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“I always saw a close kinship between the needs of "pure" mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods — but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality.”

Benoît Mandelbrot

A Theory of Roughness (2004)

“Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory, and besides were my love when I was a young man. Cauliflowers exemplify a second area of great simplicity, that of shapes which appear more or less the same as you look at them up close or from far away, as you zoom in and zoom out.
Before my work, those shapes had no use, hence no word was needed to denote them. My work created such a need and I coined "fractals."”

Benoît Mandelbrot

A Theory of Roughness (2004)

“Engineering is too important to wait for science.”

Benoît Mandelbrot

As quoted in "Fractal Finance" by Greg Phelan in Yale Economic Review (Fall 2005) http://www.yaleeconomicreview.com/issues/fall2005/fractalfinance

“There is no single rule that governs the use of geometry. I don't think that one exists.”

Benoît Mandelbrot

New Scientist interview (2004)

“My life seemed to be a series of events and accidents. Yet when I look back I see a pattern.”

Benoît Mandelbrot

New Scientist interview (2004)

“Given the profits he and Pharaoh must have made, one might call Joseph the first international arbitrageur.”

Benoît Mandelbrot

Source: The (Mis)Behavior of Markets (2004, 2008), Ch. 10, p. 201 (A reference to Genesis 41:48–49, 54–57.)

“There is a problem that is specific to financial markets. In most fields of research, when someone makes an important finding, they publish it. In the case of prices, they set up a firm and sell advice about their discovery. If they can make money from it, they will. So the research into market dynamics is a closed field.”

Benoît Mandelbrot

New Scientist interview (2004)

“I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.”

Benoît Mandelbrot

As quoted in Encyclopedia of World Biography (1997) edited by Thomson Gale

“In a different era, I would have called myself a natural philosopher. All my life, I have enjoyed the reputation of being someone who disrupted prevailing ideas. Now that I'm in my 80th year, I can play on my age and provoke people even more.”

Benoît Mandelbrot

New Scientist interview (2004)

“Unfortunately, the world has not been designed for the convenience of mathematicians.”

Benoît Mandelbrot

Source: The (Mis)Behavior of Markets (2004, 2008), Ch. 2, p. 41

“I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid — a term used in this work to denote all of standard geometry — Nature exhibits not simply a higher degree but an altogether different level of complexity … The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."”

Benoît Mandelbrot

As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594

“When the weather changes and hurricanes hit, nobody believes that the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed. It's the same stock market with the same mechanisms and the same people.”

Benoît Mandelbrot

A Theory of Roughness (2004)

“My work is more varied than at any other point in my life. I am still carrying out research in pure mathematics. And I am working on an idea that I had several years ago on negative dimensions. … Negative dimensions are a way of measuring how empty something is. In mathematics, only one set is called empty. It contains nothing whatsoever. But I argued that some sets are emptier than others in a certain useful way. It is an idea that almost everyone greets with great suspicion, thinking I've gone soft in the brain in my old age. Then I explain it and people realise it is obvious. Now I'm developing the idea fully with a colleague. I have high hopes that once we write it down properly and give a few lectures about it at suitable places that negative dimensions will become standard in mathematics.”

Benoît Mandelbrot

New Scientist interview (2004)

“How Long Is the Coast of Britain?”

Benoît Mandelbrot How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

Part of the title of his paper "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension" published in Science (1967)

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

Benoît Mandelbrot

New Scientist interview (2004)

“A branch of physics that I was working in for many years has lately become much less active. Many problems have been solved and others are so difficult that nobody knows what to do about them. This means that I do much less physics today than 15 years ago. By contrast, fractal tools have plenty to do. There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable. The hammer I crafted is the first effective tool for all kinds of roughness and nobody will deny that there is at last some roughness everywhere.”

Benoît Mandelbrot

A Theory of Roughness (2004)