[2][3] Buxton was born in 1707 and although his father was schoolmaster of Elmton, and his grandfather had been the vicar, he could not write; and his knowledge, except of numbers, was extremely limited.
It appears that he had invented an original nomenclature for large numbers, a 'tribe' being the cube of a million, and a 'cramp' (if Mr. Holliday's statement can be trusted) a thousand 'tribes of tribes'.
[1] His mental acuity was tested in 1754 by the Royal Society when he walked to London,[1] who acknowledged their satisfaction by presenting him with a handsome gratuity.
[1] Similarly, he set himself to count the steps of the dancers; and he declared that the innumerable sounds produced by the musical instruments had perplexed him beyond measure.
A memoir appeared in the Gentleman's Magazine for June 1754, to which (probably through the medium of a Mr Holliday, of Haughton Hall, Nottinghamshire), Buxton had contributed several letters.
In this memoir, his age is given as forty-nine, which points to his birth in 1705; the date adopted above is on the authority of Daniel and Samuel Lysons' Magna Britannia (Derbyshire).