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Alexander Chisholm Gooden was born on 4 April 1818, the son of James Gooden and his wife Mary, née Chisholm. He was first taught at home by his father and then attended private school before enrolling in London University School, but at the age of 15 he left school and was coached privately in mathematics by Augustus de Morgan and in classics by George Long. He was admitted to Trinity College, Cambridge, in 1836 on the tutorial side of Thomas Thorp, intending to study classics, though the nature of the mid-century Cambridge education required him to take honours in mathematics first. In March 1840 he graduated as joint-Senior Classic and in the same year gained the 1st Chancellor's Medal. He then set himself to reading in order to compete for a College Fellowship, but while studying at Bonn he succumbed to a bout of peritonitis, dying on 22 August 1841.