Introductory Reflections on Algorithms

  • Hans Hermes
Conference paper
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 127)


The concept of algorithm, i. e. of a “general procedure”, is more or less known to all mathematicians. In this introductory paragraph we want to make this concept more precise. In doing this we want to stress what is to be considered essential.


Natural Number Turing Machine Computable Function Computing Step Empty Word 
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  1. Finsler, P.: Formale Beweise und die Entscheidbarkeit. Math. Z. 25, 676–682 (1926).MathSciNetzbMATHCrossRefGoogle Scholar
  2. Gödel, K.: Die Vollständigkeit der Axiome des logischen Funktionenkalküls. Mh. Math. Phys. 37, 349–360 (1930).Google Scholar
  3. Gödel, K.: Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Mh. Math. Phys. 38, 173–198 (1931). (Incompleteness theorem.)Google Scholar
  4. Church, A.: An Unsolvable Problem of Elementary Number Theory. Amer. J. Math. 58, 345–363 (1936). (Church’s thesis on p. 346.)Google Scholar
  5. Kleene, S. C.: General Recursive Functions of Natural Numbers. Math. Ann. 112, 727–742 (1936).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1965

Authors and Affiliations

  • Hans Hermes
    • 1
  1. 1.University of MünsterMünster i. W.Germany

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