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The reason why computers work so well for so many tasks boils down to the concept of "Turing Completeness" described by Alan Turing and independantly Alonzo Church & Haskell Curry.

Which to oversimplify means that all you need to solve any math problem, or simulate another Turing Complete machine, are four operations:

1. Store arbitrary ammounts of data for later use.
2. Do different things for different data
3. Repeat Instructions
4. Communicate to, or ideally with, people. Otherwise WHY?

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