;
.AT "fl"  ⊂ IF THISFONT ≤ 4 THEN "∨"  ELSE "fαl" ⊃;
.MACRO B ⊂ BEGIN VERBATIM GROUP ⊃
.MACRO B1 ⊂ BEGIN PREFACE 0 INDENT 0 SINGLE SPACE ⊃
.MACRO E ⊂ APART END ⊃
.MACRO FAD ⊂ FILL ADJUST DOUBLE SPACE PREFACE 2 ⊃
.MACRO FAS ⊂ FILL ADJUST SINGLE SPACE PREFACE 1 ⊃
.FAS
.PAGE←0
.NEXT PAGE
.INDENT 0
.TURN OFF "{∞→}"   
.GROUP SKIP 1
.BEGIN CENTER  PREFACE 0
⊗5↓_AUTOMATED   MATHEMATICIAN_↓⊗*

⊗5Supplementary Materials⊗*

for the Stanford ⊗2Heuristic Programming Project⊗* Workshop

⊗4January 5-8, 1976⊗*


Douglas B. Lenat



.END
.SELECT 1
.EVERY HEADING(⊗7Douglas B. Lenat,Automated Mathematician,page   {PAGE})

⊗5↓_Overview_↓⊗*


Researchers in all branches of science continually face the difficult
task of formulating problems and subproblems 
which must be soluble and yet 
nontrivial.
In any given field, 
it is usually easier to
tackle a specific given problem than to
propose interesting yet managable
new questions to investigate.
For example, contrast    ⊗4solving⊗* the Missionaries and Cannibals
problem,
against the more ill-defined task of 
⊗4inventing⊗* it ("⊗6create a new puzzle, which can be explained in under a minute,
which can be solved by an  intelligent person in several minutes⊗*").

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 AM project (for ⊗2↓_A_↓⊗*utomated ⊗2↓_M_↓⊗*athematician) is an attempt to
codify some of the heuristics that mathematicians use, make them precise,
and incorporate them into a computer program which can explore a large space of
mathematical concepts. 
The program is given sketchy descriptions of a couple hundred
concepts (like ⊗6MULTISET, SET-INTERSECTION, COMPOSITION, CONJECTURE⊗*).
Its task is to "fill out" this knowledge, by completing a checklist for each
concept (e.g., its ⊗6NAME, EXAMPLES, GENERALIZATIONS, DEFINITION⊗*). Whenever a
new construct is made, or a new relationship observed, the system must decide
whether or not to make this into a full-fledged new concept (hence face the
task of filling out a checklist for ⊗4it⊗*). In general, while filling in some
information for a given concept, several brand new ones will emerge. So this
program can be viewed as growing a tree.
The math heuristics guide the program in choosing what to examine
next, in deciding what new relationships are worth naming and keeping around
as new concepts, etc. They ⊗4prune⊗* this tree, they guide the search.

The issues to be elaborated upon include:
(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?