Making sense of experimental mathematics. (English) Zbl 0874.00027

Authors’ conclusion: Results discovered experimentally will, in general, lack some of the rigor associated with mathematics, but will provide general insights into mathematical problems to guide further exploration, either experimental or traditional. Conjectures experimentally verified will give us more confidence in our direction, even when strongly held beliefs elude proof. One can hope to produce an intuitive view of mathematics that can be transferred in concrete examples and analysis, as opposed to the current system where intuitions can be transmitted only from person to person. If the mathematical community as a whole were less splintered, we would probably remove the word “codification” from the definition. But there are real communication problems between fields. Experimental investigators must make every effort to organize their insights and present their data in a manner that will be as widely accessible as possible.


00A99 General and miscellaneous specific topics
Full Text: DOI


[1] Barnsley, M., Fractals Everywhere (1988), New York: Academic Press, New York · Zbl 0691.58001
[2] Barnsley, M.; Hurd, L., Fractal Image Compression (1993), London: AK Peters, London · Zbl 0796.68186
[3] K. Gerow,An Algorithm for Random Balanced Sampling, University of Guelph, 1984.
[4] K. Gerow,Model-unbiased, Unbiased-in-general Estimation of a Regression Function, Cornell University, 1993.
[5] K. Gerow and J. Holbrook, Construction of random balanced samples, working paper, 1990.
[6] Gutmann, S.; Kemperman, J.; Reeds, J.; Shepp, L., Existence of probability measures with given marginals, Ann. Prob., 19, 1781-1797 (1991) · Zbl 0739.60001
[7] J. Holbrook, Snowflakes and statistics, lecture-demonstration at NATO Advanced Study Institute “Fractal Geometry and Analysis”, Montreal, July 1989.
[8] Hutchinson, J., Fractals and self-similarity, Indiana Univ. J. Math., 30, 713-747 (1981) · Zbl 0598.28011
[9] Mandelbrot, B., The Fractal Geometry of Nature (1983), San Francisco: W. H. Freeman, San Francisco · Zbl 1194.30028
[10] R. Ramlochan,Iterated Function Systems and Fractal Sampling, University of Guelph, 1990.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.