The Lives of the Mathematical Ninjas: Benoit B Mandelbrot

This is a guest post by Tom Briggs of The Actual Maths and Blogstronomy. I have a soft spot for Benoit B Mandelbrot* because I saw a display about his work at St Andrews while I was waiting for an interview there and got fascinated by the digital sundial one of the professors had proposed. Over to Tom...

Benoit B Mandelbrot

Benoit B Mandelbrot -- image by Rama (via Wikipedia)

I was first made vaguely aware of Mandelbrot's work before I was even aware that maths was a subject I was any good at or interested in.This was by way of Arthur C. Clarke's The Ghost From The Grand Banks. A bit later, the notion of fractals cropped up again as chapter headings in Michael Crichton's Jurassic Park.

When Colin asked "Who would you nominate as a mathematical ninja?", Benoit Mandelbrot (1924 - 2010) sprang instantly to mind. This is largely because I have a line of images of notable mathematicians and a quote attributed to each one running the length of my classroom, and Mandelbrot is the only one whose image is both a photograph and in colour. This provides an opportunity to illustrate to the kids in my care that maths is far from a dead subject, and a fair number of them are wowed by the idea that someone has discovered new maths within their own lifetime.

Born in Poland, moving to France as a child (in 1936, his Jewish family anticipating of Nazi nastiness), and then spending much of his adult life in America, Mandelbrot got around a bit. Introduced to mathematics by two of his uncles (though his mother was a dentist, so he had some direct academic lineage) he obtained a Masters degree in aeronautics in 1949 from the establishment now commonly referred to as Caltech. Back to Paris, where he obtained his Ph.D in Mathematical Sciences over the following three years.

Mandelbrot published papers in such seemingly diverse fields as fluid dynamics, cosmology and economics, but became convinced that self-similarity was a theme that ran through them all. Some such self-similar structures had been discovered by other mathematicians, but labelled as isolated and unnatural cases. Mandelbrot brought them together, coining the name fractal to describe them, and turned understanding of them on its head: far from being 'unnatural' he maintained that they were perhaps more natural than Euclidean geometry's constrained smoothness. Indeed, in his opening to The Fractal Geometry of Nature, he states:

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."

Mountains, coastlines, trees, stock market prices, architecture and Brownian motion are all modeled far more accurately and intuitively using fractals than they are with any more traditional modeling methods. Mandelbrot even put forward an alternative, fractal-based, resolution to Olbers' paradox.

Fractals are not taught in standard secondary school curricula, but I cover them anyway, from year 7 upwards, at the end of the winter term. We zoom in on the M-set, argue about how you're actually supposed to pronounce "Mandelbrot", look at broccoli, sunflowers and pinecones, think about how those awesome graphics in Halo just wouldn't exist without Benny, turn equilateral triangles into snowflakes** and then, at the denouement, create 3D fractal Christmas trees to take home as cards for family members.

He died in 2010 from pancreatic cancer, leaving behind an extraordinary branch of mathematics that has applications across multiple aspects of human life, and offers intellectual interests and challenges for every mathematician, whether pre-secondary or post-doctoral.

I've picked Benoit as a Mathematical Ninja because of this, and because he picked up stuff that a lot of people already knew about and connected them together in a way that they didn't. He thought anywhere but inside the box, but managed to make his thinking accessible to the general public by way of his books and lectures. He was innovative and creative, and wasn't tied to preconceptions, and wasn't afraid to rummage around in the toolbox of mathematics, taking things apart and not worrying about what they were supposed to do: he changed how we see the world.

* The B stands for Benoit B Mandelbrot
** And have a giggle about their name.


Any other mathematical ninjas you think ought to be celebrated? Drop me an email if you'd like to do a guest post on one.

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

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