Some Aspects of Analogical Reasoning in Mathematical Creativity

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Alison Pease, Markus Guhe, Alan Smaill: Some Aspects of Analogical Reasoning in Mathematical Creativity. In: Computational Creativity 2010 ICCC 2010. 60-64.



Analogical reasoning can shed light on both of the two key processes of creativity – generation and evaluation. Hence, it is a powerful tool for creativity. We illustrate this with three historical case studies of creative mathematical conjectures which were either found or evaluated via analogies. We conclude by describing our ongoing efforts to build computational realisations of these ideas.

Extended Abstract


author = {Alison Pease, Markus Guhe, Alan Smaill},
title = {Some Aspects of Analogical Reasoning in Mathematical Creativity},
editor = {Dan Ventura, Alison Pease, Rafael P ́erez y P ́erez, Graeme Ritchie and Tony Veale},
booktitle = {Proceedings of the First International Conference on Computational Creativity},
series = {ICCC2010},
year = {2010},
month = {January},
location = {Lisbon, Portugal},
pages = {60-64},
url = {, },
publisher = {International Association for Computational Creativity},
keywords = {computational, creativity},

Used References

[1] J. Barwise and J. Seligman. Information Flow: The logic of distributed systems. CUP, 1997.

[2] M. Boden. Computer models of creativity. AI Mag., 30(3):23–34, Fall Issue, 2009.

[3] A. L. Cauchy. Cours d’Analyse de l’Ecole Polyechnique. de Bure, Paris, 1821.

[4] Gilles Fauconnier and Mark Turner. The Way We Think: Conceptual blending and the mind’s hidden complexities. Basic Books, New York, 2002.

[5] D. Gentner. Structure-mapping: a theoretical framework for analogy. Cognitive Science, (7):155–170, 1983.

[6] Joseph Goguen. What is a concept? In F. Dau et al., editors, Conceptual Struc- tures: Common Semantics for Sharing Knowledge, Vol. 3596, LNAI. Springer, 2005.

[7] M. Guhe, A. Smaill, and A. Pease. A formal cognitive model of mathematical metaphors. In KI 2009: Advances in AI. 32nd Ann. German Conf. on AI, Ger- many, Sept., 2009, pages 323–330. LNAI 5803, Berlin, 2009. Springer.

[8] M. Guhe, A. Smaill, and A. Pease. Using information flow for modelling mathe- matical metaphors. In Proc. of the 9th Int. Conf. on Cognitive Modeling, 2009.

[9] I. Lakatos. Proofs and Refutations. Cambridge University Press, UK, 1976.

[10] I. Lakatos. Cauchy and the continuum: the significance of non-standard analysis for the history and philosophy of mathematics. In J. Worral and C. Currie, editors, Mathematics, science and epistemology, chapter 3, pages 43–60. CUP, UK, 1978.

[11] George Lakoff and Rafael N ́un ̃ez. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. Basic Books, New York, 2000.

[12] A. A. Mart ́ınez. Negative Math: How Mathematical Rules Can Be Positively Bent. Princeton University Press, 2005.

[13] G. McGraw and D. Hofstadter. Perception and creation of diverse alphabetic styles. AISBQ, (85):42–49, 1993.

[14] A. Pease, M. Guhe, and A. Smaill. Analogy formulation and modification in geometry. In Proc. of the 2nd Int. Conf. on Analogy, pages 358–364, 2009.

[15] F. C. Pereira. Creativity and AI: A Conceptual Blending Approach. Applications of Cognitive Linguistics (ACL). Mouton de Gruyter, Berlin, December 2007.

[16] G. Polya. Mathematics and plausible reasoning (Vol. 1): Induction and analogy in mathematics. Princeton University Press, Princeton, USA, 1954.

[17] A. Robinson. Non-standard Analysis. Princeton University Press, Princeton, New Jersey, 1996. Revised Edition.

[18] D. Schlimm. Bridging theories with axioms: Boole, Stone, and Tarski. Perspectives on Mathematical Practices, II, July, 2008.

[19] A. Schwering et al. Syntactic principles of heuristic-driven theory projection. Special Issue on Analogies - Integrating Cognitive Abilities in Journal of Cognitive Systems Research, 10(3):251–269, 2009.

[20] T. Veale. Re-representation and creative analogy: A lexico-semantic perspective. New Generation Computing, 24(3):pp. 223–240, 2006.


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