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On the Work of Steve Smale on the Theory of Computation

In: From Topology to Computation: Proceedings of the Smalefest

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  • Michael Shub

Abstract

The theory of computation is the newest and longest segment of Steve Smale’s mathematical career. It is still evolving and, thus, it is difficult to evaluate and isolate the more important of Smale’s contributions. I think they will be as important as his contributions to differential topology and dynamical systems. He has firmly grounded himself in the mathematics of practical algorithms, Newton’s method, and the simplex method of linear programming, inventing the tools and methodology for their analysis. With the experience gained, he is laying foundations for the theory of computation which have a unifying effect on the diverse subjects of numerical analysis, theoretical computer science, abstract mathematics, and mathematical logic. I will try to capture some of the points in this long-term project. Of course, the best thing to do is to read Smale’s original papers; I have not done justice to any of them.

Suggested Citation

  • Michael Shub, 1993. "On the Work of Steve Smale on the Theory of Computation," Springer Books, in: Morris W. Hirsch & Jerrold E. Marsden & Michael Shub (ed.), From Topology to Computation: Proceedings of the Smalefest, chapter 28, pages 281-301, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2740-3_28
    DOI: 10.1007/978-1-4612-2740-3_28
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