There are many references to it in public discussions, but trying to learn about it from Wikipedia is like reading in a new foreign language.
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Alan Turing was one of the pioners in computer science. He was early enough that computers were not really built when he was active and most of the work was theoretical mathematics. You can compare it to modern quantum computers where there is lots of papers about it and lots of algorithms written for them, but so far nobody have built a practical one.
In order to explore the possible limits of computers Alan Turing designed a theoretical computer which used punched tape for instructions and magnetic tape for memory. This was not practical and not meant to be practical but was very simple to describe mathematically. Turing was able to prove that this simple computer was able to calculate anything given enough time. When more practical computer designs came about the researchers working on it could show that they could emulate this touring computer and by extension was also able to do all the same calculations. Even today in computer science we often distinguish between computers and environments which can emulate a Turing machine and those which can not.
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