J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton University Press, 1945.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....School of Computer Science, McGill University, Montreal, Quebec, Canada (godfried cs.mcgill.ca) 1 1. 2 The psychology of discovery in computational geometry Psychologists, mathematicians and physicists have been interested for a long time in the process of discovery in mathematics [7], 8] 27] The process of discovery in the design of geometric algorithms o ers a rich environment for psychologists and arti cial intelligence researchers to study because of the strong visual and kinetic components present in geometry problems. This is even more so due to the coming of the ....

....views on this topic and conclusions regarding both the design and analysis of geometric algorithms as well as implications for education. It is by no means a report of rigorous psychological testing on subjects, but rather an account of a personal study on the subject in the spirit of Hadamard [7], Mach [27] and Lakatos [8] 1.3 Logico mathematical vs. kinesthetic or body syntonic heuristics It is useful to distinguish between various forms of knowledge [9] intelligence [10] and thinking [11] While it is true that our knowledge, intelligence, and thinking, particularly that concerned ....

J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton University Press, 1945.

....McGill University, Montreal, Quebec, Canada (godfried cs.mcgill.ca) Partially supported by NSERC and FCAR. 1 1. 2 The psychology of discovery in computational geometry Psychologists, mathematicians and physicists have been interested for a long time in the process of discovery in mathematics [7], 8] 27] The process of discovery in the design of geometric algorithms o ers a rich environment for psychologists and arti cial intelligence researchers to study because of the strong visual and kinetic components present in geometry problems. This is even more so due to the coming of the ....

....views on this topic and conclusions regarding both the design and analysis of geometric algorithms as well as implications for education. It is by no means a report of rigorous psychological testing on subjects, but rather an account of a personal study on the subject in the spirit of Hadamard [7], Mach [27] and Lakatos [8] 1.3 Logico mathematical vs. kinesthetic or body syntonic heuristics It is useful to distinguish between various forms of knowledge [9] intelligence [10] and thinking [11] While it is true that our knowledge, intelligence, and thinking, particularly that concerned ....

J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton University Press, 1945.

....SFB 314 (D2,D3) 1 Introduction In this paper we are going to describe how to represent mathematical factual knowledge for automated theorem proving. Guideline is knowledge like that of a mathematical dictionary. In particular we are here not interested in heuristic knowledge as described in [15, 16, 17, 7, 18]. The main means for our representation is higher order logic. Indeed one may ask why such a powerful logic is not sufficient for the description of the factual knowledge of mathematics, because logic has been developed in the last hundred years for that purpose. The answer is that it is possible ....

Jacques Hadamard. The Psychology of Invention in the Mathematical Field. Dover Publications, New York, USA; edition 1949.

....activities (see studies in psychology Design rationale has been used in various human decision making activities, such as legal decision making, policy making, architecture, and general design. In our approach, design rationale is used with emphasis on explanation. and creativity, for example [38, 18, 29, 30]) Moreover, IS professionals also agree with the pattern when we discuss our work with them. While we should not have been surprised, nonetheless we were because this result conflicts with the academic literature in RE, for example see the major textbooks [42, 43, 24] Not only does the textbook ....

....gain of the essential understanding of the problem at crisis points. 4.5.2 Supporting Creativity through Influencing Mental Processes Our observational data shows the insight driven nature of the RE process. Insight, while often involving surprise [27] can not happen purely by chance. Hadamard [18] asserted that insight is preceded by a previous unconscious mental process. The conscious mental process presents a presence chamber in our mind and holds the current ideas of which we are aware and on which we are working. The unconscious mental process presents an ante chamber in our mind and ....

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Hadamard, J. (1954). The Psychology of Invention in the Mathematical Field, Dover Publications, New York.

....is gained at a higher level of abstraction and logic. This is consistent with our interpretation of the evolution of the essential and accidental complexity in the requirements model. Having analysed and discussed creative activities in mathematical fields, previous thinkers like Hadamard [19] and Poincar [40] identified four stages of invention: preparation, incubation, illumination (insight) and the verification and expression of insight. At the first stage, the consciousness works as preparatory by exploring the problem areas and shaping directions that the unconscious may follow. ....

Hadamard, J. (1954). The Psychology of Invention in the Mathematical Field, Dover Publications, New York.

....method named combination retrieval. The basic idea is that an appropriate combination of existing documents may lead to creating novel knowledge, although each one document may be short of answering the novel query. Based on the principle that combining ideas triggers the creation of new ideas [1], we present a sys tem to obtain and present an optimal combination of documents to the user, optimal in that the solution forms a document set which is the most readable (understandable) and reflecting the user s context. e mail:osawa gssm.otsuka.tsukuba.ac.jp The remainder of this paper goes ....

Hadamard, J: The Psychology of Invention in the Mathematical Field, Princeton University Press (1945)

....rep for creating novel knowledge by combining complementary docuAK ts.Here, a complementary set of docuSS ts is composed of docuAW ts, and the combination of whichsuJ:SJ. a satisfactory information.This idea is based on the principle that combining ideas can trigger the creation of new ideas[1,2].Throu#5x) the discu5K.C: of the work, we verified the fact that reading muAKWSK complementary docu:W ts generates the synergy e#ects which helpu acquAx novel knowledge. In this paper, we propose a new framework of knowledge navigation, i.e. su. au:J with new knowledge, for satisfying the ....

Hadamard, J: The Psychology of Invention in the Mathematical Field. Princeton University Press, 1945.

....construct an accurate model of the cognitive processes of a human subject in a controlled experimental situation which occurs over a small period of time. Although we are encouraged that some are studying the reasoning processes of famous scientists over long periods of time (e.g. Tweeney, 1989; Hadamard, 1954; Hovey, 1962; Jenkings, 1983; Jenkins Jeffrey, 1984; Osowski, 1986; Wertheimer 1959) it is an exceedingly difficult and time consuming task. There are many advantages to studying discovery in the layperson: There are more laypeople than scientists, providing more examples to study. For ....

Hadamard, J. (1954). The Psychology of Invention in the Mathematical Field. New York: Dover.

.... construction of polyhedral models is rarely provided explicitly 1 , it reflects the widespread view among mathematicians of the 1 For an eloquent exception, see the final section in the essay by Senechal (1990) Creating Polyhedral Models by Computer 2 importance of mathematical imagery (Hadamard, 1949; Fomenko, 1994) Hilbert and Cohn Vossen s well known text on geometry opens with the first author s observation: In mathematics, as in any scientific research, we find two tendencies present. On the one hand, the tendency toward abstraction seeks to crystallize the logical relations inherent ....

Hadamard, J. (1949). The Psychology of Invention in the Mathematical Field. New York: Dover.

....patterns, examples, narrations etc. of successful instances (and sometimes unsuccessful instances, as guides to what to avoid in tackling similar exercises in the future) of solution of a problem. It is not hard to find literature on mathematical problem solving behaviour of this kind; some (e.g. [20] [21] has classic status. Even when the sources for the behaviour are learners and not professional mathematicians, it is fair to describe the actions and the results in a case . A case is a recognised knowledge representation in AI, though not primitive: it can be written in a variety of ways ....

J. Hadamard, The Psychology of Invention in the Mathematical Field. Princeton University Press, Princeton, NJ (1949)

....instance, in [124, 128] Mathematics: Polya [112] saw analogical thinking as an absolute necessity for mathematical creativity. One of Polya s well known heuristics is: Have you seen a similar problem before Try to use its solution. More reports of analogical reasoning in maths can be found in [113, 51]. Universitat des Saarlandes, Fachbereich Informatik, D 66041 Saarbrucken, Germany y School of Computer Science, Carnegie Mellon University, Pittsburgh, U.S.A. Science: Rutherford s famous solar system model of the atom (see, e.g. 56] was used to make predictions about the allowable ....

....in Theorem Proving Theorem proving by analogy, as sketched in Figure 22, finds a proof for a target theorem guided by a proof of a given source problem which is similar to the target theorem. Mathematicians have clearly recognized the power of analogical reasoning in mathematical problem solving [51, 113]. However, analogy in theorem proving has received limited attention despite its importance in mathematics and the claims made for its usefulness in theorem proving in [11, 152] 5.1 The Need for a New Model Kling s work [78] was one of the first attempts in theorem proving by analogy. His system ....

J. Hadamard. The Psychology of Invention in the Mathematical Field. Princeton Univ. Press, Princeton, 1945.

....computational geometry, artificial intelligence. CR Categories: 3.36, 3.63, 5.25, 5.32, 5.5 1. Introduction 1. 1 Computational geometry Computational geometry is claimed by many computer scientists to be a new field of computer science which began with the thesis of Michael Shamos [l] in 1978. Since that time, spurred by developments in computer graphics, VLSI (Very Large Scale Integration) computer vision and robotics, it has blossomed into a dynamic discipline of its own and has given birth to several books in the area [2] 3] 28] 29] For two existing surveys of the field ....

....about these algorithms, how they fail, and trying to correct them has led to the ideas presented in this paper. 1. 2 The psychology of discovery in computational geometry Psychologists, mathematicians and physicists have been interested for a long time in the process of discovery in mathematics [7] 8] 27] The process of discovery in the design of geo1. A preliminary version of this paper titled Computational Geometric Thinking as Kinesthetic Thinking was presented at the Conference on Thinking, Harvard University, August 1984. 2 metric algorithms offers a rich environment for ....

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J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton Uni- - 11 - versity Press, 1945.

....the HB1 proof plan. This yields an incomplete proof plan for the HB2 problem which can be extended to a proof of HB2. An evaluation of the result and future work are discussed at the end. 2 Introduction Mathematicians have clearly recognized the power of analogy in mathematical problem solving [Had45, Pol45, Pol54, vdW64] In automated and interactive theorem proving, analogy is particularly useful in situations where much search or user interaction is necessary, e.g. when many proof assumptions, difficult theorems, or long proof paths are involved. Computational accounts of theorem proving ....

J. Hadamard. The Psychology of Invention in the Mathematical Field. Princeton Univ. Press, Princeton, 1945.

....needed in complex proofs. In order to attack complex mathematical problems we need to combine the strength of traditional automated theorem provers with human like capabilities. Mathematicians have clearly recognized and emphasized the power of analogical reasoning in mathematical problem solving (Hadamard 1945; Polya 1954; 1957; van der Waerden 1964) Hence, integrating analogy into theorem provers is one of the challenging problems in automated theorem proving (Bledsoe 1986; Wos 1988) Melis analyzed several empirical sources (Melis 1994b) on how mathematicians prove theorems. As a result, she ....

Hadamard, J. 1945. The Psychology of Invention in the Mathematical Field. Princeton: Princeton Univ. Press.

....most rapidly growing areas of research in artificial intelligence and related fields of computer science and cognitive science. It should not be surprising, since visual representation and thinking were for long considered to be a widespread and effective mode of human thinking and problem solving [2, 7, 8, 10, 12, 14]. What is more surprising is that it has grown into a respectable part of mainstream AI research so late [41] The diagrammatic (visual) representation uses diagrams to represent data and knowledge, and diagrammatic reasoning uses direct manipulation and inspection of a diagram as primary means of ....

....with the help of them. It consists of perceptual part (the sense of vision) and internal processing part (visual imagery) The visual perception mechanisms are comparatively well understood, at least in their overall structure and some lowlevel technical details. The working of visual thinking [2, 7] is also understood in general terms, though far less than perception, but details of its implementation in the brain are still a subject of hot debate among cognitive scientists [62] One school, lead by Kosslyn [12] claims we reason visually by generation and examination of images on an ....

Hadamard J.: The Psychology of Invention in the Mathematical Field. Princeton University Press, Princeton, NJ. 1959

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J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton University Press, 1945.

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J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton University Press, 1945.

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J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton Uni- - versity Press, 1945.

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Hadamard, J. (1954), The Psychology of Invention in the Mathematical Field, Dover Publications, New York, USA.

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Hadamard, J., The Psychology of Invention in the Mathematical Field. Dover, 1954.

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J. Hadamard, The Psychology of Invention in the Mathematical Field. Princeton University Press, 1945.

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Hadamard, J., The Psychology of Invention in the Mathematical Field, Dover Publ. Inc., New York, 1949.

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Hadamard, J. 1945. The Psychology of Invention in the Mathematical Field. New York: Dover Publ.

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Hadamard, J., The Psychology of Invention in the Mathematical Field, Dover Publ. Inc., New York, 1949.

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Hadamard, J. (1945). The Psychology of Invention in the Mathematical Field. Princeton Univ. Press, Princeton.

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