Ten Problems in Experimental Mathematics
Abstract
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.
 Authors:
 Publication Date:
 Research Org.:
 Ernest Orlando Lawrence Berkeley NationalLaboratory, Berkeley, CA (US)
 Sponsoring Org.:
 USDOE Director, Office of Science. Office of AdvancedScientific Computing Research. Mathematical, Information, andComputational Sciences Division; National Science Foundation (NSF)
 OSTI Identifier:
 878698
 Report Number(s):
 LBNL57486
R&D Project: KC6714; BnR: YN0100000; TRN: US200611%%405
 DOE Contract Number:
 DEAC0205CH11231; NSF:DMS0342255
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: American Mathematical Monthly; Journal Volume: 113; Related Information: Journal Publication Date: 2006
 Country of Publication:
 United States
 Language:
 English
 Subject:
 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCURACY; EVALUATION; MATHEMATICS; experimental mathematics
Citation Formats
Bailey, David H., Borwein, Jonathan M., Kapoor, Vishaal, and Weisstein, Eric. Ten Problems in Experimental Mathematics. United States: N. p., 2004.
Web.
Bailey, David H., Borwein, Jonathan M., Kapoor, Vishaal, & Weisstein, Eric. Ten Problems in Experimental Mathematics. United States.
Bailey, David H., Borwein, Jonathan M., Kapoor, Vishaal, and Weisstein, Eric. 2004.
"Ten Problems in Experimental Mathematics". United States.
doi:. https://www.osti.gov/servlets/purl/878698.
@article{osti_878698,
title = {Ten Problems in Experimental Mathematics},
author = {Bailey, David H. and Borwein, Jonathan M. and Kapoor, Vishaal and Weisstein, Eric},
abstractNote = {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.},
doi = {},
journal = {American Mathematical Monthly},
number = ,
volume = 113,
place = {United States},
year = 2004,
month = 9
}

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