Fractal Geometry

Fractal Geometry

1989 | Steven G. Krantz
The Opinion column allows mathematicians to write about issues of interest to the international mathematical community, including disagreements and controversies. It should be submitted to the editor-in-chief, Sheldon Axler. Steven G. Krantz, a mathematician, wrote a review of two books on fractals, which was initially accepted by the American Mathematical Society (AMS) but later retracted due to disagreements with Benoit Mandelbrot. Krantz refused to withdraw his review and suggested the Bulletin publish Mandelbrot's rebuttal, but the AMS policy prohibited responses to reviews. The AMS Council supported the editor's decision, and Krantz's review and Mandelbrot's response were published in the Notices of the AMS. However, Krantz was not satisfied and did not agree to publish in the Notices. The Mathematical Intelligencer, which welcomes controversy, published both pieces. Krantz reflects on the challenge of explaining mathematics to non-mathematicians, noting that other fields use jargon to appear more accessible, while mathematics uses technical terms that are difficult to explain. He acknowledges that the public is often unaware of mathematics, but recent efforts by mathematicians and the AMS have increased public awareness. The AMS has a public relations firm and promotes Mathematics Awareness Week. Mathematicians like Ron Graham have also engaged with the press. The theory of fractals, popularized by Mandelbrot, is seen as a significant development in mathematics, with potential for public attention. Fractals, though studied for years, gained popularity through Mandelbrot's work. The theory is compared to calculus, which has been foundational in science. Fractal geometry, like calculus, is a field of dedicated mathematicians who share a passion for their work. However, there is no universally accepted definition of "fractal," and the field is still developing.The Opinion column allows mathematicians to write about issues of interest to the international mathematical community, including disagreements and controversies. It should be submitted to the editor-in-chief, Sheldon Axler. Steven G. Krantz, a mathematician, wrote a review of two books on fractals, which was initially accepted by the American Mathematical Society (AMS) but later retracted due to disagreements with Benoit Mandelbrot. Krantz refused to withdraw his review and suggested the Bulletin publish Mandelbrot's rebuttal, but the AMS policy prohibited responses to reviews. The AMS Council supported the editor's decision, and Krantz's review and Mandelbrot's response were published in the Notices of the AMS. However, Krantz was not satisfied and did not agree to publish in the Notices. The Mathematical Intelligencer, which welcomes controversy, published both pieces. Krantz reflects on the challenge of explaining mathematics to non-mathematicians, noting that other fields use jargon to appear more accessible, while mathematics uses technical terms that are difficult to explain. He acknowledges that the public is often unaware of mathematics, but recent efforts by mathematicians and the AMS have increased public awareness. The AMS has a public relations firm and promotes Mathematics Awareness Week. Mathematicians like Ron Graham have also engaged with the press. The theory of fractals, popularized by Mandelbrot, is seen as a significant development in mathematics, with potential for public attention. Fractals, though studied for years, gained popularity through Mandelbrot's work. The theory is compared to calculus, which has been foundational in science. Fractal geometry, like calculus, is a field of dedicated mathematicians who share a passion for their work. However, there is no universally accepted definition of "fractal," and the field is still developing.
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