He was born in England and received his professional education at Trinity College from 1870 to 1874. In 1875, he was appointed Professor of Mathematics at the University of Melbourne, in the state of Victoria, Australia where he immigrated. Nanson was an election reformer and office bearer of the Proportional Representation League of Victoria who produced several booklets on election methods. He retired from his lifetime appointment in 1922. At the time of his death, he was survived by ten children from two marriages. The Professor Nanson Prize was named in his honour, which is annually awarded to students for outstanding achievements in pure and applied mathematics.