Type of Publication:  Contribution to a collection 
Publication status:  Published 
Author:  Peitgen, HeinzOtto; Jürgens, Hartmut; Saupe, Dietmar 
Year of publication:  2004 
Published in:  Chaos and Fractals : New Frontiers of Science / Peitgen, HeinzOtto; Jürgens, Hartmut; Saupe, Dietmar (ed.).  2. ed..  New York : Springer, 2004.  pp. 129172.  ISBN 9780387202297 
DOI (citable link):  https://dx.doi.org/10.1007/0387218238_4 
Summary: 
Dyson is referring to mathematicians, like G. Cantor, D. Hilbert, and W. Sierpinski, who have been justly credited with having helped to lead mathematics out of its crisis at the turn of the century by building marvelous abstract foundations on which modern mathematics can now flourish safely. Without question, mathematics has changed during this century. What we see is an everincreasing dominance of the algebraic approach over the geometric. In their striving for absolute truth, mathematicians have developed new standards for determining the validity of mathematical arguments. In the process, many of the previously accepted methods have been abandoned as inappropriate. Geometric or visual arguments were increasingly forced out. While Newton’s Principia Mathematica, laying the fundamentals of modern mathematics, still made use of the strength of visual arguments, the new objectivity seems to require a dismissal of this approach. From this point of view, it is ironic that some of the constructions which Cantor, Hilbert, Sierpinski and others created to perfect their extremely abstract foundations simultaneously hold the clues to understanding the patterns of nature in a visual sense. The Cantor set, Hilbert curve, and Sierpinski gasket all give testimony to the delicacy and problems of modern set theory and at the same time, as Mandelbrot has taught us, are perfect models for the complexity of nature.

Subject (DDC):  004 Computer Science 
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PEITGEN, HeinzOtto, Hartmut JÜRGENS, Dietmar SAUPE, 2004. Lim and SelfSimilarity. In: PEITGEN, HeinzOtto, ed., Hartmut JÜRGENS, ed., Dietmar SAUPE, ed.. Chaos and Fractals : New Frontiers of Science. 2. ed.. New York:Springer, pp. 129172. ISBN 9780387202297. Available under: doi: 10.1007/0387218238_4
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