Source: Tw.
The case of the German man Zacharias Dase is rather curious. He began school early at age 2.5 yrs & showed remarkable interest & capacity in arithmetic. He started having seizures shortly thereafter till his death at age 37. Concomitantly his mental development was quite limited but his prodigious arithmetic capacity remained till his death. He calculate pi using a sum of arctangents formula correctly to 200 digits & performed many feats of calculating log tables & the like mentally even as he used to chat with others. It was almost as if a subconscious computer was running in his brain even as his conscious did mundane things – sometimes these computations with huge numbers 100 digits will take hours but he would ultimately print out the right answer.(4)
However, when they tried to teach him basic Euclid he could not even understand the basic theorem of Proclus – the bridge of the ass – if the two angles of a triangle are congruent the opposite sides are also congruent. Nevertheless,he caught the attention of Carl Gauss who obtained a stipend for him to prepare tables of prime factors of #s till n=10^7. He died somewhere ~8*10^6.
Ironically, before that 2 other Germanic guys a certain Hindenburg and Felkel both claimed to have invented mechanical computers based on the ideas of Johann Lambert to compute factors. Felkel claimed his computer could factorize ~240 numbers an hour. However, neither of them really got anywhere near were they promised. If my history is right, correct factorization till n=10^7 had to wait till the Lehmer family invented their computer. It shows how on the cusp of modernity the human computers still outdid mechanical ones.
It also shows like many other examples that while the human brain has the hardware to be like a mechanical (electronic included) one, if it gets routed that way it is usually at a serious cost & seems to accompany a fitness-nullifying illness, as was the case with Zacharias Dase.(5)
Dase also possessed a skill quite like the modern artist Stephen Wiltshire: he could instantaneously count a large number of same/identical objects like sheep in a herd or windows in building. He could also switch off the mental layer in which the computations happened, go to sleep & wake up switch it back on to resume wherever in the middle he had stopped the computation. However, it seems that if he was having a seizure this mental layer would spew out wrong computations as happened on an occasion when he was tested during such an episode.(5)
A facsimile of the special slips of paper that Gauss had made for computing the prime distribution recording the point where he arrived at the logarithmic integral for the same - https://t.co/s1IsYBLQ7y. He had hoped to used Dase’s tables for a more extensive exploration of the same.