Treatise on the Continuum

Thomas Bradwardine's Tractatus de continuo, completed around 1330 while he was a fellow at Merton College, Oxford, represents one of the most sophisticated medieval attempts to resolve fundamental questions about the nature of space, time, and infinity. Written during the flourishing of mathematical theology at Oxford, this treatise emerged from scholastic debates over Aristotelian physics and the theological implications of mathematical concepts, particularly how to understand God's relationship to creation through geometric and arithmetic principles.

Bradwardine develops a rigorous mathematical framework for understanding continuity, arguing that continuous quantities like lines and surfaces are composed of infinitely many indivisible points, while rejecting atomistic theories that would divide creation into discrete, finite units. He employs sophisticated geometric proofs to demonstrate that ratios and proportions reveal fundamental truths about divine order, connecting mathematical infinity to God's infinite nature. The work systematically addresses paradoxes of the infinite, offering solutions that preserve both Aristotelian natural philosophy and Christian doctrine about divine transcendence. Bradwardine's analysis of motion, change, and geometric relationships serves his larger theological project of demonstrating how mathematical reasoning supports rather than threatens Christian metaphysics.

This treatise established Bradwardine as a leading figure in medieval mathematical theology and influenced subsequent developments in both natural philosophy and scholastic theology. The work demonstrates how seriously medieval Christian thinkers engaged with mathematical concepts as tools for understanding divine truth, prefiguring later developments in mathematical physics. Scholars of medieval philosophy and theology will find here a sophisticated example of how mathematical reasoning was integrated with Christian doctrine, while those interested in the history of mathematics will discover important developments in the theory of continuity and infinity that preceded modern calculus.