Cortical collateralization induced by language and arithmetic in non-right-handers

Syntactic theory of mathematical expressions

Mathematical expressions consist of recursive combinations of numbers, variables, and operators. According to theoretical linguists, the syntactic mechanisms of natural language also provide a basis for mathematics. To date, however, no theoretically rigorous investigation has been conducted to support such arguments. Therefore, this study uses a methodology based on theoretical linguistics to analyze the syntactic properties of mathematical expressions. Through a review of recent behavioral and neuroimaging studies on mathematical syntax, we report several inconsistencies with theoretical linguistics, such as the use of ternary structures. To address these, we propose that a syntactic category called Applicative plays a central role in analyzing mathematical expressions with seemingly ternary structures by combining binary structures. Besides basic arithmetic expressions, we also examine algebraic equations and complex expressions such as integral and differential calculi. This study is the first attempt at building a comprehensive framework for analyzing the syntactic structures of mathematical expressions.

Quantitative modelling demonstrates format-invariant representations of mathematical problems in the brain

Mathematical problems can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modelling of mathematical problem solving has yet to be attempted. In the present study, subjects underwent 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel-wise encoding models. Both intra- and cross-format encoding modelling significantly predicted brain activity predominantly in the left intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the IPS. These findings support the idea that mathematical problems are represented in the brain in a format-invariant manner.

Mirrored brain organization: Statistical anomaly or reversal of hemispheric functional segregation bias?

Humans demonstrate a prototypical hemispheric functional segregation pattern, with language and praxis lateralizing to the left hemisphere and spatial attention, face recognition, and emotional prosody to the right hemisphere. In this study, we used fMRI to determine laterality for all five functions in each participant. Crucially, we recruited a sample of left-handers preselected for atypical (right) language dominance (n = 24), which allowed us to characterize hemispheric asymmetry of the other functions and compare their functional segregation pattern with that of left-handers showing typical language dominance (n = 39). Our results revealed that most participants with left language dominance display the prototypical pattern of functional hemispheric segregation (44%) or deviate from this pattern in only one function (35%). Similarly, the vast majority of right language dominant participants demonstrated a completely mirrored brain organization (50%) or a reversal for all but one cognitive function (32%). Participants deviating by more than one function from the standard segregation pattern showed poorer cognitive performance, in line with an oft-presumed biological advantage of hemispheric functional segregation.