- Title
- Making sense of experimental mathematics
- Creator
- Borwein, J.; Borwein, P.; Girgensohn, R.; Parnes, S.
- Relation
- The Mathematical Intelligencer Vol. 18, Issue 4, p. 12-18
- Publisher Link
- http://dx.doi.org/10.1007/BF03026747
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 1996
- Description
- Discovery and Verification. Philosophers have frequently distinguished mathematics from the physical sciences. While the sciences were constrained to fit themselves via experimentation to the real world, mathematicians were allowed more or less free reign within the abstract world of the mind. This picture has served mathematicians well for the past few millennia, but the computer has begun to change this. The computer has given us the ability to look at new mathematical worlds that would have remained inaccessible to the unaided human mind; but this access has come at a price. Many of these worlds, at present, can only be known experimentally. The computer has allowed us to fly through the rarefied domains of hyperbolic spaces and examine more than a billion digits of 'π', but experiencing a world and understanding it are very different. Most of these explorations into the mathematical wilderness remain isolated illustrations. Heuristic conventions, pictures, and diagrams developing in one subfield often have little content for another. In each subfield, unproven results proliferate but remain conjectures, strongly held beliefs, or perhaps mere curiosities passed like folktales across the Internet. It is our hope that by focusing on experimental mathematics today, we can develop a unifying methodology tomorrow.
- Subject
- experimental mathematics; computational mathematics; computational analysis; conjectures
- Identifier
- http://hdl.handle.net/1959.13/940889
- Identifier
- uon:13123
- Identifier
- ISSN:0343-6993
- Language
- eng
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