Henrik Kragh Sørensen, of the University of Aarhus (Denmark),
is the winner of the First ICHM Montucla Prize (2005-2008) for his article
Exceptions and counterexamples: understanding Abel’s comment on Cauchy’s Theorem
published in Historia Mathematica (Issue 32.4, 2005)
In this article Sørensen examines Abel’s criticisms of Cauchy’s theorem on the continuity of sums of continuous functions and the fact that Abel regarded a particular series as an exception rather than a counter-example. In doing so Sørensen identifies a crucial transition in analysis, from what he describes as the formula-centered approach characteristic of eighteenth-century mathematics to the concept-centered mathematics that would become dominant in the nineteenth century. Based on close reading of original texts, the article offers fresh and significant insights into the mathematics of the early nineteenth century and is likely to influence future studies of this period.
Henrik Kragh Sørensen with June Barrow-Green and Niccolò Guicciardini in Oberwolfach (Germany)