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\parttitle{AM: DISCOVERY IN MATHEMATICS AS HEURISTIC SEARCH}
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\appnxbegin{Appendix Four}
\appnxnumber{4}
\appnxtitle{BIBLIOGRAPHY}
\rjustline{\:A Bibliography}
\vskip 13pc

\ninepoint\noindent\!
Of all the articles,  books, and memos which were  read as background
for {\AM}, I have  selected those which had some impact on that work (or
at least, on this document).  While numerous, they form a far from
comprehensive  list of  publications  dealing  with automated  theory
formation, with AI in general, and with how mathematicians do research.



\yyskip

\bibentry
Adams, James L., \4Conceptual Blockbusting\1, W.\ H.\ Freeman and Co.,
San Fran\-cis\-co, 1974.

\bibentry
Amarel, Saul, \4On Representations and Modelling in Problem Solving and On
Future Directions for Intelligent Systems\1, RCA Labs Scientific Report No.\ 2,
Princeton, 1967.

\bibentry
Atkin, A.\ O.\ L., and B.\ J.\ Birch, eds., ``Computers in Number Theory,''
\4Proceedings of the 1969 SRCA Oxford Symposium\1, Academic Press, New York, 
1971.

\bibentry
Badre, Nagib A., \4Computer Learning From English Text\1, Memorandum
No.\ ERL--M372, Electronics Research Laboratory, UCB, December 20, 1972.
Also summarized in \4CLET---A Computer Program that Learns Arithmetic
from an Elementary Textbook\1, IBM Research Report RC 4235, February
21, 1973.

\bibentry
Berliner, H., \4Chess as Problem Solving: The Development of a Tactics Analyzer\1,
Carnegie-Mellon University Computer Science Department Thesis, March, 1974.

\bibentry
Beth, E.\ W., and J.\ Piaget, \4Mathematical Epistemology and
Psychology\1, Gordon and Breach, New York, 1966.

\bibentry
Beveridge, W.\ I., \4The Art of Scientific Investigation\1, Vintage Books,
N.\ Y., 1950.

\bibentry
Biermann, A.\ W., ``Approaches to Automatic Programming,'' in {\sl Advances
in Com\-pu\-ters}, v.\ 15, Academic Press, 1976.

\bibentry
Black, M., \4Margins of Precision\1, Cornell University Press,
Ithaca, New York, 1970.

\bibentry
Blalock, H.\ M., \4Theory Construction\1, Prentice-Hall, Englewood Cliffs,
N.\ J., 1969.

\bibentry
Bledsoe, W.\ W., ``Splitting and Reduction Heuristics in Automatic
Theorem Proving,'' Artificial Intelligence 2, 1971, pp. 55--77.

\bibentry
Bledsoe, W.\ W., and Bruell, Peter, ``A Man-Machine Theorem-Proving System,''
Artificial Intelligence 5, 1974, 51--72.

\bibentry
Bobrow, D., and A.\ Collins, editors, \4Representation and Understanding\1,
Academic Press, S.\ F., 1975.

\bibentry
Bobrow, D., and D. Norman, \4Some Principles of Memory Schemata\1,
XEROX PARC  Memo CSL 75--4, Palo Alto, July, 1975.

\bibentry
Bobrow, D.\ G., and T.\ Winograd,
``An Overview of KRL, A Knowledge Represen\-ta\-tion Language,''
Journal of Cognitive Science, Vol.\ 1, No 1, January 1977.

\bibentry
Bourbaki, N., ``The Architechture of Mathematics,'' American Mathematics
Month\-ly, v.\ 57, pp.\ 221--232, Published by the MAA, Albany, N.\ Y., 1950.

\bibentry
Boyer, R.\ S., and J.\ S.\ Moore, ``Proving Theorems about LISP Functions,''
JACM, v.\ 22, No.\ 1, January, 1975, pp.\ 129--144.


\comment{At this point I gave up being picky...PEG}

\bibentry
Brotz, D. K., \4Embedding Heuristic Problem Solving Methods in a
Mechanical Theorem Prover\1, Ph.D. dissertation published as Stanford Computer
Science Report STAN-CS-74-443, August, 1974.

\bibentry
Bruijn, N. G. de, \4AUTOMATH, a language for mathematics\1, Les Presses de
L'Universite de Montreal, Montreal, 1973.

\bibentry
Buchanan, B. G., G. Sutherland, and E. Feigenbaum, \4Heuristic Dendral:
A Program for Generating Explanatory Hypotheses in Organic Chemistry\1,
in (Melt\-zer and Michie, eds.) {\it Machine Intelligence 4}, 
American Elsevier Pub.,
N. Y., 1969, pp. 209-254.

\bibentry
Buchanan, B. G., E. Feigenbaum, and Sridharan, 
\4Heuristic Theory Formation\1,
{\it Machine Intelligence 7}, 1972, pp. 267-290.

\bibentry
Buchanan, B. G., \4Scientific Theory Formation by Computer\1,
NATO Advanced Study Institute on Computer Oriented Learning Processes,
Bonas, France, 1974.

\bibentry
Buchanan, Bruce G., \4Applications of Artificial Intelligence to Scientific
Reasoning\1, Second USA-Japan Computer Conference, 
Tokyo, August 26-28.
Published by AFIPS and IPSJ,
Tokyo, 1975, pp. 189-194.

\bibentry
Bundy, A., \4Doing Arithmetic with Diagrams\1, 3rd International
Joint  Conference on Artificial Intelligence (3rd IJCAI), Stanford,
1973, pp. 130-138.

\bibentry
Burstall, R., and J. Darlington, \4A Transformation System for Developing
Re\-cur\-sive Pro\-grams\1, University of Edinburgh AI Research Report,  March, 1976.

\bibentry
Church, A., \4The calculi of Lambda-conversion\1, Princeton University Press,
Prince\-ton, 1941.

\bibentry
Cohen, P. J., \4Set Theory and the Continuum Hypothesis\1,  W.A.Benjamin, Inc.,
New York, 1966.

\bibentry
Colby, K. M., \4"Simulations of belief systems"\1, in [Schank and Colby 73].

\bibentry
Copeland, R. W., \4How Children Learn Mathematics\1, The MacMillan
Company, London, 1970.

\bibentry
Courant, R., and H. Robins, \4What is Mathematics\1, 
Oxford University Press, New York, 1941.

\bibentry
Dahl, O., et. al., \4SIMULA-67: A Common Base Language\1, Norwegian
Computing Center Publication No. S-2, Oslo, 1968.

\bibentry
Darlington, J., and R. Burstall, 
\4A System Which Automatically Improves
Pro\-grams\1, 3rd IJCAI, 1973, pp. 479-485. 

\bibentry
Davis, R., and J. King, \4An Overview of Production Systems\1,
Stanford AI Lab Memo 271, October, 1975.

\bibentry
Dijkstra, E. W., \4A Discipline of Programming\1, Prentice-Hall, Inc., 
Englewood Cliffs, N.J., 1976.


\bibentry
Eddington, Sir A. S., \4New Pathways in Science\1, Macmillan Co., N. Y., 1935.

\bibentry
Engelman, C., \4MATHLAB: A Program for On-Line Assistance in Symbolic Computation\1,
in Proceedings of the FJCC, v. 2, Spartan Books, 1965.

\bibentry
Engelman, C., \4MATHLAB '68\1, in IFIP, Edinburgh, 1968.

\bibentry
Evans, T. G., \4A 
Program for the Solution of Geometric-Analogy Intelligence Test
Questions\1, in [Minsky 68], pp. 271-353.

\bibentry
Eynden, C. V., \4Number Theory: An Introduction to Proof\1, 
Internation\-al Text\-book Com\-pany, Scranton, Pennsylvania, 1970.

\bibentry
Feigenbaum, E. A., \4EPAM: The Simulation of Verbal Learning Behavior\1, in
[Feigenbaum & Feldman 63], Part 2, Section 2, pp. 297-309.

\bibentry
Feigenbaum, E. A., and J. Feldman, editors, \4Computers and
Thought\1, McGraw-Hill Book Company, New York, New York, 1963.

\bibentry
Feigenbaum, E., B. Buchanan,
and J. Lederberg,
\4On Generality and Problem Solving: A Case
Study Using The DENDRAL Program\1, in (Meltzer and Michie, eds.) {\it Machine
Intelligence 6}, 1971, pp 165-190.

\bibentry
Fogel, L., A. Owens, and M. Walsh, \4Artificial Intelligence
Through Simulated Evolution\1, John Wiley & Sons, Inc., N. Y., 1966.
 
\bibentry
Fuller, R. B., \4Synergetics\1, Macmillan Co., N. Y., 1975.

\bibentry
Gardner, M., \4Mathematical Games\1, Scientific American [numerous columns,
including especially:  February, 1975.]

\bibentry
Gelernter, H., \4Realization of a Geometry-Theorem Proving Machine\1,
in [Fei\-gen\-baum & Feldman 63], Part 1, Section 3,
pages 134-152.

\bibentry
Goldstein, I., \4Elementary Geometry Theorem Proving\1, MIT AI Memo 280,
April, 1973.

\bibentry
Goodstein, R. L., \4Fundamental Concepts of Mathematics\1, Pergamon Press, 
New York, 1962.

\bibentry
Green, C. C., R. Waldinger, D. Barstow, R. Elschlager, D. Lenat, B. McCune, 
D. Shaw, and L. Steinberg,
\4Progress Report on Program-Understanding Systems\1, Memo AIM-240,
CS Report STAN-CS-74-444,Artificial Intelligence Laboratory,
Stanford University, August, 1974.

\bibentry
Guard, J. R., Eastman  et al., \4Semi-Automated Mathematics\1, JACM 16,
January, 1969, pp. 49-62.

\bibentry
Hadamard, J., \4The Psychology of Invention in the Mathematical
Field\1, Dover Publications, New York, 1945.

\bibentry
Halmos, P. R., \4Innovation in Mathematics\1, in
[Kline 68].
Originally in
Scientific American, September, 1958.

\bibentry
Hardy, G. H.,  and E. M. Wright, \4An Introduction to the Theory of Numbers\1,
Oxford U. Press, London, 1938. (Fourth edition, 1960)

\bibentry
Hayes-Roth, F., and V. R. Lesser, \4Focus of Attention in a Distributed
Speech Understanding System\1, Computer Science Dept. Memo, Carnegie-Mellon
Uni\-ver\-si\-ty, Pittsburgh, Pa., January 12, 1976.

\bibentry
Hempel, C. G., \4Fundamentals of Concept Formation in Empirical
Science\1, Uni\-ver\-si\-ty of Chicago Press, Chicago, 1952.

\bibentry
Hewitt, C., \4A Universal Modular ACTOR Formalism for
Artificial Intelligence\1, Third International Joint Conference on
Artificial Intelligence,
1973, pp. 235-245.

\bibentry
Hewitt, C., \4Viewing Control Structures as Patterns of Passing Messages\1,
MIT AI Lab Working Paper 92, April, 1976.

\bibentry
Hilpinen, R., \4Rules of Acceptance and Inductive Logic\1, Acta
Philosophica Fennica, Fasc. 22, North-Holland Publishing Company,
Amsterdam, 1968.

\bibentry
Hintikka, J., \4Knowledge and Belief\1, Cornell U. Press, Ithaca, N. Y., 1962.

\bibentry
Hintikka, J., and P. Suppes, editors, \4Aspects of Inductive
Logic\1, North-Holland Publishing Company, Amsterdam, 1966.

\bibentry
Iberall, A. S., \4Toward a General Science of Viable Systems\1,
McGraw-Hill Book Co., N. Y. 1972.

\bibentry
Kershner, R. B., and L. R. Wilcox, \4The Anatomy of Mathematics\1, The Ronald
Press Company, New York, 1950.

\bibentry
Kline, M. (ed), \4Mathematics in the Modern World: Readings from Scientific
American\1, W.H.Freeman and Co., San Francisco, 1968.

\bibentry
Kling, R. E., \4Reasoning by Analogy with Applications to Heuristic
Problem Solving: A Case Study\1, Stanford Artificial Intelligence Project
Memo AIM-147, CS Department report CS-216, August, 1971.

\bibentry
Knuth, D. E., 
\4Fundamental Algorithms\1, v. 1 of
{\it The Art of Computer Programming}, Addison-Wesley Publishing Company,
Menlo Park, 1968.

\bibentry
Knuth, D.  E., \4Surreal Numbers\1, Addison-Wesley Publishing Company,
Reading, Mass., l974.

\bibentry
Knuth, D. E., \4Ancient Babylonian Algorithms\1,
CACM 15, July, 1972, pp. 671-677.

\bibentry
Koestler, A., \4The Act of Creation\1,  New York, Dell Pub., 1967.

\bibentry
Koppelman, E., ``Progress in Mathematics", in the proceedings of the
Workshop on the Historical Development of Modern Mathematics, July, 1975.

\bibentry
Lamon, W. E., \4Learning and the Nature of Mathematiccs\1, Science
Research Associates, Palo Alto, 1972.

\bibentry
Lederberg, J., \4DENDRAL-64: A System for Computer Construction,
Enume\-ra\-ion, and Notation of Organic Molecules as Tree Structures and
Cyclic Graphs\1, Parts I-V of the Interim Report to NASA, 1964.

\bibentry
Lederberg, J.; Review of [Weizenbaum 76], originally intended for the
New York Times. This can be obtained
as file WEIZEN.LED[pub,jmc]$@$SAIL, archived in 1976.

\bibentry
Lefrancois, G. R., \4Psychological Theories and Human Learning\1, 
Wadsworth Publishing, Belmont, Ca.,
1972.

\bibentry
Lenat, D., \4Synthesis of Large Programs from Specific Dialogues\1,
Proceedings of the
International Symposium on Proving and Improving Programs, Le Chesnay,
France, July, 1975a.

\bibentry
Lenat, D., \4BEINGs: Knowledge as Interacting Experts\1, 4th IJCAI, Tbilisi,
Georgian SSR, USSR, 1975b.

\bibentry
Lenat, D., \4The Ubiquity of Discovery: The 5IJCAI Computers and Thought
Lecture\1, Proceedings of the Fifth International Joint Conference on
Artificial Intellience, Cambridge, 1977.

\bibentry
Lesser, V., R.D. Fennell, L. D. Erman, and D. R. Reddy, \4Organization of
the Hearsay-II Speech Understanding System\1, in IEEE Transactions on
Acoustics, Speech, and Signal Processing, v. ASSP-23, 1975, pp. 11-23.

\bibentry
Linderholm, C. E., \4Mathematics Made Difficult\1, World Publishing Co., N. Y. 1972.

\bibentry
Lombardi, L.A., and B. Raphael, \4LISP as the language for an incremental
computer\1, in 
(E. C. Berkeley and D. G. Bobrow, eds.)
{\it The Programming Language LISP: Its Operation and Applications},
Information
International Inc., 1964.

\bibentry
McDermott, D., \4Artificial Intelligence Meets Natural Stupidity\1,
in Sigart News\-let\-ter, No. 57, April, 1976, pp. 4-9.

\bibentry
Martin, W., and R. Fateman, \4The MACSYMA System\1, in (S. Petrick, ed.) Second
Symposium on Symbolic and Algebraic Manipulation,
ACM SIGSAM, N. Y. (conference was held in Los Angeles),
1971, pp. 59-75.

\bibentry
Minsky, M., editor, \4Semantic Information Processing\1, The
MIT Press, Cambridge, Massachusetts, 1968.

\bibentry
Minsky, M., \4Frames\1, in [Winston 75].

\bibentry
Mirsky, L., \4Studies in Pure Mathematics\1, Academic Press, New
York, 1971.

\bibentry
Moore, J S., \4Introducing Iteration into the Pure LISP Theorem Prover\1,
XE\-R\-OX PARC report CSL-74-3, Palo Alto, 1975.

\bibentry
Moore, J. and A. Newell, ``How can MERLIN understand?,"
in (Gregg,  ed.) {\it Knowledge and Cognition}, Lawrence
Erlbaum Associates, 1973.

\bibentry
Moore, R. C., \4D-SCRIPT: A Computational Theory of Descriptions\1,
MIT AI Memo 278, February, 1973.

\bibentry
Neumann, J. von, \4The Mathematician\1, in R.B. Heywood (ed), {\it The Works
of the Mind}, U. Chicago Press, pp. 180-196, 1947.

\bibentry
Nevins, Arthur J., \4A Human Oriented Logic for Automatic Theorem
Proving\1, MIT AI Memo 268, October, 1972.

\bibentry
Nevins, Arthur J., \4Plane Geometry Theorem Proving Using Forward Chaining\1,
Artificial Intelligence 6, Spring 1975, pp. 1-23.

\bibentry
Newell, A. \4Heuristic Programming: Ill-Structured Problems\1, in
(A. Aronofsky, ed.) {\it Progress in Operations Research III},
John Wiley and Sons, 1969.

\bibentry
Newell, A., \4Production Systems: Models of Control Structures\1, May,
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Information Processing}, N. Y.: Academic Press, Chapter 10, pp. 463-526. 

\bibentry
Newell, A., J. Shaw, and H. Simon, \4Empirical Explorations of the Logic
Theory Machine: A Case Study in Heuristics\1, RAND Corp. Report P-951,
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\bibentry
Newell, A., and H. Simon, \4Human Problem Solving\1,
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\bibentry
Newell, A. and H.  Simon, \4Computer Science as Empirical Inquiry: Symbols
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\bibentry
Nilsson, N. J., \4Problem-solving Methods in Artificial
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\bibentry
Norman, D., and D. Bobrow, \4On Data-limited and Resource-limited Processes\1,
Journal of Cognitive Psychology, v. 7, 1975, pp. 44-64.

\bibentry
Norman, D., and D. Rumelhart, \4Explorations in Cognition\1, W. H. Freeman & Co.,
S.F., 1975.

\bibentry
Ore, O., \4Number Theory and its History\1, McGraw-Hill, 
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\bibentry
Papert, S., \4Teaching Children to be Mathematicians Versus Teaching
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\bibentry
Piaget, J., \4The Language and Thought of the Child\1, The World Publishing Co.,
N. Y., 1955.

\bibentry
Pietarinen, J., \4Lawlikeness, Analogy, and Inductive Logic\1,
North-Holland, Am\-ster\-dam, published as v. 26 of the series
Acta Philosophica Fennica (J. Hintikka, ed.), 1972.

\bibentry
Pitrat, J., \4Heuristic Interest of using Metatheorems\1,
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\bibentry
Poincar\'e, H., \4The Foundations of Science: Science and Hypothesis,
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\bibentry
P\'olya, G., \4Mathematics and Plausible Reasoning\1, Princeton
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\bibentry
P\'olya, G., \4How To Solve It\1, Second Edition, Doubleday Anchor Books, 
Garden City, New York, 1957.

\bibentry
P\'olya, G., \4Mathematical Discovery\1, John Wiley & Sons,
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\bibentry
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\bibentry
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J. Derksen, and R. Waldinger,
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\bibentry
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\bibentry
Samuel, A., \4Some Studies in Machine Learning Using the Game of Checkers II.
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\bibentry
Schank, R. and K. Colby, \4Computer Models of Thought and
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\bibentry
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\bibentry
Simon, H. A., and L. Siklossy, editors,
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\bibentry
Skemp, R. R., \4The Psychology of Learning Mathematics\1, 
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Sloman, A., \4Interactions Between Philosophy and Artificial 
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Stein, S. K., \4Mathematics: The Man-Made Universe: An Introduction
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Teitelman, W., \4INTERLISP Reference
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Tullock, G.,  \4The Organization of Inquiry\1, Duke U. Press, Durham, N. C.,
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Venn, J., \4The Principles of Empirical or Inductive Logic\1,
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Waismann, F., \4Introduction to Mathematical Thinking\1, 
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Weizenbaum, J., \4Computer Power and Human Reason\1, W. H. Freeman, S.F., 1976.

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\bibentry
Winston, P., \4Learning Structural Descriptions
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Winston, P., editor,
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\bibentry
Winston, P., editor,
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\bibentry
Wittner, G. E., \4The Structure of Mathematics\1, Xerox College Publishing,
Lex\-ing\-ton, Mass., 1972.

\worldend