section_path: History of the theory of infinite series/Uniform convergence
section_name: Uniform convergence
paragraph_text: Uniform convergence
  
  The theory of uniform convergence was treated by Cauchy (1821), his limitations being pointed out by Abel, but the first to attack itsuccessfully were Seidel and Stokes (1847–48). Cauchy took up theproblem again (1853), acknowledging Abel's criticism, and reachingthe same conclusions which Stokes had already found. Thomae used thedoctrine (1866), but there was great delay in recognizing the importance of distinguishing between uniform and non-uniformconvergence, in spite of the demands of the theory of functions.