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C00017 00004	Kershner, R. B., and L. R. Wilcox, \4The Anatomy of Mathematics\1, The Ronald
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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.


{\parindent 0pt \parskip 4pt plus 1pt \lineskip 0pt

\yyskip

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

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.

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

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.


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

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

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

Biermann, A. W., \4Approaches to Automatic Programming\1, in {\it Advances
in Com\-pu\-ters}, v. 15, Academic Press, 1976.

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

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

Bledsoe, W. W., \4Splitting and Reduction Heuristics in Automatic
Theorem Proving\1, Artificial Intelligence 2, 1971, pp. 55-77.

Bledsoe, W. W., and Bruell, Peter, \4A Man-Machine Theorem-Proving System\1,
Artificial Intelligence 5, 1974, 51-72.

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

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

Bobrow, D. G., and T. Winograd,
\4An Overview of KRL, A Knowledge Represen\-ta\-tion Language\1,
Journal of Cognitive Science, Vol 1, No 1, January 1977.

Bourbaki, N., \4The Architechture of Mathematics\1, American Mathematics
Month\-ly, v. 57, pp. 221-232, Published by the MAA, Albany, N. Y., 1950.

Boyer, R. S., and J S. Moore, \4Proving Theorems about LISP Functions\1,
JACM, v. 22, No. 1, January, 1975, pp. 129-144.

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.

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

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.

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

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

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.

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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.

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

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

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

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

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

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.

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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.

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.

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

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.

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

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.

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.

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

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.

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

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.

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

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

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

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

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

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

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

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

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

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

Newell, A., \4Production Systems: Models of Control Structures\1, May,
1973 CMU Report, also published in (W.G. Chase, ed.) {\it Visual
Information Processing}, N. Y.: Academic Press, Chapter 10, pp. 463-526. 

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,
March, 1957.

Newell, A., and H. Simon, \4Human Problem Solving\1,
Prentice-Hall, Englewood Cliffs, New Jersey, 1972. 

Newell, A. and H.  Simon, \4Computer Science as Empirical Inquiry: Symbols
and Search\1, the 1975 ACM Turing Award Lecture, printed in CACM 19, No. 3,
March, 1976, pp. 113-126.

Nilsson, N. J., \4Problem-solving Methods in Artificial
Intelligence\1, McGraw-Hill Book Company, New York, New York, 1971

Norman, D., and D. Bobrow, \4On Data-limited and Resource-limited Processes\1,
Journal of Cognitive Psychology, v. 7, 1975, pp. 44-64.

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

Ore, O., \4Number Theory and its History\1, McGraw-Hill, 
New York, 1948.

Papert, S., \4Teaching Children to be Mathematicians Versus Teaching
About Mathematics\1, in the International Journal of Mathematical Education in
Science and Technology, v. 3, No. 3, July-September, 1972, pp. 249-262.

Piaget, J., \4The Language and Thought of the Child\1, The World Publishing Co.,
N. Y., 1955.

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.

Pitrat, J., \4Heuristic Interest of using Metatheorems\1,
Symposium on Automatic Demonstration, Springer-Verlag, 1970.

Poincar\'e, H., \4The Foundations of Science: Science and Hypothesis,
The Value of Science, Science and Method\1, The Science Press, New York,
1929. 

P\'olya, G., \4Mathematics and Plausible Reasoning\1, Princeton
University Press, Princeton, Vol. 1, 1954;  Vol. 2, 1954.

P\'olya, G., \4How To Solve It\1, Second Edition, Doubleday Anchor Books, 
Garden City, New York, 1957.

P\'olya, G., \4Mathematical Discovery\1, John Wiley & Sons,
New York, Vol. 1, 1962; Vol. 2, 1965.

Ramanujan, S. A., \4Collected Papers\1, (Hardy, Aiyar, and Wilson, eds.),
Chelsea Publishing Company, N. Y., 1927.

Rulifson, J., 
J. Derksen, and R. Waldinger,
\4QA4: A Procedural Calculus for Intuitive Reasoning\1, SRI Project 8721,
Technical Note 73, Artificial Intelligence Center, SRI, Menlo
Park, California, November, 1972.

Saaty, T. L., and F. J. Weyl, editors, \4The Spirit and the Uses
of the Mathematical Sciences\1, McGraw-Hill Book Company, New York, 1969.

Samuel, A., \4Some Studies in Machine Learning Using the Game of Checkers II.
Recent Progress\1,
in the IBM Journal of Research and Development, vol. 11, no. 6, pp. 610-617,
November, 1967.

Schank, R. and K. Colby, \4Computer Models of Thought and
Language.\0 , W. H. Freeman, 1973.

Schminke, C. W., and W. R. Arnold, editors, \4Mathematics is a Verb\1,
The Dryden Press, Hinsdale, Illinois, 1971.

Simon, H. A., \4The Heuristic Compiler\1, in
[Simon & Siklossy 72], Part 1, Chapter 1, pp. 9-43, 1972.

Simon, H. A., \4Does Scientific Discovery Have a Logic?\1, Philosophy of
Science, v. 40, No. 4, December, 1973, pp. 471-480.

Simon, H. A., and L. Siklossy, editors,
\4Representation and Meaning: Experiments with
Information Processing Systems\1, Prentice-Hall Inc., Englewood Cliffs, N.J.,
1972.

Skemp, R. R., \4The Psychology of Learning Mathematics\1, 
Penguin Books, Ltd., Middlesex, England, 1971.

Sloman, A., \4Interactions Between Philosophy and Artificial 
Intelligence: The Role of Intuition and Non-Logical Reasoning in
Intelligence\1, Artificial Intelligence 2, 1971, pp. 209-225.

Smith, N. W., \4A Question-Answering System for Elementary Mathematics\1,
Stan\-ford Institute for Mathematical Studies in the Social Sciences (IMSSS), 
Tech\-ni\-cal
Report 227, April 19, 1974.

Spivak, M., \4Calculus on Manifolds\1,  W.A.Benjamin, Inc., N. Y. 1965.

Stein, S. K., \4Mathematics: The Man-Made Universe: An Introduction
to the Spirit of Mathematics\1, Second Edition, W. H. Freeman and 
Company, San Francisco,  1969.

Teitelman, W., \4INTERLISP Reference
Manual\1, XEROX PARC, 1974.

Tullock, G.,  \4The Organization of Inquiry\1, Duke U. Press, Durham, N. C.,
1966.

Venn, J., \4The Principles of Empirical or Inductive Logic\1,
MacMillan and Co., London, 1889.

Waismann, F., \4Introduction to Mathematical Thinking\1, 
Frederick Ungar Pub\-lish\-ing Co., New York, 1951.

Wang, H., \4Toward Mechanical Mathematics\1, IBM Journal of Research and
Development, v. 4, Number 1, January, 1960, pp. 2-22.

Weizenbaum, J., \4Computer Power and Human Reason\1, W. H. Freeman, S.F., 1976.

Wickelgren, W. A., \4How to Solve Problems: Elements of a Theory of Problems
and Problem Solving\1, W. H. Freeman and Co., Sanf Francisco, 1974.

Wilder, R. L., \4Evolution of Mathematical Concepts\1, John Wiley & Sons,
Inc., N. Y., 1968.

Winograd, T., \4Understanding Natural Language\1, Academic
Press, Inc., New York, New York, 1972.

Winston, P., \4Learning Structural Descriptions
from Examples\1, Ph.D. thesis, Dept. of Electrical Engineering,
TR-76, Project MAC, TR-231, MIT AI Lab, September, 1970.

Winston, P., editor,
\4New Progress in Artificial Intelligence\1,
MIT AI Lab Memo AI-TR-310, June, 1974. 

Winston, P., editor,
\4The Psychology of Computer Vision\1,
McGraw Hill, N. Y. 1975.

Wittner, G. E., \4The Structure of Mathematics\1, Xerox College Publishing,
Lex\-ing\-ton, Mass., 1972.

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