NEUROIMAGING OF MATHEMATICAL COGNITION: REGIONS OF THE BRAIN ASSOCIATED WITH MATHEMATICAL PROBLEM SOLVING

ABSTRACT

Mathematical cognition relies on coordinated neural systems that support symbolic number processing and the execution of arithmetic procedures under varying computational demands. This study examined the neural architecture of mental arithmetic using task-based fMRI while participants solved addition, subtraction, multiplication, and division problems across three levels of complexity (1-, 2-, and 3-digit operands). Twenty right-handed young adults completed block-designed arithmetic trials with multiple-choice responses; fixation and a font-matching task served as baseline and low-level control conditions. Across operations, arithmetic elicited robust engagement of a predominantly left-lateralized fronto–parietal network, including superior and middle frontal gyri, parietal regions consistent with intraparietal involvement, and midline cingulate areas, alongside bilateral insula. Direct contrasts against fixation and the control task showed a consistent left-hemisphere predominance in both the number and extent of suprathreshold clusters, with multiplication and division producing the largest and most widespread activation patterns relative to addition and subtraction. Complexity effects were most evident in prefrontal and insular recruitment, indicating that as arithmetic procedures become more demanding, mathematical cognition increasingly depends on executive coordination and integrative control resources. Conjunction analyses further revealed overlapping activation across all four arithmetic operations in left medial frontal and cingulate regions, consistent with a shared core system supporting diverse calculation types.

Keywords: Mathematical cognition; arithmetic; mental calculation; fMRI; fronto–parietal networks; intraparietal regions; task complexity.

INTRODUCTION

Contemporary theories posit that human mathematical cognition builds on an evolutionarily older “number sense” for approximate quantity, implemented as an analog magnitude code that supports non-symbolic numerosity judgments (e.g., dot arrays). This approximate number system (ANS) is thought to provide a neurobiological platform that is progressively linked to symbolic systems (digits, number words) during development (Skagenholt et al., 2018). At the level of arithmetic and algebra, meta-analytic and single-study work converges on a distinction between magnitude-based calculation and transformation, which rely more heavily on quantity representations,  fact retrieval and rule-based operations, which draw on verbal/semantic systems and long-term memory (Sokolowski et al., 2022).

Researchers have found that the relationship between inhibitor control and mathematics is sometimes "weaker than expected," despite the fact that people explicitly use inhibitory control in mathematical settings, and they will soon be able to fully explore the mechanical role of the cognitive processes involved in math problems, taking into account the context (e.g., participant state, previous knowledge) (Medrano & Prather, 2023). The increasing involvement of context suggests new perspectives on executive functions, and these perspectives have implications for mathematical cognition research (Medrano & Prather, 2023).

fMRI research on developmental dyscalculia illustrates both the importance and heterogeneity of neural substrates. Single-case and multivariate approaches comparing dyscalculic and typically developing children performing non-symbolic number comparison and exact calculation tasks reveal:

- Relatively subtle group-level differences in parietal regions (e.g., angular gyrus, parieto-occipital sulcus).

- Pronounced individual differences, often centered on visual processing areas, with some children showing compensatory upregulation of higher visual or fronto-parietal regions.

- The possibility to distinguish most dyscalculic from typically developing children using multivariate activation patterns across fronto–parietal systems, suggesting that deficits in visual–parietal number representation may be compensated by finger- or strategy-related fronto–parietal processes (Dinkel et al., 2013).

Such findings underscore that the mathematical network is not fixed but can be reorganized, with implications for targeted interventions and for understanding the neural basis of mathematical learning difficulties.

Because the ventral temporal cortex contains math-selective hubs, it has been demonstrated that specific brain regions code for symbolic numerical representations when visualizing numbers and performing arithmetic operations (Daitch et al., 2016). Bilateral ventral temporal areas implicated in elementary number sense are recycled during mathematical reflection, according to fMRI studies (Amalric & Dehaene, 2017). Recent research employing intracranial electroencephalography has identified a particular location in the temporal cortex that becomes active during the visual processing of numerals.  In a study, temporal cortex sites displayed an initial burst of high-frequency broadband activity that diminished as the operands grew larger but had a constant integral throughout the whole trial.  It was speculated that, beyond just digit recognition, the temporal cortex may play a role in early identification of problem difficulty (Daitch et al., 2016).

METHODS

While inside the Siemens Magnetom Verio (Syngo MR B17) 3 Tesla functional magnetic resonance imaging scanner at the Kurchatov Institute in Moscow,  20 young right-handers (10 women) with an average age of 23.85 years solved mathematical problems (addition, subtraction, multiplication and division), which appeared on a screen with four answer options, from which participants were asked to choose the correct one. There were three levels of difficulty, which were indexed by including 1-digit, 2-digit, and 3-digit numbers. In addition to math tasks, there were font control tasks in which participants were asked to compare fonts between written numbers.

RESULTS AND DISCUSSION

Activation is observed in areas of the prefrontal cortex of the brain. Specifically, activated brain regions include the left inferior frontal gyrus (15 clusters), right inferior frontal gyrus (15 clusters), left middle frontal gyrus (29 clusters), right middle frontal gyrus (17 clusters), left superior frontal gyrus (37 clusters), and right superior frontal gyrus (17 clusters). Furthermore, activation is observed in areas of the temporal cortex of the brain (left: 14 clusters right: 11 clusters), the cingulate cortex of the brain (left: 12 clusters right: 4 clusters), the precuneus (left: 12 clusters, right: 15 clusters)  and the insula (left: 4 clusters, right: 2 clusters).

With the help of magnetoencephalography, the effect of oscillations associated with blinking on mental arithmetic and passive fixation tasks while maintaining the same sensory environment was studied. The results showed that cognitive load induced by mental arithmetic influences the impact of vibrations associated with blinking, inducing cortical activation in important brain regions such as the bilateral precuneus (Liu et al., 2019). Another study examined the neural underpinnings of the approximate computational estimation methodology. Individual accuracy and level of activation of the inferior frontal gyrus have been closely correlated, suggesting that the inferior frontal gyrus is critical for approximate calculation (Ashkenazi et al., 2022). In this experiment, when mathematical problems were contrasted with fixation , the bilateral precuneus prevailed with the largest clusters by volume size. Suprathreshold clusters were also observed in the bilateral inferior frontal gyrus.

The left medial frontal gyrus, the left cingulate gyrus, and the left insula are common areas for all four types of computational conditions, according to the results of a study that compared four different forms of mental computational tasks with the initial fixation condition (Kong et al., 2005). In this experiment, when different mathematical operations were compared with each other, activation was observed in the prefrontal regions, as well as in the left insula and left cingulate gyrus.

In an fMRI study, BOLD signal was monitored during computational tasks involving addition, subtraction, multiplication, and division of several arithmetic operations of varying complexity. All arithmetic processes were associated with a sequential pattern of activation in the left and right, middle and superior frontal regions (Fehr et al., 2007). In this experiment, when the math problems were matched to the font control task, large clusters were found mainly in the left hemisphere compared to the right hemisphere. Noticeable activation was observed in the bilateral superior frontal gyrus and the bilateral middle frontal gyrus.

People suffering from injuries to the left hemisphere may have difficulty understanding precise mathematical values and performing accurate calculations (Dehaene & Cohen 1995). The left hemisphere of right-handers is home to most higher mathematical skills, with the exception of a few space-specific learning abilities (Semenza, 2008). In this experiment, when mathematical problems were contrasted with fixation and a font control problem, addition showed 42 clusters in the left hemisphere and 36 clusters in the right hemisphere, subtraction showed 47 clusters in the left hemisphere and 39 in the right hemisphere, multiplication showed 51 clusters in the left hemisphere and 43 in the right hemisphere, and division showed 53 clusters in the left hemisphere and 45 in the right hemisphere. In all cases, the number of clusters and the amount of activation were greater in the left hemisphere than in the right.

CONCLUSION

Overall, the results support the existence of a core cognitive system for processing math problems. The results show activation in the left and right inferior frontal gyrus, left and right middle frontal gyrus, and left and right superior frontal gyrus. Furthermore, activity is observed in areas of the temporal cortex, the cingulate cortex, the precuneus, and the insula, all involved in mathematical cognition. In addition, the left hemisphere has been found to be dominant over the right hemisphere. These findings could have both theoretical implications for future research involving neuroarchitectural models of mathematical cognition and practical implications for designing machines with autonomous and self-learning abilities based on mathematical functions.

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