Abstract
The authors present the main ideas of the computer-assisted proof of Mischaikow and Mrozek that chaos is really present in the Lorenz equations. Methodological consequences of this proof are examined. It is shown that numerical calculations can constitute an essential part of mathematical proof not only in the discrete mathematics but also in the mathematics of continua.
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References
Chang, Ch-L., Lee, R. (1973), Symbolic Logic and Mechanical Theorem Proving, Boston: Harcourt.
Gallier, J.H. (1986), Logic for Computer Science: Foundations of Automatic Theorem Proving, New York: Harper Row.
Lanford, O.E. (1982), ‘A computer-assisted proof of the Feigenbaum conjectures’, Bull. AMS (N.S.) 6, 427–434.
Mischaikow, K., Mrozek, M. (1995), ‘Chaos in the Lorenz equations: a computer-assisted proof’, Bull. AMS, (N.S.) 33, 66–72; ‘Part II: Details’, Mathematics of Computation, in print.
Mrozek, M. (1996), ‘Inheritable properties and computer assisted proofs in dynamics,’ in: Alefeld, G., Frommer A. and Lang B. (eds.) (199?), Scientific Computing and Validated Numerics, Berlin: Akademie Verlag, 245–253.
Steen, L.A. (1978), Mathematics Today: Twelve Informal Essays, New York: Springer Verlag.
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Mrozek, M., Urbaniec, J. Evolution of Mathematical Proof. Foundations of Science 2, 77–85 (1997). http://doi.org/10.1023/A:1009683412188
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DOI: http://doi.org/10.1023/A:1009683412188