Ten Problems in Experimental Mathematics

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This article was stimulated by the recent SIAM ''100 DigitChallenge'' of Nick Trefethen, beautifully described in a recent book. Indeed, these ten numeric challenge problems are also listed in a recent book by two of present authors, where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent was to present ten problems that are characteristic of the sorts of problems that commonly arise in ''experimental mathematics''. The challenge in each case is to obtain a high precision numeric evaluation of the quantity, and then, if possible, to obtain a symbolic answer, ideally ... continued below

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Bailey, David H.; Borwein, Jonathan M.; Kapoor, Vishaal & Weisstein, Eric September 30, 2004.

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This article was stimulated by the recent SIAM ''100 DigitChallenge'' of Nick Trefethen, beautifully described in a recent book. Indeed, these ten numeric challenge problems are also listed in a recent book by two of present authors, where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent was to present ten problems that are characteristic of the sorts of problems that commonly arise in ''experimental mathematics''. The challenge in each case is to obtain a high precision numeric evaluation of the quantity, and then, if possible, to obtain a symbolic answer, ideally one with proof. Our goal in this article is to provide solutions to these ten problems, and in the process present a concise account of how one combines symbolic and numeric computation, which may be termed ''hybrid computation'', in the process of mathematical discovery.

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  • Journal Name: American Mathematical Monthly; Journal Volume: 113; Related Information: Journal Publication Date: 2006

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  • Report No.: LBNL--57486
  • Grant Number: DE-AC02-05CH11231
  • Grant Number: NSF:DMS-0342255
  • Office of Scientific & Technical Information Report Number: 878698
  • Archival Resource Key: ark:/67531/metadc879570

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  • September 30, 2004

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  • Sept. 21, 2016, 2:29 a.m.

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  • Sept. 29, 2016, 7:11 p.m.

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Bailey, David H.; Borwein, Jonathan M.; Kapoor, Vishaal & Weisstein, Eric. Ten Problems in Experimental Mathematics, article, September 30, 2004; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc879570/: accessed June 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.