In order to achieve the present study's goal--to understand better the phenomenon of mathematical giftedness--we performed a multidimensional examination of the mental processing in students who exhibited mathematical expertise (EM) at the secondary school level. The study included participants from the three groups: students who excelled in school mathematics but were not identified as generally gifted (NG-EM), generally gifted excelling in mathematics (G-EM) students, and students with superior performance in mathematics (S-MG). The research integrated three salient dimensions of mental processing: domain-general cognitive traits, domain-specific (mathematical) creativity, and neuro-cognitive functioning expressed in event-related potentials (ERPs) when solving mathematical problems. In the three study dimensions, we found four types of characteristics of S-MG students: accumulative, G-related, unique and unraveling. This paper defines and exemplifies the characteristics of the four types.