Mandelbrot-Interesting tidbit.

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In summary, the conversation discusses the unique problem-solving abilities of mathematician Benoit Mandelbrot, who had a visual mind that allowed him to solve problems through geometric intuition rather than formal algebraic training. This method was also mentioned in Mandelbrot's own writings, though he did not provide specific details. Some speculate that he may have used techniques such as the method of images and conformal maps. However, others suggest that Mandelbrot may have exaggerated his abilities and reputation.
  • #1
shadowboy13
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One of my hobbies (or procrastinations :tongue:) is reading the bios of several mathematicians, and i was recently checking out a bio of Mandelbrot when i came across this:

"He has a visual mind, which allows him to solve problems with great leaps of geometric intuition, having no formal training in algebra, he once passed an important exam with the highest grade by mentally translating all of the problems into pictures"

Now this really interests me, how is this even possible?

This looks to be the method I've always used, where i utilize numbers alongside geometric facts and intuition to solve relatively hard problems that may be algebraic in nature, but with no formal training? That seems a bit dubious at best.

But apparently it's not false, given that one of his examiners said the same thing regarding another sort of problem that I'm to lazy to go find now.

...so does anyone know what this "method" is supposed to be?
 
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  • #2
I suspect that the passage you quote from Nowlan, reflect some remarks Mandelbrot penned in his A maverick's apprenticeship. In the Self-Discovery section he explains how he used geometrical tricks to solve algebra and analytical geometry problems. He does not give details, but the method of images and conformal maps are some of the tricks I imagine he is writing about.
 
  • #3
Something I read about Mandelbrot is that he was quite the legend in his own mind, and often made sensational claims about himself. In addition to whatever math he actually did, he seems to have spent even more energy trying to manipulate how he was perceived.

I make no guarantee, but it could be I read this in Chaos by James Gleik.
 

1. What is the Mandelbrot set?

The Mandelbrot set is a mathematical set of complex numbers that are plotted on a two-dimensional plane. It is named after mathematician Benoit Mandelbrot who first described it in 1975.

2. Why is the Mandelbrot set considered interesting?

The Mandelbrot set is considered interesting because it is a visual representation of a complex mathematical concept. The set has a unique and intricate structure, with intricate patterns that repeat infinitely. It also has many properties that have been studied and discovered by mathematicians.

3. How is the Mandelbrot set generated?

The Mandelbrot set is generated using a simple mathematical formula called the Mandelbrot function. This function is applied to each point on the complex plane, and the results are plotted on a graph. Points that do not escape to infinity after a certain number of iterations are considered part of the Mandelbrot set.

4. What are some applications of the Mandelbrot set?

The Mandelbrot set has been used in many fields, including physics, biology, and computer graphics. It has also been used to create beautiful and intricate fractal images, and has been studied for its connections to chaos theory and the concept of self-similarity.

5. Can the Mandelbrot set be explored visually?

Yes, the Mandelbrot set can be explored visually using computer programs and specialized software. These programs allow users to zoom in and out of different regions of the set to reveal its intricate structure and patterns. This has made the Mandelbrot set a popular subject for both mathematicians and artists alike.

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