He co-founded what became the Royal Society and was 
      appointed by Oliver Cromwell to the  
Savilian Chair of Geometry at age 33 despite political and religious opposition, a fair amount 
of which was caused by Wallis' signing a document opposing 
      the execution of King Charles I. A 
bitter twenty year dispute with Thomas Hobbes started in 1655: whatever points Hobbes may 
have had as a philosopher,  his claim of squaring the 
      circle was demolished by Wallis. In 1657 
there was more controversy when Wallis was appointed keeper of the Oxford University 
Archives. When the monarchy was restored in 1660, King Charles II confirmed 
      Wallis' 
appointment to the Savilian Chair , made Wallis the Royal Chaplain and nominated him to a 
committee to revise the Prayer Book.
      a third-order 
cochleoid