Experimental mathematics is a type of mathematical investigation in which computation is used to investigate mathematical structures and identify their fundamental properties and patterns. As in experimental science, experimental mathematics can be used to make mathematical predictions which can then be verified or falsified on the bases of additional computational experiments.
Borwein and Bailey (2003, pp. 2-3) use the term "experimental mathematics" to mean the methodology of doing mathematics that includes the use of computation for:
1. Gaining insight and intuition.
2. Discovering new patterns and relationships.
3. Using graphical displays to suggest underlying mathematical principles.
4. Testing and especially falsifying conjectures.
5. Exploring a possible result to see if it is worth formal proof.
6. Suggesting approaches for a formal proof.
7. Replacing lengthy hand derivations with computer-based derivations.
8. Confirming analytically derived results.
Examples of tools of experimental mathematics include computer algebra , symbolic algebra , Gröbner
basis , integer relation algorithms (such
as the LLL algorithm and PSLQ
algorithm ), arbitrary precision numerical
evaluations, computer visualization, cellular automata
and related structures, and databases of mathematical structures such as the Online
Encyclopedia of Integer Sequences (http://www.research.att.com/~njas/sequences )
by Neil Sloane, The Wolfram Functions Site (http://functions.wolfram.com )
by Michael Trott and Oleg Marichev, and MathWorld (http://mathworld.wolfram.com )
by Eric Weisstein.
See also Arbitrary Precision ,
Cellular Automaton ,
Computational Algebra ,
Computer Algebra ,
Integer
Relation ,
LLL Algorithm ,
New
Kind of Science ,
Proof ,
PSLQ
Algorithm ,
Simple Program ,
Symbolic
Algebra ,
Triangle Geometry
Explore with Wolfram|Alpha
References Bailey, D. H. and Borwein, J. M. "Sample Problems of Experimental Mathematics." 22 Sept. 2003. http://crd.lbl.gov/~dhbailey/expmath/expmath-probs.pdf . Bailey,
D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.;
and Moll, V. H. Experimental
Mathematics in Action. Bailey,
D. H.; Borwein, J. M.; Kapoor, V.; and Weisstein, E. W. "Ten
Problems in Experimental Mathematics." Amer. Math. Monthly 113 ,
481-509, 2006. Boros, G. and Moll, V. Irresistible
Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals. Borwein, J. and
Bailey, D. Mathematics
by Experiment: Plausible Reasoning in the 21st Century. Borwein, J.; Bailey, D.; and Girgensohn, R. Experimentation
in Mathematics: Computational Paths to Discovery. Borwein, J. M.; Borwein, P. B.; Girgensohn, R.; and Parnes,
S. "Making Sense of Experimental Mathematics." Math. Intell. 18 ,
12-18, 1996. Reprinted in Borwein, J. and Bailey, D. Mathematics
by Experiment: Plausible Reasoning in the 21st Century. Borwein, P. B. Computational
Excursions in Analysis and Number Theory. Epstein,
D. and Levy, S. "Experimentation and Proof in Mathematics." Not. Amer.
Math. Soc. 42 , 670-674, 1995. Experimental Mathematics. http://www.expmath.org/ .Gibbs, W. W.
"A Digital Slice of Pi. The New Way to do Pure Math: Experimentally." Sci.
Amer. 288 , 23-24, May 2003. Guénard, F. and Lemberg,
H. La
méthode expérimentale en mathématiques. Kimberling, C. "Encyclopedia of
Triangle Centers." http://faculty.evansville.edu/ck6/encyclopedia/ . Li,
S.; Chen, F.; and Wu, Y.; and Zhang, Y. Mathematics
Experiments. Sloane, N. J. A.
"The On-Line Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/ . Weisstein,
E. W. "MathWorld." http://mathworld.wolfram.com/ . Wolfram
Institute. "The Wolfram Atlas of Simple Programs." http://atlas.wolfram.com/ . Wolfram
Research, Inc. "The Wolfram Functions Site." http://functions.wolfram.com/ . Wolfram,
S. A
New Kind of Science. 337 -342,
2002. Referenced on Wolfram|Alpha Experimental Mathematics
Cite this as:
Weisstein, Eric W. "Experimental Mathematics."
From MathWorld https://mathworld.wolfram.com/ExperimentalMathematics.html
Subject classifications
