Will the digital computer transform classical mathematics?
Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.
Rotman
Brian
B
Division of Comparative Studies in the Humanities, Ohio State University, Columbus, OH 43210, USA.
D001185:Artificial Intelligence; D003198:Computer Simulation; D003201:Computers / Q000639:trends*; D003205:Computing Methodologies; D008432:Mathematical Computing; D008433:Mathematics; D008962:Models, Theoretical; D013673:Technology Assessment, Biomedical / Q000379:methods*