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Activation of how and where arithmetic operations are displayed in the brain has been observed in various number-processing tasks. However, it remains poorly understood whether stabilized memory of Boolean rules are associated with background knowledge. The present study reviewed behavioral and imaging evidence demonstrating that Boolean problem-solving abilities depend on the core systems of number-processing. The core systems account for a mathematical cultural background, and serve as the foundation for sophisticated mathematical knowledge. The Ebbinghaus paradigm was used to investigate learning-induced changes by functional magnetic resonance imaging (fMRI) in a retrieval task of Boolean rules. Functional imaging data revealed a common activation pattern in the left inferior parietal lobule and left inferior frontal gyrus during all Boolean tasks, which has been used for number-processing processing in former studies. All other regional activations were tasks-specific and prominently distributed in the left thalamus, bilateral parahippocampal gyrus, bilateral occipital lobe, and other subcortices during contrasting stabilized memory retrieval of Boolean tasks and number-processing tasks. The present results largely verified previous studies suggesting that activation patterns due to number-processing appear to reflect a basic anatomical substrate of stability of Boolean rules memory, which are derived from a network originally related to the core systems of number-processing.

The Stability of Memory Rules Associative with the Mathematical Thinking Core