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A computer aid for symbolic mathematics

Published: 12 November 1963 Publication History

Abstract

Long before it is solved, many a problem has been tossed aside by creative scientists simply because of the sheer tedium in carrying out repeated mathematical operations. In addition to being time consuming, this "clerical" activity is a frequent source of trivial errors which can invalidate the entire analysis. One approach toward solving this problem is the creation of computer aids that will assist the scientist as he develops a theory or tries to solve a mathematical problem. However, when a scientist is trying to develop a theory he does not only want numbers or graphs that satisfy a particular case. He is most happy when he can derive a general formula that not only describes a large number of cases, but also shows how the various cases are interrelated. The theoretician often starts with a set of postulates or some initial equations and manipulates them symbolically to get resulting equations and conditions. Occasionally the scientist has to develop his own mathematics as he works out a problem by creating new symbols, operators, and functions. A computer system that will aid the scientist in the creative process must be flexible enough to accept these new rules with a minimum of effort on the scientist's part. Our work in developing one experimental system of this nature (Magic Paper 1) will be described and several possible extensions to this program will be suggested.

References

[1]
The term "Magic Paper" was first suggested by Professor Richard P. Feynman of the California Institute of Technology. The authors have adopted the name because it is an excellent characterization of the computer's role. The scientist uses the machine in much the same manner as a sheet of paper. As he thinks out various steps in the process, the paper magically responds by performing the indicated operation.
[2]
Glen J. Culler and Burton D. Fried, "An On-Line Computing Center for Scientific Problems," Report M19--3U3, Thompson Ramo Wooldridge, Inc., Canoga Park, California, 11 January, 1963.
[3]
D. C. Engelbart, "Augmenting Human Intellect: A Conceptual Framework," Summary Report AFOSR-3223, Stanford Research Institute, Menlo Park, California, October, 1962.
[4]
Vannevar Bush, "As We May Think," The Atlantic Monthly, July, 1945.
[5]
Personal Communication.
[6]
R. Fano, Report of Project MAC 1963 Summer Study at MIT in preparation.
[7]
The PDP--1 computer is manufactured by the Digital Equipment Corporation of Maynard, Massachusetts.
[8]
Richard McQuillin, "Decal-BBN (Intermediate Operating Manual)," Report Decus T-39, Digital Equipment Users Society, Maynard, Massachusetts.
[9]
Warren Teitelman, "ARGUS---A Handwritten-Character-Recognition Program," (paper presented at the ACM National Conference, Denver, Colorado, August, 1963).
[10]
Development of the BBN Graph Display was supported by the Council on Library Resources, Washington, D. C.

Cited By

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  • (1993)The beginning and development of FORMAC (FORmula MAnipulation Compiler)ACM SIGPLAN Notices10.1145/155360.15537228:3(209-230)Online publication date: 1-Mar-1993
  • (1993)The beginning and development of FORMAC (FORmula MAnipulation Compiler)The second ACM SIGPLAN conference on History of programming languages10.1145/154766.155372(209-230)Online publication date: 1-Apr-1993
  • (1974)A brief review and bibliography of investigations into automation of search of theorem proofs in formal theoriesCybernetics10.1007/BF010684448:5(714-729)Online publication date: 1974
  • Show More Cited By

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cover image ACM Other conferences
AFIPS '63 (Fall): Proceedings of the November 12-14, 1963, fall joint computer conference
November 1963
654 pages
ISBN:9781450378833
DOI:10.1145/1463822
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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  • AFIPS: American Federation of Information Processing Societies

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 November 1963

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Cited By

View all
  • (1993)The beginning and development of FORMAC (FORmula MAnipulation Compiler)ACM SIGPLAN Notices10.1145/155360.15537228:3(209-230)Online publication date: 1-Mar-1993
  • (1993)The beginning and development of FORMAC (FORmula MAnipulation Compiler)The second ACM SIGPLAN conference on History of programming languages10.1145/154766.155372(209-230)Online publication date: 1-Apr-1993
  • (1974)A brief review and bibliography of investigations into automation of search of theorem proofs in formal theoriesCybernetics10.1007/BF010684448:5(714-729)Online publication date: 1974
  • (1966)Symbolic factoring of polynomials in several variablesCommunications of the ACM10.1145/365758.3658099:8(638-643)Online publication date: 1-Aug-1966
  • (1966)Survey of formula manipulationCommunications of the ACM10.1145/365758.3657629:8(555-569)Online publication date: 1-Aug-1966
  • (1965)MATHLABProceedings of the November 30--December 1, 1965, fall joint computer conference, part II: computers: their impact on society10.1145/1464013.1464034(117-126)Online publication date: 30-Nov-1965
  • (1965)MATHLABProceedings of the November 30--December 1, 1965, fall joint computer conference, part I10.1145/1463891.1463938(413-421)Online publication date: 30-Nov-1965
  • (1964)Remote computing--an experimental systemProceedings of the April 21-23, 1964, spring joint computer conference10.1145/1464122.1464164(413-423)Online publication date: 21-Apr-1964

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