A number simplex in the human medial temporal lobe

Humans handle numbers nimbly, suggesting a richer neural manifold structure than the prevalent mental number line model. In populations of medial temporal lobe (MTL) neurons in humans performing two simple tasks (dot counting and arithmetic), we find robust neural coding of numerosity that results in high dimensional, simplex-shaped manifolds. This shape affords more flexibility than a linear manifold due to its high shattering dimensionality and expressibility. Dot arrays and Arabic numerals evoked distinct simplicial population codes, yet they were linked by a linearly transferable latent structure within the same task. We find similar simplicial geometry of number representations in large language models (LLMs). Moreover, subjects' internally computed arithmetic results were decodable during the calculation period, with decoding accuracy correlating with individual mathematical capacity. Finally, linear transformations of simplicial operand representations modeled the brain's conversion of operands into decodable results, suggesting that the brain's arithmetic procedures have some resemblance to the attention architecture of LLMs. Together, these findings establish a high dimensional representational foundation for numerical cognition in the brain.