St. George Ashe was born in County Roscommon and educated at Trinity College, Dublin. He became a fellow of the College in 1679 and then professor of Mathematics. During the political unrest of James II reign, he left Ireland and became Chaplain and Secretary to Lord Paget, Ambassador to William III at the Court of Vienna. He returned to Ireland and became Provost of the College in 1692. At Trinity, Ashe together with William Molyneux were prominent members of the Dublin Philosophical Society which had been established in the early 1680's. It was a forum were new ideas and especially those which reflected the growth of natural science and philosophy could be debated and discussed. In 1686, for instance, Ashe read a paper to the Society outlining his invention of a new solid fuel which consisted of a combination of clay and coal dust. In addition, Ashe became a college tutor to Jonathan Swift at Trinity. It proved to be the beginning of a lifelong friendship, and the academic is to have married Swift and Hester Johnson (Stella) when he was Bishop of Clogher.
Ashe was to hold three bishoprics during his lifetime:
Cloyne, 1695;Clogher,1697, where he spent £900 on improving the episcopal palace and lands;
Derry, 1717. He had been offered the archbishopric of Tuam on the death of John Vesey in 1716, but refused on account of his inadequate income. Archbishop King censured him for his absenteeism when he was Bishop of Clogher. Writing in September 1714, the Archbishop urged him to reform his ways:
"Your friends murmur at your deserting them, and your enemies excuse their negligence by your absence; and the common enemies of the church conclude that bishops are not necessary, since they can be so long spared. I, therefore, entreat you to think of coming home as soon as possible."
Ashe died in Dublin on the 27th February 1718 and left his mathematical books to Trinity College, Dublin. Joseph Addison, the Whig secretary of state, commiserated with Swift over the death of Ashe. He was a man, Addison remarked, "who has scare left behind him his equal in humanity, agreeable conversation, and all kinds of learning".