We know that a group or a topology, for example, are purely mathematical objects. But what, for example, about a turing machine, or a normal-form game? They are also structures, but one could say that they belong to computer science and ecomonics, respectively, and that they are not mathematical structures. But they all are rigorously defined using logic and sets, so, what makes them different to say that one is a mathematical object and another one not?
2026-03-24 23:41:50.1774395710
When a structure is a mathematical structure?
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Turing machines and normal-form games are definitely mathematical structures. Although these concepts have applications in computer science or economics, they are also studied as abstract structures in their own right, leaving aside the limitations of any particular computer system or economy.
Many mathematical concepts start out from the consideration of physical "real world" examples, but they become mathematical structures when the essential parts of these examples are abstracted and studied independently. For instance, the whole field of probability and statistics originated from studying practical problems of calculating fair odds in gambling.