COMMENT ⊗   VALID 00005 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	.DEVICE XGP
C00004 00003	↓_Brief Summary of Thesis_↓
C00006 00004	5↓_Publications and work in progress_↓*
C00010 00005	5↓_Plans for Future Research_↓*
C00014 ENDMK
C⊗;
.DEVICE XGP
.FONT 1 "BASL30"
.FONT 2 "BASB30"
.FONT 4  "BASI30"
.FONT 5  "BDR40"
.FONT 6  "NGR25"
.TURN ON "↑α↓_π[]{"
.TURN ON "⊗" FOR "%"
.TURN ON "@" FOR "%"
.PAGE FRAME 54 HIGH 83 WIDE
.AREA TEXT LINES 1 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" ⊃;
.SELECT 1
.MACRO B ⊂ BEGIN VERBATIM GROUP ⊃
.MACRO E ⊂ APART END ⊃
.MACRO FAD ⊂ FILL ADJUST DOUBLE SPACE PREFACE 2 ⊃
.MACRO FAS ⊂ FILL ADJUST SINGLE SPACE PREFACE 1 ⊃
.FAS
.COMPACT
.SELECT 1
.PORTION THESIS
.PAGE←0
.NEXT PAGE
.INDENT 0
.TURN OFF "{∞→}"   
.BEGIN CENTER 

.GROUP SKIP 3


⊗5↓_Automated Math Theory Formation_↓⊗*

⊗2Douglas B. Lenat⊗*
Artificial Intelligence Lab
Stanford University
Stanford, California 94305


.GROUP SKIP 3

↓_Brief Summary of Thesis_↓

.GROUP SKIP 3

.END


Investigations of creative theory formation in empirical science have
led to  the construction of AM, a  heuristic search program which can
do  simple  mathematical  research.    AM  examines  empirical  data,
proposes  plausible  conjectures,  formulates  new  definitions,  and
judges  the worth  of each new  concept. AM's  guiding heuristics are
used  as  a  rudimentary  calculus  to   evaluate  "interestingness".
Currently, AM is given  prenumerical knowledge, and makes forays into
arithmetic and elementary number theory.


.SKIP TO COLUMN 1
.BEGIN CENTER 


⊗2Douglas B. Lenat⊗*
Artificial Intelligence Lab
Stanford University
Stanford, California 94305


.GROUP SKIP 3

⊗5↓_Publications and work in progress_↓⊗*

.GROUP SKIP 1

.END

.BEGIN INDENT 0,8,7 PREFACE 2

Green, C. C., R. Waldinger, D. Barstow, R. Elschlager, D. Lenat, B. McCune, 
D. Shaw, and L. Steinberg,
⊗4Progress Report on Program-Understanding Systems⊗*, Memo AIM-240,
CS Report STAN-CS-74-444, Artificial Intelligence Laboratory,
Stanford University, August, 1974. 

Lenat, D. B., ⊗4Synthesis of Large Programs from Specific Dialogues⊗*, 
Proceedings of the
International Symposium on Proving and Improving Programs, Le
Chesnay, France, sponsored by IRIA, July, 1975.

Lenat, D. B., ⊗4Duplication of Human Actions by an 
Interacting Community of Knowledge
Modules⊗*, Proceedings of the Third International Congress of 
Cybernetics and Systems, Bucharest, Roumania, August, 1975.

Lenat, D. B., ⊗4BEINGS: Knowledge as Interacting Experts⊗*, 
Proceedings of the Fourth
International Joint Conference on Artificial Intelligence, 
Tbilisi, Georgia, USSR, September, 1975.

Lenat, D. B., ⊗4The Automated Mathematician⊗*, (forthcoming ACM paper).


.SKIP TO COLUMN 1
.CENTER 
⊗2Douglas B. Lenat⊗*
Artificial Intelligence Lab
Stanford University
Stanford, California 94305


.GROUP SKIP 2


⊗5↓_Plans for Future Research_↓⊗*

.GROUP SKIP 1

.END

The  fascinating  task of  understanding  and  automating  scientific
theory formation  will probably occupy my research  time for the next
few years.    Some of  the projects  I  am contemplating  are  direct
outgrowths of AM,  the "Automated Mathematician" project  which is my
dissertation.

For   example,  attention  should  be   paid  to  those  mathematical
discoveries which ⊗4can't⊗* be  synthesized by the kind  of heuristic
procedure AM follows; that is, what historical inductive leaps remain
when all the "hack" discoveries are discounted?

Another possible direction for my work next year is to take the first
step toward the codification of the heuristics necessary for creative
work in  mathematics.  The AM program can  be used as an experimental
instrument, to help clarify the role of each heuristic.   Ultimately,
such a codification  could lead to a programme  for teaching students
how  to do creative research.  If  AM can do useful theory formation,
then certainly  so  can bright  students who  have  learned the  same
heuristics.

An orthogonal  research interest of mine  is to expand  AM to domains
other than  elementary  number  theory.   Apparently,  the  harder  a
science is, the more  appropriate it is to try  to automate formation
of  its  theories.    So  some  candidate domains  include  geometry,
cryptography, calculus, and  algebra.  Still  plausible are parts  of
chemistry and physics  (e.g., mechanics).  ⊗4Very⊗*  soft fields like
sociology  and psychology have primitive concepts  which are just too
slippery to deal with or even represent adequately using the ideas AM
is based on.

Periodically,  I  will  return  to  the  general  problem  of  theory
formation, and analyze the  information gleaned from my  experimental
systems.  This might result in a  list of general-purpose heuristics,
some notion about  how best to proceed to uncover valuable new ideas,
or some  handles  on  how  to more  effectively  formalize  inductive
heuristics into a program. I believe that we can learn much more from
studying  (and trying to  emulate) problem-⊗4proposing⊗* tasks rather
than from problem-solving tasks.