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

The belated introduction of "continental" analysis to Britain was led by the Scottish mathematicians James Ivory and William Wallace in the early part of the 19th century, some years before its adoption at Cambridge University. William Wallace succeeded John Leslie as professor of mathematics at Edinburgh University, where birth confronted the conflicting ideologies of Euclidean geometry and algebraic analysis. The transitional state of Scottish mathematics at this time is vividly portrayed in their letters and publications and in letters of the writer Thomas Carlyle. Though Leslie and Wallace appreciated the power of the new analysis, and Wallace was an able exponent, both chose to emphasize Euclidean geometry in their courses. The philosophical, educational, and practical reasons for this are explored. Publication 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 concerned the logical foundations of analysis and geometry and nicely illustrates prevailing attitudes and rivalries. Though Leslie and Wallace began as friends, an intense animosity developed. This culminated in a quarrel over the teaching of astronomy, which highlights the difficulties of recruiting students to mathematics. (C) 2000 Academic Press.