An algorithm's theoretical role in complexity class separations and reductions retains practical significance even without physical instantiation, as it bounds what efficient solutions must look like.

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Complexity class(Computational complexity theory): A set of languages all of which can be decided within a given time or space complexity bound t(n) or s(n) with respect to a fixed model of computation.
Efficient solutions(as used in computer science and philosophy of computation): Ways of solving problems that use a reasonable amount of time and computing power, rather than taking forever or requiring massive resources.
Physical instantiation(what the statement says mathematical entities don't depend on): When an abstract concept becomes real in a concrete, physical form—like how the number 5 might be instantiated by five actual apples sitting on a table.
Reductions (in computational theory)(as used in computer science and logic): A method of showing that one problem is as hard as another by demonstrating you can transform one into the other.

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