It seems that individuals who are naturally gifted at mental calculation possess a sort of encoding mechanism for rapid recall of previously acquired mental facts.Calculating prodigies are individuals who are exceptional at quickly and accurately solving complex mental calculations. With positron emission tomography (PET), we investigated the neural bases of the cognitive abilities of an expert calculator and a group of non-experts, contrasting complex mental calculation to memory retrieval of arithmetic facts. We demonstrated that calculation expertise was not due to increased activity of processes that exist in non-experts; rather, the expert and the non-experts used different brain areas for calculation. We found that the expert could switch between short-term effort-requiring storage strategies and highly efficient episodic memory encoding and retrieval, a process that was sustained by right prefrontal and medial temporal areas.
Fortunately, I believe our brains are not hard-wired but able to adapt to imposed stresses and routines so that even non-prodigies can become proficient at performing tasks such as these.
http://en.wikipedia.org/wiki/Mental_calculation
http://www.nature.com/neuro/journal/v4/n1/full/nn0101_103.html