Mathematics Magazine for Grades 112 





We look here at a few mathematicians who have shown extraordinary powers of memory and calculating. First we mention John Wallis (Born: 23 Nov 1616 in
Ashford, Kent, England Died: 28 Oct 1703 in Oxford, England) whose calculating
powers are described: [Wallis] occupied himself in finding (mentally) the integral part of the square root of 3 10^{40}; and several hours afterwards wrote down the result from memory. This fact having attracted notice, two months later he was challenged to extract the square root of a number of 53 digits; this he performed mentally, and a month later he dictated the answer that he had not meantime committed to writing. Von Neumann (Born: 28 Dec 1903 in Budapest, Hungary
 Died: 8 Feb 1957 in Washington D.C., USA) whose feats of memory are described
by Herman Goldstine: As far as I could tell, von Neumann was able on
once reading a book or article to quote it back verbatim; moreover he could do
it years later without hesitation. He could also translate it at no diminution
in speed from its original language into English. On one occasion I tested his
ability by asking him to tell me how the 'Tale of Two Cities' started.
Whereupon, without pause, he immediately began to recite the first chapter and
continued until asked to stop after about ten or fifteen minutes. Von Neumann's ability to do mental arithmetic is the source of a large number of stories which no doubt have grown the more impressive with the telling. It is hard to decide between fact and fiction. However, it is clear that multiplying two eight digit numbers in his head was a task that he could accomplish with little effort. Again it would appear that von Neumann's 'almost perfect' memory played a large part in his ability to calculate. Only one mathematician has ever described in detail how he was able to perform incredible feats of memory and calculating. This is A C Aitken,( Born: 1 April 1895 in Dunedin, New Zealand Died: 3 Nov 1967 in Edinburgh, Scotland) . He could instantly give the product of two numbers each
of four digits but hesitated if both numbers exceeded 10,000. Among
questions asked him at this time were to raise 8 to the 16th
power; in a few seconds he gave the answer 281,474,976,710,656 which is
correct. ... he worked less quickly when asked to raise numbers of two digits
like 37 or 59 to high powers. ... Asked for
the factors of 247,483 he replied 941 and 263; asked for
the factors of 171,395 he gave 5, 7, 59 and 83, asked for
the factors of 36,083 he said there were none. He, however, found it
difficult to answer questions about numbers higher than 1,000,000. Another mathematician George Parker Bidder was born
in 1806 at Moreton Hampstead in Devonshire, England. He was not one to lose his
skills when educated and wrote an interesting account of his powers in
calculating. Again it is worth noting that other members of his family had
exceptional powers of memory and calculating. One of his brothers knew the Bible by heart, another brother, who was an actuary, had the misfortune of having all his books destroyed in a fire. This was not the problem it might have been to an ordinary person since he was able, in the period of six months, to rewrite them from memory. One of Bidder's sons was able to multiply two numbers of 15 digits but he was slow, and less accurate, compared with his father. 
