Editing Imre Lakatos (section)

==== Cauchy and uniform convergence ====
In a 1966 text ''Cauchy and the continuum'', Lakatos re-examines the history of the calculus, with special regard to [[Augustin-Louis Cauchy]] and the concept of uniform convergence, in the light of [[non-standard analysis]]. Lakatos is concerned that historians of mathematics should not judge the evolution of mathematics in terms of currently fashionable theories. As an illustration, he examines Cauchy's proof that the sum of a series of continuous functions is itself continuous. Lakatos is critical of those who would see Cauchy's proof, with its failure to make explicit a suitable convergence hypothesis, merely as an inadequate approach to Weierstrassian analysis. Lakatos sees in such an approach a failure to realize that Cauchy's concept of the continuum differed from currently dominant views.