Mathematician and academic. Born in OldMeldrum and educated at the Grammar School and University in Aberdeen, excelling in both institutions. He studied under James Clerk Maxwell (1831-79) at Cambridge. Appointed to the Regius Chair of Mathematics at St. Andrews, he became a regular contributor to the Encyclopaedia Britannica. In 1879, he accepted the Chair in Mathematics at the University of Edinburgh.
Perhaps Chrystal's greatest contribution was in educational reform. He was an enthusiastic contributor to the framing of The Universities (Scotland) Act, 1889 which liberalised University constitutions and curricula. Chrystal was instrumental in the introduction in 1888 of a Leaving Certificate Examination common to all schools.