Wilson was born in St. Andrews, Fife, the son of Patrick Wilson, the town clerk. Alexander was educated at the University of St. Andrews from where he graduated MA in 1733, at the age of 18. He was first apprenticed to a physician in St Andrews where he became skilled in constructing mercury thermometers in glass. In 1737 he left for London, to make his fortune and found work as assistant to a French surgeon-apothecary, which included caring for his patients. During this time he was introduced to Lord Isla who like Wilson was interested in astronomy, and Wilson constructed instruments for Isla during 1738. After visiting a type foundry with a friend in London, he had an idea for making better typefaces. He and his friend John Baine returned to St Andrews in 1739, where they started a type-founding business in 1742.
The company moved to Camlachie, near Glasgow in 1744. In 1748 he was appointed type-founder to Glasgow University. In the following year the partnership with Baine was dissolved. Later his sons became partners. He supplied types to the Foulis press making possible their beautiful and artistic publications. Among modern typefaces, Fontana, Scotch Roman, and Wilson Greek are based on types cut by Alexander Wilson. In 1749 Wilson made the first recorded use of kites in meteorology with his lodger, a 23-year-old Glasgow University student Thomas Melvill, who went on to discover sodium light. They measured air temperature at various levels above the ground simultaneously with a train of kites. With the help of his friend Lord Isla, now the 3rd Duke of Argyle, he was appointed in 1760 to the new chair of practical astronomy at the University of Glasgow, which had recently built the Macfarlane Observatory. Wilson primarily made contributions to astronomy and meteorology, and posited that "what hinders the fixed stars from falling upon one another", the question that Newton had posed in his Opticks, was that the entire universe rotated around its centre. Wilson noted that sunspots viewed near the edge of the Sun's visible disk appear depressed below the solar surface, a phenomenon referred to as the Wilson effect. When the Royal Danish Academy of Sciences and Letters announced a prize to be awarded for the best essay on the nature of solar spots, Wilson submitted an entry. On 18 February 1772 the Academy presented Wilson with a gold medal for his work on sunspots. The crater Wilson on the Moon is named for him, Ralph Elmer Wilson and CTR Wilson. He, and his second son Patrick Wilson, were two of the founding members of the Royal Society of Edinburgh. Patrick wrote a biographical article of his father which was published both in the Transactions of the RSE and EdinburghJournal of Science. In 1783 he was a joint founder of the Royal Society of Edinburgh. He died in Edinburgh on 16 October 1786.
