Geometry versus analysis in early 19th-century Scotland: John Leslie, William Wallace, and Thomas Carlyle

The belated introduction of "continental" analysis to Britain was led by th e Scottish mathematicians James Ivory and William Wallace in the early part of the 19th century, some years before its adoption at Cambridge Universit y. William Wallace succeeded John Leslie as professor of mathematics at Edi nburgh University, where birth confronted the conflicting ideologies of Euc lidean geometry and algebraic analysis. The transitional state of Scottish mathematics at this time is vividly portrayed in their letters and publicat ions and in letters of the writer Thomas Carlyle. Though Leslie and Wallace appreciated the power of the new analysis, and Wallace was an able exponen t, both chose to emphasize Euclidean geometry in their courses. The philoso phical, educational, and practical reasons for this are explored. Publicati on by David Brewster of Legendre's Geometrie, translated by Thomas Carlyle, provoked a scholarly dispute among various protagonists, including Leslie, Adrien-Marie Legendre, James ivory, and an anonymous "Sigma" This concerne d the logical foundations of analysis and geometry and nicely illustrates p revailing attitudes and rivalries. Though Leslie and Wallace began as frien ds, an intense animosity developed. This culminated in a quarrel over the t eaching of astronomy, which highlights the difficulties of recruiting stude nts to mathematics. (C) 2000 Academic Press.