Bounded arithmetic

Bounded arithmetic is a branch of mathematical logic that studies systems of arithmetic constrained by limits on the size or complexity of the numbers involved. It focuses on formalizing and understanding what can be proven using only numbers and operations within specific bounds, such as small or computationally manageable sizes. This helps clarify the connections between mathematical provability, computational complexity, and algorithms, by analyzing which problems and properties can be verified within those constraints. Essentially, bounded arithmetic investigates how reasoning and computation behave when restricted to finite, controlled resources.