## Spot the flaw

Mathematical talent varies widely. It was a humbling thing a few years ago to sit in an upper level college math class on Abstract Algebra with a 16 year old high school student taking the course, listening with one ear while he did his German homework. He was later a double summa in both math and physics at Yale. So do mathematicians think differently? A fascinating paper implies that they use different parts of their brain doing math than when not doing it. The paper has one methodological flaw — see if you can find it.

[ Proc. Natl. Acad. Sci. vol. 113 pp. 4887 – 4889, 4909 – 4917 ’16 ] 15 expert mathematicians and 15 nonMathematicians with comparable academic qualifications were studied (3 literature, 3 history 1 philosophy 2 linguistics, 1 antiquity, 3 graphic arts and theater 1 communcation, 1 heritage conservation — fortunately no feminist studies). They had to listen to mathematical and nonMathematical statements and decide true false or meaningless. The nonMathematical statements referred to general knowledge of nature and history. All this while they were embedded in a Magnetic Resonance Imager, so that functional MRI (fMRI) could be performed.

In mathematicians there was no overlap of the math responsive network (e.g. the areas of the brain activated by doing math) with the areas activated by sentence comprehension and general semantic knowledge.

The same brain networks were activated by all types of mathematical statement (geometry, analysis, algebra and topology) as opposed to nonMathematical statement. The areas activated were the dorsal parietal, ventrolateral temporal and bilateral frontal. This was only present in the expert mathematicians (and only to mathematical statements) These areas are outside those associated with language (inferior frontal gyrus of the left hemisphere). The activated areas are also involved in visual processing of arabic numbers and simple calculation. The activated areas in mathematicians were NOT those related to language or general knowledge.

So what’s wrong with the conclusion? The editorialist (pp. 4887 – 4889) pointed this out but I thought of it independently.

All you can say is that experts working in their field of expertise use different parts of their brain than they use for general knowledge. The nonMathematicians should have been tested in their field of expertise. Shouldn’t be hard to do.

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