Fractal Geometry

Fractal Geometry

1989 | Steven G. Krantz
The Opinion column in the American Mathematical Society's Bulletin allows mathematicians to write about any issue of interest to the international mathematical community, including disagreements and controversies. This section features an article by Steven G. Krantz on fractal geometry, which has a unique history involving a review he submitted for the Bulletin and a subsequent controversy with Benoit Mandelbrot. In 1988, Krantz submitted a review of two books on fractals to the Bulletin, which was accepted after minor revisions. However, Mandelbrot strongly disagreed with the review and wrote a rebuttal. The Bulletin's editor, Edgar Lee Stout, encouraged Krantz to withdraw the review but was met with resistance. Despite making further revisions, the Bulletin ultimately retracted the review due to AMS policy, which prohibits responses to reviews. Krantz appealed to the AMS Council, which supported Stout's decision. The Council suggested publishing the review and Mandelbrot's response in the Notices of the AMS, but Krantz refused, leading to the Mathematical Intelligencer publishing the review and Mandelbrot's response. The article also discusses the challenges of explaining mathematics to non-mathematicians and the efforts to promote mathematics in the public sphere. It highlights the potential for fractal theory to become a significant and widely recognized area of mathematics, drawing comparisons to the development of calculus. The theory of fractals, popularized by Mandelbrot, is seen as a lingua franca for science, potentially rivaling calculus in importance.The Opinion column in the American Mathematical Society's Bulletin allows mathematicians to write about any issue of interest to the international mathematical community, including disagreements and controversies. This section features an article by Steven G. Krantz on fractal geometry, which has a unique history involving a review he submitted for the Bulletin and a subsequent controversy with Benoit Mandelbrot. In 1988, Krantz submitted a review of two books on fractals to the Bulletin, which was accepted after minor revisions. However, Mandelbrot strongly disagreed with the review and wrote a rebuttal. The Bulletin's editor, Edgar Lee Stout, encouraged Krantz to withdraw the review but was met with resistance. Despite making further revisions, the Bulletin ultimately retracted the review due to AMS policy, which prohibits responses to reviews. Krantz appealed to the AMS Council, which supported Stout's decision. The Council suggested publishing the review and Mandelbrot's response in the Notices of the AMS, but Krantz refused, leading to the Mathematical Intelligencer publishing the review and Mandelbrot's response. The article also discusses the challenges of explaining mathematics to non-mathematicians and the efforts to promote mathematics in the public sphere. It highlights the potential for fractal theory to become a significant and widely recognized area of mathematics, drawing comparisons to the development of calculus. The theory of fractals, popularized by Mandelbrot, is seen as a lingua franca for science, potentially rivaling calculus in importance.
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