He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor, the leading master of his time, left a valuable historical record for future generations.
Atwood was born in Westminster, with the date remaining unknown, but presumed to have been shortly before his baptism on 15 October 1745.
In 1784, he left Cambridge and soon afterwards received from William Pitt the Younger the office of patent searcher of the customs, which required but little attendance, enabling him to devote a considerable portion of his time to mathematics and physics.
Atwood died unmarried in Westminster at the age of 61, and was buried there at St. Margaret's Church.
Atwood's published works, exclusive of papers contributed to the Philosophical Transactions, for one of which he obtained the 1796 Copley Medal, are as follows: