The mathematical capabilities of autistic savants are often among of the most difficult parts of their repertoire to understand or explain. These may include lightening-fast calculation or other feats of computation. And oftentimes, as in Daniel Tammet's case, their description of numbers as having color and texture or shape is likewise difficult to conceive. Tammet is famous for reciting pi accurately to 22,000 digits, a virtually inconceivable accomplishment, but aided by his of pi as not just a number, but a landscape so-to-speak.
Interestingly in his new book Tammet hypothesizes that his math prowess stems from "abnormal cross-communication" between areas of the brain that govern math skill and those that govern language, and specifically syntactic rules, which normally are separate. He points out that the two areas (left parietal lobe and and left frontal lobe) lay physically next to each other in the brain, and that his "numerical abilities are rapid, intuitive, and largely unconscious" very much like the way most people speak and process language. Also, he notes that along with his mathematical talents he has already learned a dozen languages, and very easily picks up new languages to a conversational level. His explanation is purely intuitive and speculative (so far as I know), but seems to make as much sense as anything else offered by others.
In a totally different section of the book (on logical thinking) Tammet throws out this simple, yet interesting old puzzle-example of Lewis Carroll's:
a) My saucepans are the only things I have that are made of tin.
b) I find all your presents very useful.
c) None of my saucepans are of the slightest use.
...and then asks, what is the 'ultimate' logical implication arising from these statements? (answer below)
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answer: your presents are not made of tin
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