Abstract I propose to consider the question,“Can machines think?”♣ This should begin with
definitions of the meaning of the terms “machine” and “think”. The definitions might be
framed so as to reflect so far as possible the normal use of the words, but this attitude is …

It is suggested that a system of chemical substances, called morphogens, reacting together
and diffusing through a tissue, is adequate to account for the main phenomena of
morphogenesis. Such a system, although it may originally be quite homogeneous, may later …

The" computable" numbers may be described briefly as the real numbers whose
expressions as a decimal are calculable by finite means. Although the subject of this paper
is ostensibly the computable numbers. it is almost equally easy to define and investigate …

The well-known theorem of Godel (Godel [1],[2]) shows that every system of logic is in a
certain sense incomplete, but at the same time it indicates means whereby from a system L
of logic a more complete system L'may be obtained. By repeating the process we get a …

Most machinery developed for commercial purposes is intended to carry out some very
specific job, and to carry it out with certainty and considerable speed. Very often it does the
same series of operations over and over again without any variety. This fact about the actual …

Abstract A number of methods of solving sets of linear equations and inverting matrices are
discussed. The theory of the rounding-off errors involved is investigated for some of the
methods. In all cases examined, including the well-known 'Gauss elimination process', it is …

Abstract Several definitions have been given to express an exact meaning corresponding to
the intuitive idea of 'effective calculability'as applied for instance to functions of positive
integers. The purpose of the present paper is to show that the computable functions …

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… View issue TOC Volume s2-43, Issue 1 1938 Pages 544–546. Articles On Computable Numbers,
with an Application to the Entscheidungsproblem. A Correction. Authors. AM Turing. The Graduate
College, Princeton, NJ, USA. Search for more papers by this author. First published: 1938 Full …

“If one is given a puzzle to solve one will usually, if it proves to be difficult, ask the owner
whether it can be done. Such a question should have a quite definite answer, yes or no, at
any rate provided the rules describing what you are allowed to do are perfectly clear. Of …