Kent Scientists

John Wallis  (1616-1703) 

Born in Ashford

A brilliant mathematician and codebreaker, and 'a most ill-natured man'.

John Wallis

John Wallis in 1678

Three centuries before anyone had heard of Bletchley Park and its wartime codebreakers, a one-man codebreaking service was in operation in London. The man behind it was John Wallis, a brilliant mathematician born in 1625 in Ashford, where his father was the vicar at St Mary’s church.  

Wallis began his education in Ashford, but when plague broke out in the town he was moved to schools in Tenterden and then Felsted in Essex. By the age of 24 he had received a degree from Cambridge and become an ordained minister of the church. In 1642 he was serving as private chaplain to a devout widow of the puritan persuasion, Lady Mary Vere, and it was while there that his remarkable talent as a code-breaker first came to light. With the country descending into civil war, coded messages were essential to enable the leaders of both factions, parliamentarians and royalists, to communicate securely with their own supporters. At dinner one evening in the Vere household an intercepted coded letter was passed round. The key to the code was unknown, but Wallis was challenged, half in jest, to reveal what the letter said. This he succeeded in doing by the time he retired to bed.  

News of this unexpected success spread, and over the coming years Wallis was called on to decipher messages on many occasions, serving first the parliamentarians and later the royal court. The first message had employed a simple alphabetical code, in which each letter of the alphabet is replaced by a different one. As time went on, more and more complex numerical codes came into use, but Wallis managed to break almost all of them. At the age of 84 he was appointed to the paid position of official decipherer to King William III.  

Code-breaking was only ever a sideline for John Wallis. His main fame rests on his prowess as a mathematician, one of the greatest of the 17th century. When Isaac Newton famously asserted that in making his own discoveries he “stood on the shoulders of giants”, Wallis is undoubtedly one of the giants he had in mind.  

A page from one of Wallis' books in which he introduces a symbol for infinity (an 8 on its side) for the first time. The underlined words translate 'as denotes an infinite number'.

Remarkably, Wallis never received any formal education in mathematics. He was introduced to the rudiments of arithmetic during a fortnight's school holiday at home in Ashford by one of his brothers who was training for a career for which some grounding in accountancy was needed. After that Wallis taught himself in his spare time from books. By the mid-1640s he was making his mark as a regular attender at meetings held in London and later in Oxford at which the latest developments in ‘Natural Philosophy’ – including the circulation of the blood – were discussed. These meetings would later evolve into the famous Royal Society, founded in 1660 with Wallis an active founder member.

 John Wallis was appointed Professor of Geometry at Oxford University by Oliver Cromwell in 1649, and held the post for 54 years. His great output of books and other writings during this time earned him the accolade of ‘most influential English mathematician before Isaac Newton’. Among his many contributions were a formula for calculating the value of pi and the introduction of a symbol for infinity – a figure eight on its side.  

Map showing The College

Parts of the timber-framed building where Wallis was probably born, known as The College, can still be seen  to the south-east of Ashford parish church.

Wallis was not a likeable man, and made enemies of many of his contemporaries. John Aubrey, who knew Wallis, described him as a ‘most ill-natured man, an egregious liar and backbiter’. But he did possess extraordinary mental powers and a prodigious memory. On one occasion, unable to sleep during an attack of the Ague, he passed the hours of darkness devising a 53 digit number (24,681,357,910,121,411,131,516,182,017,192,122, 242,628,302,325,272,931) and calculating and memorising its 27 digit square root (157,103,016,871,482,805,817,152,171). He recalled the numbers weeks later, when the result was independently tested and found to be correct.  

Wallis was married for 42 years. He died in 1703 and is buried at the university church, St Mary’s, in Oxford. One of his daughters is remembered as the author of an early recipe book, while one of his grandsons inherited his post as official decipherer.  

A school in Ashford was renamed the John Wallis Academy in 2010, and there is a John Wallis pub in the High Street. A Wallis Professorship of Mathematics was instituted at Oxford University in 1969.