The Church-Turing Thesis: Consensus and Opposition

  • Martin Davis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)


Many years ago, I wrote [7]:

It is truly remarkable (Gödel ...speaks of a kind of miracle) that it has proved possible to give a precise mathematical characterization of the class of processes that can be carried out by purely machanical means. It is in fact the possibility of such a characterization that underlies the ubiquitous applicability of digital computers. In addition it has made it possible to prove the algorithmic unsolvability of important problems, has provided a key tool in mathematical logic, has made available an array of fundamental models in theoretical computer science, and has been the basis of a rich new branch of mathemtics.

A few years later I wrote [8]:

The subject Alan Turing’s discovery of the universal (or all-purpose) digital computer as a mathematical abstraction. ...We will try to show how this very abstract work helped to lead Turing and John von Neumann to the modern concept of the electronic computer.


Turing Machine Theoretical Computer Science Quantum Adiabatic Universal Machine Positive Integer Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Davis
    • 1
  1. 1.Mathematics Dept.University of CaliforniaBerkeleyUSA

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