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C00004 00003	.BEGIN FILL SINGLE SPACE  PREFACE 1 INDENT 0,4,0  ONCE PREFACE 2
C00022 00004	Kershner, R.B., and L.R.Wilcox, 4The Anatomy of Mathematics*, The Ronald
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.ASEC(Bibliography)

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.

.BIB: ASECNUM ;

.BEGIN FILL SINGLE SPACE  PREFACE 1 INDENT 0,4,0 ; ONCE PREFACE 2

Adams, James L., ⊗4Conceptual Blockbusting⊗*, W.H. Freeman and Co.,
San Francisco, 1974.

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

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

Badre, Nagib A., ⊗4Computer Learning From English Text⊗*, 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⊗*, IBM Research Report RC 4235, February
21, 1973.


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

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

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

Biermann, A. W., ⊗4Approaches to Automatic Programming⊗*, in ↓_Advances
in Computers_↓, v. 15, Academic Press, 1976.

Black, M., ⊗4Margins of Precision⊗*, Cornell University Press,
Ithaca, New York, 1970.

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

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

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

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

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

Bobrow, D. G., and T. Winograd,
⊗4An Overview of KRL, A Knowledge Representation Language⊗*,
Journal of Cognitive Science, Vol 1, No 1, January 1977.

Bourbaki, N., ⊗4The Architechture of Mathematics⊗*, American Mathematics
Monthly, 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⊗*,
JACM, v. 22, No. 1, January, 1975, pp. 129-144.

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

Bruijn, N. G. de, ⊗4AUTOMATH, a language for mathematics⊗*, 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⊗*,
in (Meltzer and Michie, eds.) Machine Intelligence 4, American Elsevier Pub.,
N. Y., 1969, pp. 209-254.

Buchanan, B. G., E. Feigenbaum, and Sridharan, 
⊗4Heuristic Theory Formation⊗*,
Machine Intelligence 7, 1972, pp. 267-290.

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

Buchanan, Bruce G., ⊗4Applications of Artificial Intelligence to Scientific
Reasoning⊗*, 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⊗*, 3rd International
Joint  Conference on Artificial Intelligence (3rd IJCAI), Stanford,
1973, pp. 130-138.

Burstall, R., and J. Darlington, ⊗4A Transformation System for Developing
Recursive Programs⊗*, University of Edinburgh AI Research Report,  March, 1976.

Church, A., ⊗4The calculi of Lambda-conversion⊗*, Princeton University Press,
Princeton, 1941.

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

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

Copeland, R. W., ⊗4How Children Learn Mathematics⊗*, The MacMillan
Company, London, 1970.

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

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

Darlington, J., and R. Burstall, 
⊗4A System Which Automatically Improves
Programs⊗*, 3rd IJCAI, 1973, pp. 479-485. 

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

Davis, R., ⊗4Applications of Meta Level Knowledge to the Construction,
Maintenance and Use of Large Knowledge Bases,⊗* Stanford AI Lab Memo 283, July, 1976.

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


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

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

Engelman, C., ⊗4MATHLAB '68⊗*, in IFIP, Edinburgh, 1968.

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

Eynden, C. V., ⊗4Number Theory: An Introduction to Proof⊗*, 
International Textbook Company, Scranton, Pennsylvania, 1970.

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

Feigenbaum, E. A., and J. Feldman, editors, ⊗4Computers and
Thought⊗*, 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⊗*, in (Meltzer and Michie, eds.) Machine
Intelligence 6, 1971, pp 165-190.

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

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

Gelernter, H., ⊗4Realization of a Geometry-Theorem Proving Machine⊗*,
in [Feigenbaum & Feldman 63], Part 1, Section 3,
pages 134-152.

Goldstein, I., ⊗4Elementary Geometry Theorem Proving⊗*, MIT AI Memo 280,
April, 1973.

Goodstein, R. L., ⊗4Fundamental Concepts of Mathematics⊗*, 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⊗*, 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⊗*, JACM 16,
January, 1969, pp. 49-62.

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

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

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

Hayes-Roth, F., and V. R. Lesser, ⊗4Focus of Attention in a Distributed
Speech Understanding System⊗*, Computer Science Dept. Memo, Carnegie-Mellon
University, Pittsburgh, Pa., January 12, 1976.

Hempel, C. G., ⊗4Fundamentals of Concept Formation in Empirical
Science⊗*, University of Chicago Press, Chicago, 1952.

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

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

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

Hintikka, J., ⊗4Knowledge and Belief⊗*, Cornell U. Press, Ithaca, N. Y., 1962.

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

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

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

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

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

Knuth, D. E., 
⊗4Fundamental Algorithms⊗*, v. 1 of
↓_The Art of Computer Programming_↓, Addison-Wesley Publishing Company,
Menlo Park, 1968.

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

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

Koestler, A., ⊗4The Act of Creation⊗*,  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⊗*, Science
Research Associates, Palo Alto, 1972.

Lederberg, J., ⊗4DENDRAL-64: A System for Computer Construction,
Enumeration, and Notation of Organic Molecules as Tree Structures and
Cyclic Graphs⊗*, Parts I-V of the Interim Report to NASA, 1964.

Lederberg, J.; New York Times review of [Weizenbaum 76]; 1976.

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

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

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

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

Linderholm, C. E., ⊗4Mathematics Made Difficult⊗*, World Publishing Co., N. Y. 1972.

Lombardi, L.A., and B. Raphael, ⊗4LISP as the language for an incremental
computer⊗*, in 
(E. C. Berkeley and D. G. Bobrow, eds.)
↓_The Programming Language LISP: Its Operation and Applications_↓,
Information
International Inc., 1964.

McDermott, D., ⊗4Artificial Intelligence Meets Natural Stupidity⊗*,
in Sigart Newsletter, No. 57, April, 1976, pp. 4-9.

Martin, W., and R. Fateman, ⊗4The MACSYMA System⊗*, 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⊗*, The
MIT Press, Cambridge, Massachusetts, 1968.

Minsky, M., ⊗4Frames⊗*, in [Winston 75].

Mirsky, L., ⊗4Studies in Pure Mathematics⊗*, Academic Press, New
York, 1971.

Moore, J S., ⊗4Introducing Iteration into the Pure LISP Theorem Prover⊗*,
XEROX PARC report CSL-74-3, Palo Alto, 1975.

Moore, J. and A. Newell, "How can MERLIN understand?,"
in (Gregg,  ed.) ↓_Knowledge and Cognition_↓, Lawrence
Erlbaum Associates, 1973.

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

Neumann, J. von, ⊗4The Mathematician⊗*, in R.B. Heywood (ed), ↓_The Works
of the Mind_↓, U. Chicago Press, pp. 180-196, 1947.

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

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

Newell, A. ⊗4Heuristic Programming: Ill-Structured Problems⊗*, in
(A. Aronofsky, ed.) ↓_Progress in Operations Research III_↓,
John Wiley and Sons, 1969.

Newell, A., ⊗4Production Systems: Models of Control Structures⊗*, May,
1973 CMU Report, also published in (W.G. Chase, ed.) ↓_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⊗*, RAND Corp. Report P-951,
March, 1957.

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

Newell, A. and H.  Simon, ⊗4Computer Science as Empirical Inquiry: Symbols
and Search⊗*, 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⊗*, McGraw-Hill Book Company, New York, New York, 1971

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

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

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

Papert, S., ⊗4Teaching Children to be Mathematicians Versus Teaching
About Mathematics⊗*, 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⊗*, The World Publishing Co.,
N. Y., 1955.

Pietarinen, J., ⊗4Lawlikeness, Analogy, and Inductive Logic⊗*,
North-Holland, Amsterdam, published as v. 26 of the series
Acta Philosophica Fennica (J. Hintikka, ed.), 1972.

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

Poincare', H., ⊗4The Foundations of Science: Science and Hypothesis,
The Value of Science, Science and Method⊗*, The Science Press, New York,
1929. 

Polya, G., ⊗4Mathematics and Plausible Reasoning⊗*, Princeton
University Press, Princeton, Vol. 1, 1954;  Vol. 2, 1954.

Polya, G., ⊗4How To Solve It⊗*, Second Edition, Doubleday Anchor Books, 
Garden City, New York, 1957.

Polya, G., ⊗4Mathematical Discovery⊗*, John Wiley & Sons,
New York, Vol. 1, 1962; Vol. 2, 1965.

Ramanujan, S. A., ⊗4Collected Papers⊗*, (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⊗*, 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⊗*, McGraw-Hill Book Company, New York, 1969.

Samuel, A., ⊗4Some Studies in Machine Learning Using the Game of Checkers II.
Recent Progress⊗*,
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.⊗* , W. H. Freeman, 1973.

<<Schlick ref?>

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

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

Simon, H. A., ⊗4Does Scientific Discovery Have a Logic?⊗*, 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⊗*, Prentice-Hall Inc., Englewood Cliffs, N.J.,
1972.

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

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

Smith, N. W., ⊗4A Question-Answering System for Elementary Mathematics⊗*,
Stanford Institute for Mathematical Studies in the Social Sciences (IMSSS), 
Technical
Report 227, April 19, 1974.

Spivak, M., ⊗4Calculus on Manifolds⊗*,  W.A.Benjamin, Inc., N. Y. 1965.

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

Teitelman, W., ⊗4INTERLISP Reference
Manual⊗*, XEROX PARC, 1974.

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

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

Waismann, F., ⊗4Introduction to Mathematical Thinking⊗*, 
Frederick Ungar Publishing Co., New York, 1951.

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

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

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

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

Winograd, T., ⊗4Understanding Natural Language⊗*, Academic
Press, Inc., New York, New York, 1972.

Winston, P., ⊗4Learning Structural Descriptions
from Examples⊗*, 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⊗*,
MIT AI Lab Memo AI-TR-310, June, 1974. 

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

Wittner, G. E., ⊗4The Structure of Mathematics⊗*, Xerox College Publishing,
Lexington, Mass., 1972.

.END