Exploratory Experimentation and Computation.

Bailey, D. H. ; Borwein, J. M.

Technical Information Center Oak Ridge Tennessee

关键词: Capacity;    Classification;    Computers;    Internet;    Poincare conjecture;   

RP-ID  :  DE2010983178

学科分类：工程和技术（综合）

美国|英语

来源: National Technical Reports Library

【 摘 要 】

We believe the mathematical research community is facing a great challenge to re-evaluate the role of proof in light of recent developments. On one hand, the growing power of current computer systems, of modern mathematical computing packages, and of the growing capacity to data-mine on the Internet, has provided marvelous resources to the research mathematician. On the other hand, the enormous complexity of many modern capstone results such as the Poincare conjecture, Fermat's last theorem, and the classification of finite simple groups has raised questions as to how we can better ensure the integrity of modern mathematics. Yet as the need and prospects for inductive mathematics blossom, the requirement to ensure the role of proof is properly founded remains undiminished.