Knowing that "the sine function is periodic" and knowing that "London buses are red" engage different brain networks. For the brain, mathematics constitutes a distinct semantic system, independent of natural language and grounded in universal numerical and spatial intuitions.
Mathematics is often described as a "universal language." The phrase is appealing: like a language, mathematics uses symbols, obeys rules, and can express an infinite number of ideas. Yet if you ask a mathematician "Do you think in words?", the answer will likely be "no," or "not really."
Mathematicians more often describe images, structures, sensations of movement within an abstract space. Albert Einstein, questioned about his mental processes by the mathematician Jacques Hadamard in 1943, was particularly explicit: "Words or language, whether written or spoken, do not seem to play the slightest role in the mechanism of my thought. The psychical entities that serve as elements of my thought are certain signs or more or less clear images."
Two different processes
This famous introspection is not merely anecdotal. It points to a fundamental question for cognitive neuroscience: are mathematics and natural language, in the brain, two genuinely different processes?
