The structure of the mathematical brain
Keywords: cognitive training
brain stimulation
longitudinal design
MRI
brain connectivity
brain structure
mathematical expertise
musical pitch
learning

Humans have an innate ability to deal with numerosity and other aspects of magnitude. This ability is generally honed through education in and experience with mathematics, which necessarily changes the brain structurally and functionally. These changes can be further manipulated through non-invasive electrical brain stimulation. Studying these processes in the case of maths not only constitutes research of great practical impact – given the importance of numerical skills in today's society – but also makes use of maths as a suitable domain in which to study plasticity. In this thesis, I aimed to explore how expertise with numbers shapes brain and behaviour, and also the degree to which processing numbers is similar to other domains in terms of the necessity of healthy brain regions believed to underlie normal processing within and across these domains.
In Study 1, behavioural and structural brain differences were found cross-sectionally between mathematicians and non-mathematicians. A double dissociation between those groups was found between grey matter density in the frontal lobe and behavioural performance: their correlation was positive for mathematicians but negative for controls. These effects may have been caused by years of experience, by congenital predispositions, or, plausibly, by both of these factors, whose disambiguation is non-trivial. Study 2 used transcranial random noise stimulation (tRNS) to assist arithmetic learning. A novel montage was used to enhance brain function during the stage when it is believed to be most involved. Real as compared to sham tRNS enhanced reaction times (RTs) and learning rate on a calculation-based task, but not on a retrieval-based task. The effects were only observed in conditions of high task difficulty. Study 3 examined structural MRI measures before and after arithmetic training to determine how either frontal or parietal tRNS applied with the task changes the structure of the brain longitudinally as compared to sham. Previous results (including those of Study 2) of behavioural facilitation in terms of enhanced RTs to calculation problems were replicated, and further interpreted. Both frontal and parietal tRNS modulated the changes that occurred, pre-to-post training, in terms of cortical volume and gyrification of frontal, parietal and temporal areas. Study 4 investigated the shared neural and cognitive resources used for processing numerical magnitude and musical pitch, by probing how stimulus-response compatibility (SRC) effects for each of the two dimensions compare in a group of mainly temporoparietal lesion patients with numerical impairments versus controls. A double dissociation was found in that numerically impaired patients did not show the number-based SRC effect but did show the pitch-based one, while control subjects demonstrated the opposite trend.
Overall, the results of these studies leave us with three main messages. First, expertise in numbers and mathematics, whether acquired through years of experience (Study 1) or through a few days of tRNS-assisted training (Study 3), appears to be associated with complex changes in the morphology of several brain structures. Some – but not all – of these structures are maths-relevant, and, in the case of tRNS-assisted training, they are distal to the site of the stimulating electrodes. Second, tRNS can improve performance in arithmetic (Studies 2 and 3), although the mechanisms by which this occurs are not yet fully understood, neither neurally nor behaviourally. Third, I found (Study 4) that brain lesions leading to impairment in the number domain do not necessarily affect processing in other domains – such as pitch – that are otherwise linked to number via a putative common code in the parietal lobes.