Math Education: RIP Benoit Mandelbrot

As noted on the MathNotations blog and several other outlets including the New York Times, Benoit Mandelbrot passed away last week. Dr. Mandelbrot’s ideas about geometry and repeated processes changed the way mathematicians look at the world.

Think about how a graph of stock market levels look. If you look at a graph showing stock market data, but don’t see the scale, you can’t tell if it is a graph for a day or a decade. Similarly, when you look at turbulent water, it’s hard to tell if you’re looking at something the width of the Mississippi or the width of a canoe. Dr. Mandelbrot studied all these things and saw that these phenomena had a self-similar nature: as you zoom in, the tiniest little area looks a whole lot like the big picture.

Dr. Mandelbrot coined the phrase fractal to describe structures that look similar as you zoom farther and farther in (or out).  You can see the beauty of his idea in everything from a tree branch to a fern frond to a jagged coastline. What’s really amazing is that he took this idea and showed how repeating a very simple mathematical process over and over can produce remarkably complex, beautiful, and self-similar figures.

The Mandelbrot Set is absolutely incredible. Check out the video below in which you keep on zooming in to the set.

This is math made so beautiful that I could stare at it for hours. Heck, I have stared at it for hours. All this from the equation z = z^2 + c. Seriously. If that doesn’t wow you, then I don't know what to tell you. By the way, page 240 of K¹²’s Algebra II textbook has an image for which I received an illustration credit. That I got any credit for it is ridiculous. All I did was find some nice parameters for a little corner of the Mandelbrot Set. All credit for that lovely image goes to the late, great Dr. Mandelbrot.

When I was a high school teacher, I was lucky enough to meet Dr. Mandelbrot. He was an accessible, engaging man who really seemed interested in our students’ projects. Matt Blum, a former student at that school, wrote “He Gave Us Order Out of Chaos” for Wired’s GeekDad blog. Matt is not alone. Many of us were inspired by the man who brought his prodigious mathematical talents to our little corner of the world for an afternoon.