in a scene *The man who knew infinity* (2015), a biopic of mathematician Srinivasa Ramanujan, G.H. Hardy (played by Jeremy Irons) asks Ramanujan (Dev Patel), “How did you know that theorem?” “I knew it,” Ramanujan says. The scene brought to life a well-known aspect of Ramanujan's mathematical ability: he knew the answers to complex problems and often did not explain how he figured them out.

Could his biology have given him this amazing ability?

one of Studies published In the journal *Progress of science* In May, Stanford University researchers found a link between school students' performance on math tests and their brain anatomy. The authors also identified genes whose expression was related to students' ability to do math.

These correlations could be used to estimate how much tutoring might increase a student's mathematical proficiency, the authors said.

These findings have caused a stir, but neuroscientists and education researchers caution against reducing complex human abilities to biological descriptions.

#### Mathematics in the brain

The researchers scanned the brains of 219 students aged 7-13 years using magnetic resonance imaging (MRI). MRI is a non-invasive imaging technique that uses magnetic fields and radio waves to create detailed images of the body's internal structures. They then measured the students' various mathematical skills, including “arithmetic calculations, number sense, and problem-solving abilities,” said Vinod Menon, director of the Stanford Cognitive and Systems Neuroscience Laboratory and one of the authors of the study.

Their performance on these tests was used to define their “mathematical ability”.

The researchers then calculated gray matter volume for 246 regions of the brains of all the students. Gray matter is the part of the brain that consists mainly of neuronal cells, and is said to be involved in vision, hearing, memory, emotions, speech, decision-making, self-control and muscle control.

The group used a statistical tool called canonical correlation analysis to identify the relationship between gray matter volume and mathematical ability. They found that students who performed poorly on the assessment had greater gray matter volume in three brain regions: the posterior parietal cortex, the ventrotemporal occipital cortex, and the prefrontal cortex. These regions have been “implicated in numerical cognition,” the authors wrote in their paper.

These students also had less gray matter in other parts of the brain, including parts associated with vision, subcortical regions, and the posterior insula. The researchers called this pattern of high and low volume in different parts the “mathematical ability-related imaging phenotype” (MAIP).

#### Mathematics in genes

The authors then investigated how patterns of gene expression in the brain relate to MAIP. To do this, they used the Allen Human Brain Atlas, a publicly available dataset that contains expression patterns of more than 60,000 genes in nearly 500 human brains.

The researchers found specific, brain-wide gene expression profiles related to MAIP in the brain.

Which specific genes contribute the most to this correlation? Gene ontology enrichment analysis is a method that identifies genes that are over- or under-represented in a set of genes whose expression patterns correlate with a biological observation.

They found that MAIP was most significantly associated with genes expressed at synapses – the places where neurons connect to one another – and which determine the activity of voltage-gated potassium channels (VGPCs). In the brain, VGPCs return neurons to their resting state after stimulation.

#### Predictability of mathematical performance

The authors hypothesized that if MAIP and the associated gene expression profile do indeed determine students’ mathematical ability, we should be able to use this information to predict how well a student might learn math during tutoring. To test this hypothesis, the team worked with two groups of students being tutored in math. The first group had 24 students and were taught arithmetic problem-solving for eight weeks. The second group had 61 students; they were taught number sense for four weeks.

Before tutoring each group, the researchers scanned their students' brains and generated their MAIP scans. They then calculated a “transcriptome similarity index” (TSI) — a number that accounted for the students' individual MAIP and gene expression profiles. Finally, the researchers developed a model that could predict how much a student's TSI would improve after a learning course.

They found that their predictions were very close to the improvements observed in the students.

#### Interpreting the data correctly

Bittu Rajaraman, associate professor of biology and psychology at Ashoka University and who studies numerical cognition, said the findings do not indicate that mathematical ability is “innate”. Instead, they suggest that an individual mathematical performance has neurobiological and transcriptomic correlates, “both of which may change with social experience”.

Professor Menon agreed, adding that “quality of education, socio-economic status, cultural influences and even attitudes towards learning mathematics” as well as biological factors play an important role in students' mathematical proficiency.

However, he also said it is important to study the neurobiology of mathematical proficiency, because non-biological factors “manifest through biological pathways” by altering gene expression and the strength of connections between neurons.

#### How do children learn maths?

Upinder Bhalla, who studies memory and plasticity at the Bengaluru-based National Centre for Biological Sciences, also raised three concerns. (i) A small group of participating students: “Small samples can sometimes yield unusual results that are not suitable for large-scale analysis.” (ii) While there are correlations between MAIP, gene expression patterns, TSI scores and students’ performance, they are “mostly weak.” (iii) The study did not control for family income and education levels of students’ parents.

Mathematics education researchers expressed more concern. Zeenat Rahman, assistant professor of mathematical education at Azim Premji University, Bhopal, said the brain provides only the basic structural capacity for any kind of learning. To make mathematics accessible and meaningful to students, it is more important to understand “the relationship between learners, teachers, the nature of mathematics and the content of mathematics education”.

Professor Bhalla agreed. He said that limiting mathematical efficiency to biological readouts would be like reducing the beauty of the Taj Mahal to marble pieces.

Jayashri Subramanian, associate professor of mathematics at SRM University, Andhra Pradesh, and a mathematics education researcher, also pointed to existing criticisms of standardised tests, which the study also uses. She said that in the school classroom, while students were unable to guess whether ½ was bigger or smaller than ¼, they were quick to say that “adha” (half) was bigger than “paav” (quarter) – words they were familiar with in their languages.

Without incorporating context when interpreting a student's mathematical ability, we risk misjudging their proficiency, Dr. Subramanian said. This in turn will affect the physiological and gene expression correlates of mathematical ability, he said.

*Sayantan Dutta is a science journalist and faculty member at Krea University. He tweets at @queersprings.*