The polynomial/exponential boundary in complexity theory is a formal, machine-model-relative result dependent on Church-Turing thesis assumptions that strict finitists explicitly rejected.

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Church-Turing thesis(Presented as a thesis about the upper bound of computational power, not a proven fact.): The thesis that no computational system stronger than the class of Turing machines exists.
Complexity theory(where analogous issues might appear): A branch of computer science and mathematics that studies how difficult different problems are to solve and how much computational power they require.
Machine model(computer science): A theoretical blueprint for how a computer works—different designs (like a standard computer versus a quantum computer) count as different 'machine models,' and they can solve problems at different speeds.
Polynomial(as used in mathematics and computer science): A mathematical expression (like x² + 3x + 2) whose growth rate is reasonable and manageable, as opposed to exponential growth which explodes very quickly.
Strict finitists(as used in philosophy of mathematics): Philosophers and mathematicians who believe that only finite (limited, numbered) things truly exist, and that infinity is just a useful fiction rather than something real.
exponential(describing the speed of improvements in computer hardware): Growing at an increasingly rapid rate, where the amount of growth itself keeps getting bigger (like compound interest in a bank account).

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