Wilson"s theorem is named after him. Wilson attended school in Staveley, Cumbria before going up to Peterhouse, Cambridge in 1757, where he was a student of Edward Waring. He was Senior Wrangler in 1761.
He was later knighted, and became a Fellow of the Royal Society in 1782.
He was Judge of Common Pleas from 1786 until his death in 1793.