# How Does a Mathematician’s Brain Differ from That of a Mere Mortal?

Alan Turing, Albert Einstein, Stephen Hawking, John Nash—these “beautiful” minds never fail to enchant the public, but they also remain somewhat elusive. How do some people progress from being able to perform basic arithmetic to grasping advanced mathematical concepts and thinking at levels of abstraction that baffle the rest of the population? Neuroscience has now begun to pin down whether the brain of a math wiz somehow takes conceptual thinking to another level.

Specifically, scientists have long debated whether the basis of high-level mathematical thought is tied to the brain’s language-processing centers—that thinking at such a level of abstraction requires linguistic representation and an understanding of syntax—or to independent regions associated with number and spatial reasoning. In a study published this week in *Proceedings of the National Academy of Sciences*, a pair of researchers at the INSERM–CEA Cognitive Neuroimaging Unit in France reported that the brain areas involved in math are different from those engaged in equally complex nonmathematical thinking.

The team used functional magnetic resonance imaging (fMRI) to scan the brains of 15 professional mathematicians and 15 nonmathematicians of the same academic standing. While in the scanner the subjects listened to a series of 72 high-level mathematical statements, divided evenly among algebra, analysis, geometry and topology, as well as 18 high-level nonmathematical (mostly historical) statements. They had four seconds to reflect on each proposition and determine whether it was true, false or meaningless.

The researchers found that in the mathematicians only, listening to math-related statements activated a network involving bilateral intraparietal, dorsal prefrontal, and inferior temporal regions of the brain. This circuitry is usually not associated with areas involved in language processing and semantics, which were activated in both mathematicians and nonmathematicians when they were presented with the nonmathematical statements. “On the contrary,” says study co-author and graduate student Marie Amalric, “our results show that high-level mathematical reflection recycles brain regions associated with an evolutionarily ancient knowledge of number and space.”

Previous research has found that these nonlinguistic areas are active when performing rudimentary arithmetic calculations and even simply seeing numbers on a page, suggesting a link between advanced and basic mathematical thinking. In fact, co-author Stanislas Dehaene, director of the Cognitive Neuroimaging Unit and experimental psychologist, has studied how humans (and even some animal species) are born with an intuitive sense of numbers—of quantity and arithmetic manipulation—closely related to spatial representation. How the connection between a hardwired “number sense” and higher-level math is formed, however, remains unknown. This work raises the intriguing question of whether an innate capability to recognize different quantities—that two pieces of fruit are greater than one—is the biological foundation on which can be built the capacity to master group theory. “It would be interesting to investigate the causal chain between lower-level and higher-level mathematical competency,” says Daniel Ansari, a cognitive neuroscientist at the University of Western Ontario who did not participate in the study. “Most of us master basic arithmetic, so we’re already recruiting these brain regions, but only a fraction of us go on to do high-level math. We don’t yet know whether becoming a mathematical expert changes the way you do arithmetic or whether learning arithmetic lays out the foundation for acquiring higher-level mathematical concepts.”

Ansari suggests that a training study, in which nonmathematicians are taught advanced mathematical concepts, could provide a better understanding of these connections and how they form. Moreover, achieving expertise in mathematics may affect neuronal circuitry in other ways. Amalric’s study found that mathematicians had reduced activity in the visual areas of the brain involved in facial processing. This could mean that the neural resources required to grasp and work with certain math concepts may undercut—or “use up”—some of the brain’s other capacities. Although additional studies are needed to determine whether mathematicians actually do process faces differently, the researchers hope to gain further insight into the effects that expertise has on how the brain is organized.

“We can start to investigate where exceptional abilities come from, and the neurobiological correlates of such high-level expertise,” Ansari says. “I just think it’s great that we now have the capability to use brain imaging to answer these deep questions about the complexity of human abilities.”