2006/10/08 by Jf. Colombeau, JF. Colombeau, Colombeau, JF. · 2 citations
Computer Science · Mathematics · #03H99 #35D05 #35D10 #35L67 #35R05 #46F30 #82D20 #83C35 #83C57 #83C75 #FOS: Mathematics #Functional Analysis (math.FA) #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Numerical Methods and Algorithms #math.FA #math.GM #msc:03H99 #msc:35D05 #msc:35D10 #msc:35L67 #msc:35R05 #msc:46F30 #msc:82D20 #msc:83C35 #msc:83C57 #msc:83C75
paper · pdf · doi:10.48550/arxiv.math/0610264
7 pages,research-expository paper
arxiv created 2006/10/08 · openalex publication_date 2006/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It has been widely believed for half a century that there will never exist a nonlinear theory of generalized functions, in any mathematical context. The aim of this text is to show the converse is the case and invite the reader to participate in the debate and to examine the consequences at an unexpectedly elementary level. The paradox appears as another instance of the historical controversy on the existence of infinitesimals in mathematics, which provides a connection with nonstandard analysis. This text is the written version of a talk at the meeting of Nonstandard Analysis, Pisa, june 2006.