How Did Mandelbrot Solve Problems with Geometric Intuition Instead of Algebra?

[shadowboy13]

One of my hobbies (or procrastinations ) 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?

 

[ZetaGuy]

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.

 

[zoobyshoe]

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.