Pupil size variations reveal Bayesian inference in cognitive arithmetic

This research is very interesting because its "findings show that Bayesian inference is central to arithmetic problem-solving and that information gains consequent to the integration of the operands can be tracked over time through pupillometry." However, what the article did for me was to cause me to reflect on my ability to do mental arithmetic.

My mental arithmetic abilities are poor. I compensated for this problem when I was teaching by using numerous tricks to fool my students. One easy trick was to memorize all of the computations before class using my ability to easily memorize numbers. Of course, computations I hadn't memorized would usually be necessary, so I had little delaying tactics which gave me the extra time I needed to complete those in my head. I'd often get lucky by facing special numbers which allowed me to take shortcuts. I felt like a magician using sleight of mind to deceive the audience of students.

One doesn't have to be good at mental arithmetic to be a good mathematician. Ernst Kummer (1810–1893) didn't know his multiplication tables, yet he made fundamental contributions to number theory—something I find to be ironic. Stephen Smale (1930–present) won a Fields Medal despite his struggles with mental arithmetic. When asked to give an example of a prime number, Alexandre Grothendieck—a mathematician supreme—gave 57 which is obviously divisible by 3. On the other hand, the great Carl Friedrich Gauss (1777-1855) could perform amazingly complex computations in his head with ease.

A friend of mine from graduate school has incredible mental arithmetic abilities. I once watched him humiliate an arrogant professor we all hated by crushing the guy in a contest to mentally find the mean of 50 exam scores written on a chalkboard. We had a long laugh after the professor left the room in a fit of rage.

My take on this is that there are many types of mathematical minds. Diversity is the rule here.

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