The task you have set me, of surveying in the space of 50 minutes the contribution of the Scots to mathematics, is a well-nigh impossible one. Such a survey must begin with the revival of learning in western Europe, and may appropriately end shortly before the middle of the nineteenth century, when the concept of Scottish mathematics begins to lose definition; an exact date might be fixed, rather arbitrarily, by the first appointment of an Englishman to a Scottish mathematical chair in 1838, when Philip Kelland succeeded William Wallace at Edinburgh. These limits will exclude many distinguished mathematicians of Scottish birth active during the last 100 years, such as Sir Thomas Muir and Maclagan Wedderburn, not to speak of the applied mathematicians Kelvin, Tait and Clerk Maxwell.