Benoit Mandelbrot

1924–2010 · Polish-born, French and American mathematician

Topics: mathematics, creativity, simplicity, learning

• Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

  — Benoit Mandelbrot

• For many years I had been hearing the comment that fractals make beautiful pictures, but are pretty useless. I was irritated because important applications always take some time to be revealed.

  — Benoit Mandelbrot

• Many creative minds overrate their most baroque works, and underrate the simple ones.

  — Benoit Mandelbrot

• Here is the curious thing: the first night I saw the set, it was just wild. The second night, I became used to it. After a few nights, I became familiar with it. It was as if somehow I had seen it before. Of course I hadn't. No one had seen it.

  — Benoit Mandelbrot

• Contrary to popular opinion, mathematics is about simplifying life, not complicating it.

  — Benoit Mandelbrot

• I think it's very important to have both cartoons and more realistic structures. The cartoons have the power of representing the essential very often, but have this intrinsic weakness of being in a certain sense predictable.

  — Benoit Mandelbrot

• People want to see patterns in the world. It is how we evolved. We descended from those primates who were best at spotting the telltale pattern of a predator in the forest, or of food in the savannah. So important is this skill that we apply it everywhere, warranted or not.

  — Benoit Mandelbrot

• Engineering is too important to wait for science.

  — Benoit Mandelbrot

• How could it be that the same technique applies to the Internet, the weather and the stock market? Why, without particularly trying, am I touching so many different aspects of many different things?

  — Benoit Mandelbrot

• I was asking questions which nobody else had asked before, because nobody else had actually looked at certain structures.

  — Benoit Mandelbrot

• What motivates me now are ideas I developed 10, 20 or 30 years ago, and the feeling that these ideas may be lost if I don't push them a little bit further.

  — Benoit Mandelbrot

• I always felt that science as the preserve of people from Oxbridge or Ivy League universities — and not for the common mortal — was a very bad idea.

  — Benoit Mandelbrot

• If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.

  — Benoit Mandelbrot

• For most of my life, one of the persons most baffled by my own work was myself.

  — Benoit Mandelbrot

• A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals.

  — Benoit Mandelbrot

• The Mandelbrot set covers a small space yet carries a large number of different implications. Is it a fitting epitaph? Absolutely.

  — Benoit Mandelbrot

• Most of the world is of great roughness and infinite complexity. However, the infinite sea of complexity includes two islands of simplicity: one of Euclidean simplicity and a second of relative simplicity in which roughness is present but is the same at all scales.

  — Benoit Mandelbrot

• 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.

  — Benoit Mandelbrot

• Being a language, mathematics may be used not only to inform but also, among other things, to seduce.

  — Benoit Mandelbrot

• A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension.

  — Benoit Mandelbrot