How does our brain work when we reason? Reasoning is an intricate cognitive process involving attention, memory, executive functions, symbolic processing, and fluid intelligence. Necessarily, various brain regions are inevitably implicated in orchestrating the reasoning process. Therefore, researchers have used meta-analyses, i.e., combining and analyzing results of multiple studies, for a better understanding of neural mechanisms of reasoning. However, previous meta-analysis techniques include weaknesses such as inadequate representation of the highly folded geometry of the brain's cortical surface. Accordingly, we developed a new meta-analysis method called Bayesian meta-analysis of the cortical surface (BMACS). BMACS offers a fast, accurate, and accessible inference of the spatial patterns of cognitive processes from peak brain activations across studies by applying spatial point processes to the cortical surface. Using BMACS, we found that the common pattern of activations from inductive and deductive reasoning was colocalized with the multiple-demand system, indicating that reasoning is a high-level convergence of complex cognitive processes. We anticipate that surface-based meta-analysis will be facilitated by BMACS, bringing more profound knowledge of various cognitive processes.