Mathematics has been studied at the University of Edinburgh from its very foundation in 1583. In the early years, all students followed the same MA curriculum, modelled on that of other European universities such as Paris and Bologna. It included Greek, Logic, Philosophy, Natural Philosophy (as Physics was then known) and Mathematics. Notable amongst the early Professors of Mathematics were the three Gregory's - James, his nephew David and David's brother James - who held the Chair in succession from 1674 to 1742. They were enthusiastic supporters of Isaac Newton and incorporated his ideas into their teaching, ideas which at that time were controversial and considered quite revolutionary.

Colin Maclaurin joined the younger James Gregory in 1725, formally as his assistant but actually undertaking his duties, as Gregory was unable to teach because of poor health. As an assistant, Maclaurin was not entitled to a salary. However Newton, who by then was Master of the Mint and had a very high opinion of Maclaurin's ability, offered to contribute £20 per annum towards his support. Maclaurin eventually succeeded Gregory as Professor of Mathematics in 1742 and occupied the Chair until his own death in 1746. He was a mathematician of considerable international repute, described in the Dictionary of National Biography as "the one mathematician of first rank trained in Great Britain in the eighteenth century". A brilliant lecturer, his courses covered a whole range of topics from geometry, trigonometry, algebra and calculus to optics, astronomy and even the theory of gunnery. He also advised the Church of Scotland when it set up a fund to provide pensions for the widows of ministers - some say that this represented the birth of actuarial science.

In the latter part of the eighteenth century, the University saw a number of mathematicians such as Adam Ferguson, John Playfair and Sir John Leslie who were typical of their time, the age of the Scottish Enlightenment. They were all-round scholars who could well move from a chair in Moral Philosophy to one in Mathematics or from one in Mathematics to Natural Philosophy. The nineteenth century saw the controversial appointment of the Rev Philip Kelland as Professor of Mathematics. He was the first Englishman with an entirely English education admitted to a chair in the University and held the Chair for 41 years. He would have taught James Clerk Maxwell, one of the great scientists of the nineteenth century and perhaps Scotland's greatest. Kelland was succeeded by George Chrystal who, although an applied mathematician, is best known for his book on Algebra. This was intended for secondary schools and indeed remained a standard text well into the twentieth century. The Faculty of Science was created in 1893, during Chrystal's tenure of office, but Mathematics was to remain within the Arts Faculty for some time to come.

Chrystal's successor, Sir Edmund Whittaker, was appointed in 1912. He was a highly influential figure within UK mathematics, with interests spanning many areas, and the Department flourished under the 34 years of his leadership. The second half of the twentieth century saw a substantial increase in the size of the Department, from around 12 members of staff to over 40. A second Chair of Mathematics, named after Colin Maclaurin, was created in 1964 followed by a Chair of Applied Mathematics in 1968.

Statistics had been taught within the mathematics curriculum for many years - indeed, Whittaker's successor, Alexander Aitken, was an eminent theoretical statistician. In 1966 a separate Chair of Statistics was created and with it a separate Department within the then Faculty of Science. At the same time, Mathematics finally moved from the Arts to the Science Faculty. However, the two Departments came together again in 1991 in the Department of Mathematics and Statistics and, with the restructuring of the University in 2002, this transformed into the School of Mathematics in the College of Science and Engineering.