Abstract
It could be said that the modern theory of computation began with Alan Turing in the 1930's. After a period of steady development, work in complexity, specially that of Steve Cook and Richard Karp around 1970, gave a deeper tie of the Turing framework to the practice of the machine. I will discuss an expansion of the above to a theory of computation and complexity over the real numbers (joint work with L. Blum and M. Shub).
Fields Medal 1966 for his work in differential topology, where he proved the generalized Poincaré conjecture in dimension n≥5: Every closed n-dimensional manifold homotopy equivalent to the n-dimensional sphere is homeomorphic to it. He introduced the method of handle-bodies to solve this and related problems.
Transcribed from the videotape of the talk by Felipe Cucker, Francesc Rosselló and Álvaro Vinacua; revised by the author.
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© 1992 Springer-Verlag
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Smale, S. (1992). Theory of computation. In: Casacuberta, C., Castellet, M. (eds) Mathematical Research Today and Tomorrow. Lecture Notes in Mathematics, vol 1525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089205
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DOI: https://doi.org/10.1007/BFb0089205
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