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We investigated the biological bases of verbal and logic reasoning in a large sample of participants from the UK Biobank. In particular, we explored the genetic underpinnings of verbal and logic reasoning via genome-wide association analysis (N=108,147), and examined its brain morphological correlates (N=7,485). Importantly, we developed novel statistical methods that enable high-dimensional co-heritability analysis, and computed high-resolution surface maps for the co-heritability and genetic correlations between verbal and logic reasoning and cortical thickness measurements. Our analyses revealed the genetic overlap between verbal and logic reasoning and brain morphology in predominately left inferior precentral gyrus, pars opercularis, superior temporal cortex, supramarginal gyrus, and their proximal regions. These results suggest a shared genetic basis between verbal and logic reasoning and Broca's speech and Wernicke's language areas and motor regions, and may contribute to our understanding of the biological substrate of human cognitive ability.