Purser is the son of John Tertius Purser (1809–1893), the general manager of the well known A Guinness, Son & Co. brewery, and Anna Benigna Fridlezius (1803-1881). He is educated in a wealthy family, which includes artists, as his cousin Sarah Purser, or engineers, as his brother-in-law John Purser Griffith. He is the brother of mathematician Frederick Purser. He receives his early education at the private boarding school run by his uncle, Dr. Richard W. Biggs, at Devizes, Wiltshire. He completes his schooling at Devizes and begins his university studies at Trinity College, Dublin, graduating BA in mathematics in 1856. He is the best mathematician of his year at the University and in 1855 he gains the Lloyd Exhibition.
Purser becomes a tutor to the four sons of William Parsons, 3rd Earl of Rosse (1800-1867) in 1857. Lord Rosse’s 72-inch reflecting telescope, built in 1845 and colloquially known of as the “Leviathan of Parsonstown,” is the world’s largest telescope when it is built and continues to hold this distinction until the early 20th century. As well as acting as tutor to the children, Purser does become involved in Lord Rosse’s interest in astronomy but never does any observing.
In 1863, Purser is appointed professor of mathematics at Queen’s College, Belfast, a position he maintains until his retirement in 1901.
Purser is much better known as a teacher than as a researcher, and he has a good number of notable students, including Sir Joseph Larmor, theoretical physicist who serves as Lucasian Professor of Mathematics at the University of Cambridge; Charles Parsons, the inventor of the steam turbine; Sir John Henry MacFarland, who becomes Chancellor of the University of Melbourne; and William McFadden Orr.
Purser never marries. When his father dies on April 5, 1893, Rathmines Castle passes to him. He dies at Rathmines Castle on October 18, 1903, a very wealthy man. In his will he leaves £100,000 to his brother Frederick Purser, £40,000 to his sister Anna Griffith and £5,000 to each of her children. In addition to the money, he owns property in Blessington Street, Essex Street and Eustace Street which he leaves to his brother-in-law John Purser Griffith. Other properties and interests that he owns he divides between his brother Frederick and his sister Anna. After his death, his sister Anna and her husband John Purser Griffith move into Rathmines Castle although, at this time, its ownership has gone to Frederick Purser. After Frederick dies in August 1910, the Castle and his considerable wealth passes to Anna.
(Pictured: Portrait of John Purser painted by the artist Sarah Purser, daughter of Tertius Purser’s brother Benjamin Purser. The portrait hangs in Queen’s College, Belfast.)