Sir James Stirling, FRS (3 May 1836 – 27 June 1916) was a British barrister, judge, and amateur scientist. In his youth he demonstrated exceptional ability in mathematics, becoming Senior Wrangler at Cambridge in 1860, regarded at the time as "the highest intellectual achievement attainable in Britain". He was a High Court judge in the Chancery Division from 1886 to 1900, and a Lord Justice of Appeal from 1900, when he was made a Privy Counsellor, until his retirement in 1906. He continued to pursue his scientific and mathematical interests during his legal career, and after retiring from the bench became vice-president of the Royal Society in 1909–1910.