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Enlarging the Scope of Applicability of Successful Techniques for Automated Reasoning in Mathematics

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 7364)

Abstract

In mathematics sometimes methods from one area can be fruitfully applied for getting results in another area, occasionally looking very remote from the other area. A well-known example is given by analytic geometry that enables us, besides proving “elementary” geometrical theorems, to establish otherwise untractable results like unsolvability of the problems of angle trisection and doubling the cube by compass and straightedge and to reduce calculation of the kissing numbers of spheres to verification of a first-order formula about real numbers (and that could be done, in principle, by Tarski algorithm).

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References

  1. Margenstern, M., Matiyasevich, Y.: A binomial representation of the 3x + 1 problem. Acta Arith. 91(4), 367–378 (1999)

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  2. Matiyasevich, Y.: Some arithmetical restatements of the four color conjecture. Theor. Comput. Sci. 257(1-2), 167–183 (2001)

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© 2012 Springer-Verlag Berlin Heidelberg

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Matiyasevich, Y. (2012). Enlarging the Scope of Applicability of Successful Techniques for Automated Reasoning in Mathematics. In: Gramlich, B., Miller, D., Sattler, U. (eds) Automated Reasoning. IJCAR 2012. Lecture Notes in Computer Science(), vol 7364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31365-3_2

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  • DOI: https://doi.org/10.1007/978-3-642-31365-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31364-6

  • Online ISBN: 978-3-642-31365-3

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