While there's no doubt that mathematics is organized like a language, with its own lexicon and rules, the nature of this " mathematical language " and its links with natural language is open to question. For Noam Chomsky, " mathematical abilities originate in an abstraction from linguistic operations ". Many physicists and mathematicians, however, agree with Albert Einstein that :
[...] words and language, written or spoken, do not seem to play the slightest role in the mechanism of my thought. The psychic entities that serve as elements of thought are certain signs or images of varying clarity, which can be reproduced or combined at will.
To determine which brain areas are involved in high-level mathematical thinking, Marie Amalric, as part of her thesis at the laboratory, scanned some 15 professional mathematicians using functional MRI, when they were asked to think for four seconds about high-level mathematical and non-mathematical statements, in order to judge them as true, false or absurd. When they thought about mathematical objects, a dorsal parietal and frontal network was activated, which showed no overlap with language areas. Conversely, when they were asked to think about a history or geography problem, the network activated was completely different from the mathematical regions and involved certain language areas. There is thus a mathematical network in the brain, which is not the same as the language network. This result is consistent with many other observations, for example : the activation of this network when listening to stories about numbers, quantities or measurements (Jack Gallant's work) ; intracranial recordings during number processing and mental arithmetic (Josef Parvizi's work) ; or the fact that some aphasic patients remain competent in arithmetic and even algebra (Rosemary Varley's work).
