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In 1937 how was Alan Turing so sure that all that can be done using algorithms can be implemented using a Turing machine? Since that period many new algorithms were implemented. What was his hypothesis behind this theory ?

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  • $\begingroup$ Did you read Turing's 1936 paper "On computable numbers" (e.g. here)? Paragraph 9 addresses exactly this question and is quite clear and readable. $\endgroup$ – cody Apr 26 '16 at 17:24
  • $\begingroup$ Common researcher's reasoning: "I'm an expert and I can not imagine a way. So I conjecture it's impossible." $\endgroup$ – Raphael Apr 27 '16 at 11:12
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The hypotesis is the following:

"Since an algorithm is a well-defined sequence of steps we can always execute an algorithm in a piece of paper(sometimes we may need a really big paper) using a pencil."

Then he created the Turing Machine who can simulate a hand using a pencil with an infinite paper.

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