Are Albert Einstein, Alan Turing, Cédric Villani and other brilliant mathematicians’ brains different from ours? The answer appears to be no. The difference lies in how they use their brains. According to a recent study, math experts use particular areas of their brains that remain inactive in “novices." So how do the brains of great mathematicians work?

The origins of the human brain's capacity for mathematics are still being debated even today. Certain theories suggest that the basis lies in ancient brain circuits (initially involved in space and numbers); others hypothesize that it is related to language processing. In order to determine the origin of superior mathematical abilities and the underlying brain systems, M. Amalric and S. Dehaene, researchers in cognitive neuroimaging at Inserm-CEA (France), recorded the brain activity of 15 expert mathematicians (men and women, average age 29 years) and those of 15 people with a similar level of education (but non-experts in mathematics). The participants were asked to categorize statements as true, false, or meaningless. They listened to 72 complex mathematical statements (divided evenly between algebra, analysis, geometry, and topology) and 18 complex non-mathematical statements (history in most cases). They were given 4 seconds to think about each statement and determine whether it was true, false or meaningless. Examples of complex sentences: “Any convex compact set of a Euclidean space is the intersection of a family of closed balls” (mathematics) or “in Ancient Greece, a citizen who could not pay his debts was made a slave," (non mathematical).

The results of this study showed that when subjects reflected on the non-mathematical statements, the areas associated with language and language comprehension were activated. At this level, all participants correctly judged two thirds of the sentences. However, when it came to analyzing the mathematical statements, the researchers noticed that the areas involved in numbers, calculation, and spatial representation were only activated in the math experts. The experts produced correct answers 65% of the time compared to 37% among non-experts. This shows that high-level mathematical reasoning relies on a number of brain areas that do not overlap with the typical left-hemisphere regions involved in language. All of the mathematical areas tested activated a bilateral network including the prefrontal cortex, the intra-parietal ridges and the inferior temporal lobes.

It is also interesting to note that earlier research has shown that these (non-language) areas are active when we carry out simple arithmetic (from the age of 5 or 6). According to M. Amalric, the results indicate that “high-level mathematical reflection recycles brain regions associated with an evolutionary ancient knowledge of number and space.” This may also explain why this basic knowledge (the gift for math we all have) during early childhood precedes success in math. Still, the relationship between basic “number sense” and high-level mathematical skills remains a mystery.