Dixon's fellowship allowed him to remain at Merton College until he was appointed to the Savilian chair of pure mathematics in Oxford in 1922. Arthur and Catherine Dixon had one daughter and after Catherine's death in 1930, Dixon made his home with his daughter who by this time was married to F J Baden Fuller and living in Sandgate, Kent.
Dixon ng relasyon na pinahihintulutan sa kanya upang manatili sa Merton College hanggang siya ay hihirangin upang angkinin ang Savilian chair ng purong matematika sa Oxford in 1922. Arthur at Catherine Dixon nagkaroon ng isang anak na babae at pagkatapos Catherine ng kamatayan sa 1930, Dixon ginawa sa kanyang tahanan sa kanyang anak na babae na ayon sa oras na ito ay kasal sa FJ Baden Fuller at nakatira sa Sandgate, Kent.