# Resting-State Functional Connectivity in Mathematical Expertise
## 1 Introduction  
Recently, the differences between professional mathematicians and non-mathematicians have been investigated with respect to functional specificity and structural connectivity with functional magnetic resonance imaging (fMRI) and diffusion MRI [1, 2]. Mathematicians' high level of expertise in mathematics yielded a focal activation in the dorsolateral prefrontal cortex, whereas non-mathematicians recruited a broadly distributed brain network, including the left inferior frontal gyrus, frontal sulcus, intraparietal sulcus, and right inferior parietal lobule. Different levels of expertise were also reflected in the psychophysiological interaction, showing divergent connectivity among the precentral gyrus-putamen-caudate nucleus and the superior parietal lobule-precentral gyrus between the two groups. With respect to the architecture of white matter tracts, dorsal and cortico-thalamic structureswere modulated by the level of mathematical expertise. The structural integrity of the arcuate fasciculus and superior longitudinal fasciculus was higher in mathematicians, whereas stronger cortico-thalamic connectivity was observed in non-mathematicians. These previous studies demonstrated expertise-dependent modulation on the functional specificity and anatomical connectivity using task-related fMRI and diffusion MRI, respectively. Experts' functional connectivity in large-scale brain networks, associated with high-level mathematical skill, is still called into question. Considering the pivotal roles of mathematical ability in learning and education [3], as well as in the prediction of academic achievement of children [4], a thorough investigation on the brain connectivity in association with mathematical expertise should not go unheeded. However, previous neuroimaging studies showed varying results because of their different task demands or diverse study designs, and this makes it difficult to compare those findings across studies. To avoid this problem, in the present study, we used resting-state fMRI, in which no specific tasks are needed. Resting-state fMRI is known to play a pivotal role in understanding the functional connectivity of brain regions. It detects low-frequency blood oxygenation level-dependent (BOLD) signal fluctuations during rest, demonstrating connectivity between anatomically distinct but functionally related regions [5; 6; 7; 8]. These spontaneous BOLD activities unveil intrinsic functional architectures such as visual networks, auditory networks, sensorimotor networks, default mode networks (DMNs), basal ganglia networks, language networks, executive control networks, and dorsal/ventral attention networks [7; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Interestingly, these intrinsic connectivity networks have been constantly observed within and across people [26]. Regions that activate together during specific functional tasks are known to be correlated among themselves during resting state as well, maintaining their traits of functional specificity. Many studies have suggested that spontaneous BOLD activities in resting state provide useful information on the human brain that is organized into multiple distinct yet inherently interactive regions that have specific functions [27]. Using this approach, researchers have elucidated how functional connectivity in resting state is related to large-scale brain networks that are allocated to specific cognitive functions [28]. Moreover, resting-state fMRI has been used to demonstrate group-specific features such as early adolescents' network maturation [29], highly intelligent individuals' functional connectivity and global efficiency [30; 31], and individuals with better set-shifting functions showing positive resting-state connectivity between frontoparietal and visual networks [32]. Therefore, using resting-state fMRI enables us to understand the linked functions of anatomically separate areas through the correlation of resting BOLD activities with individual differences.