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Universal Turing machine (UTM) is machine which can simulate any other TM, thus can compute anything computable

Halting problem: given randomly chosen TM with finite randomly chosen input tape, decide that this machine will ever halt (i.e. reach state which never changes, doesn't change tape or move TM head). Halting problem for arbitrary TM was proven undecidable

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Q: What is universal turing machine and halting problem?
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What did Alan turing do for the computer?

proved "the halting problem" was false.


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What kind of machine is a busy beaver?

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That sounds like the description of a Turing machine, which was a theoretical machine described by Alan Turing.


Who proved that a machine was capable of processing a stream of 1s and 0s was capable of solving any problem?

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