Both parents worshiped individual achievement, but because of the Depression and the war, they never achieved what they wanted and deserved. So their ambition and high expectations were transferred to me.
— Benoit Mandelbrot
An exquisitely complex shape now known as the Mandlebrot set has been called the most complex object in mathematics.
There's nothing really connecting the behavior of the Nile, metallurgy, and the behavior of prices except that I had the mathematical tools to explain them.
Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics.
The techniques I developed for studying turbulence, like weather, also apply to the stock market.
Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.
Most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, but largely went their own way.
For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale.
Father was bold, and Mother was cautious. They never shouted at each other but argued constantly about strategy, and they taught me very early that before taking big risks, one must carefully figure the odds.
Most economists, when modeling market behavior, tend to sweep major fluctuations under the rug and assume they are anomalies. What I have found is that major rises and falls in prices are actually inevitable.
When the weather changes, nobody believes the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed.
There is a saying that every nice piece of work needs the right person in the right place at the right time.
Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.
Nobody will deny that there is at least some roughness everywhere.
I was in an industrial laboratory because academia found me unsuitable.
An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
Where do I really belong? I avoid saying everywhere - which switches all too easily to nowhere. Instead, when pressed, I call myself a fractalist.
When I first began studying prices, it wasn't a topic that mathematicians were working on. Purely by accident, I saw a set of data on price changes presented in a lecture and realized they behaved similarly to the geometric models I was already studying.
Until a few years ago, the topics in my Ph.D. were unfashionable, but they are very popular today.
There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable.
Order doesn't come by itself.
My fate has been that what I undertook was fully understood only after the fact.
I don't seek power and do not run around.
Although computer memory is no longer expensive, there's always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills.