Two researches from a joint CEA-Inserm-Université Paris Sud-Collège de France unit at the NeuroSpin neuroimaging centre, have just revealed that the brain has a network of brain regions involved in advanced mathematics, as well as simpler arithmetic operations. This network is only activated when numbers are seen, in a population of high-level university students including both experts in mathematics and non-mathematicians. These results, published in PNAS, were obtained using functional MRI on university students specialising in mathematics and other disciplines.
Can there be thought without language? Brain imaging is now being used to investigate this question in the laboratory. In order to ascertain which brain regions are involved in advanced mathematical thinking, neuroscientists (NeuroSpin, CEA/Inserm/Université Paris Sud Saclay, Collège de France) studied the brains of fifteen professional mathematicians using functional MRI (fMRI). The fMRI images were taken while they thought for 4 seconds about advanced mathematical and non-mathematical statements, in order to assess them as true, false, or absurd. When they were thinking about mathematical subjects, a dorsal frontoparietal network of the brain was activated, a network which showed no overlap with the language regions. Inversely, when they were asked to think about a history or geography problem, the network which activated was completely different to the mathematical regions, and involved certain language regions.
The network of brain regions discovered in this study is not only involved in very advanced mathematics, but also when processing numbers and mental arithmetic. Researchers also observed that this network also activates in response to simply seeing numbers or mathematical formulae, among professional mathematicians as well as non-mathematicians (researchers at the same university level, but with no scientific training) who had participated in this experiment.
Furthermore, recent studies suggest that this network is already involved in identifying numbers by young children who are not yet at school, and that it is very ancient in evolution, as it is present when macaque monkeys recognise physical objects. This suggest that this network of brain regions exists prior to learning mathematics at school, and that it then develops with the education we receive. Indeed, researchers have found that the activation of regions of this network was amplified among mathematicians compared to non-mathematicians. This observation coincides with the theory of neuronal recycling, developed by Stanislas Dehaene, and which stipulates that advanced cultural cognitive processes, such as mathematics, recycle ancient evolutionary brain functions, such as a sense of number, space and time.
There is therefore a mathematical network in the brain, which is not that of language. This result is consistent with other observations, for example the fact that some children or adults, with a very poor numerical vocabulary, are able to perform advanced arithmetic, or that even some patients with aphasia can still do calculation and algebra.
In the age-old debate about thought without language, mathematics has a special status. For some, such as Noam Chomsky, mathematical activity emerged in humans as a result of their capacity for language. Most mathematicians and physicists believe instead that mathematical thought is independent of languages, such as Albert Einstein who said that, "The words of language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thoughts are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined."
 A patient with aphasia is someone who has lost the ability to control language. This disorder can range from uncertainty over words, to total loss of expression through language, but the patient can write.
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