The Experimental Mathematics is a discipline of mathematics , which is located between classical mathematics and calculations with the computer. In contrast to scientific computing , which serves to solve practical problems, experimental mathematics supports mathematical research itself. The computer is a tool for applying methods of numerical mathematics and computer algebra . Prominent application examples are the four-color problem and Kepler's conjecture . By using the LLL algorithm published since 1982, Andrew Odlyzko and Herman te Riele were able to refute Mertens' conjecture in 1985 .
The journal Experimental Mathematics was founded in 1992 to promote the subject and its methodology . The Journal of Experimental Algorithmics was first published in 1996 as a paperless publication by the Association for Computing Machinery .
In February 2002 the British numeric specialist Lloyd Nicholas Trefethen called a competition under the title 100-Digit Challenge to solve ten extremely difficult calculation problems in the field of scientific computing. Their solution with the greatest possible accuracy required both mathematical ingenuity and mastery of the most advanced numerical methods. After a large number of participants, the varied solutions with the solutions achieved were published and showed the unexpected efficiency of the combined efforts.
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- Tewodros Amdeberhan, Victor H. Moll (Ed.): Tapas in Experimental Mathematics. Contemporary Mathematics Volume 457, AMS 2008, ISBN 0821843176 .
- Christoph Pöppe: The computer as a formula discoverer . Spectrum of Science Publishing Company, Heidelberg January 2009, p. 76-78 .
- Tewodros Amdeberhan, Luis A. Medina, Victor H. Moll (Eds.): Gems in Experimental Mathematics. Contemporary Mathematics Volume 517, AMS 2010, ISBN 0821848690 .
- Website of the journal Experimental Mathematics
- Website for Experimental Mathematics (English)
- Website for the German edition of the book by Bornemann et al.
- Institute for Experimental Mathematics
- David H. Bailey, Jonathan M. Borwein: Exploratory experimentation and computation , Notices AMS 58 (2011) No. 10, pp. 1410–1419 (pdf, 464 kB)