James Lockhart (1763–1852) was an English banker who wrote on numerical analysis. Life He was one of three children and two sons of James Lockhart (1735–1814), a Scottish banker, and his wife Mary Harriot Gray or Grey, from a Quaker family; John Ingram Lockhart was his brother, and the daughter was Mary Harriett, married name Greenwollers. He was educated at Reading School and Eton College. Lockhart worked as a banker in Pall Mall, London, in his father's firm Lockhart, Wallace, & Co. He became a partner, and set up the Cattle Insurance Company. Retiring from the bank in 1799, he moved north to the Windermere area after the death of his first wife. Lockhart knew Walking Stewart, and stated he had learned from him. He knew also William Combe, and the idea for Combe's "Dr Syntax" has been attributed to him. He taught mathematics to his own children, and pupils including Joshua King. For about 15 years Lockhart and his family resided in the Netherlands, from 1819, in Leyden and then Haarlem. He returned to England on the death in 1835 of his brother John, who left no heir. Living first at Aylesbury, Lockhart moved to the rectory at Cowley in 1837. After a legal case on his brother's will, the estate at Cowley was sold in 1841. He moved to Brompton. In 1847 his address was given as Lanhams, near Braintree, Essex. Taking a lease on shooting on the Scottish island of Raasay, Lockhart spent time from 1845 on the Isle of Skye. He then lived in an Argyllshire mansion. He moved in 1851 to Clitsome House near Washford in Somerset. He died there the following year. Works Lockhart proposed challenge problems on the separation of the roots of equations of degree five and six, some being published in 1841. He was still writing on the theory of equations while in Argyllshire. The challenges were considered by Florian Cajori to have influenced the work of John Radford Young; William Rutherford noted an analysis by Young of an equation proposed by Lockhart, in a book of 1849. Detailed analysis of a quintic using Budan's theorem for separation of roots was given in 1842, by James R. Christie; it was noted by Young. In 1843 Young commented that Budan's approach, and Lockhart's own ideas, could now be simplified on the basis of recent developments, which had led to Sturm's theorem. Young