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“The word fractal, once introduced, had an extraordinary integrating effect upon myself and upon many people around.”

Benoît Mandelbrot

Segment 67
Peoples Archive interview
Context: The word fractal, once introduced, had an extraordinary integrating effect upon myself and upon many people around. Initially again it was simply a word to write a book about, but once a word exists one begins to try to define it, even though initially it was simply something very subjective and indicating my field. Now the main property of all fractals, put in very loose terms, is that each part — they're made of parts — each part is like the whole except it is smaller. After having coined this word I sorted my own research over a very long period of time and I realised that I had been doing almost nothing else in my life.

People

“To appreciate the nature of fractals, recall Galileo's splendid manifesto that "Philosophy is written in the language of mathematics and its characters are triangles, circles and other geometric figures, without which one wanders about in a dark labyrinth." Observe that circles, ellipses, and parabolas are very smooth shapes and that a triangle has a small number of points of irregularity. Galileo was absolutely right to assert that in science those shapes are necessary. But they have turned out not to be sufficient, "merely" because most of the world is of infinitely great roughness and complexity. However, the infinite sea of complexity includes two islands: one of Euclidean simplicity, and also a second of relative simplicity in which roughness is present, but is the same at all scales.”

Benoît Mandelbrot

A Theory of Roughness (2004)

World , Mathematics , Nature , Science

“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.”

Benoît Mandelbrot

New Scientist interview (2004)

People , Idea , Universe , Science

“My efforts over the years had been successful to the extent, to take an example, that fractals made many mathematicians learn a lot about physics, biology, and economics. Unfortunately, most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, had been changed by considering the new problems I raised, but largely went their own way.”

Benoît Mandelbrot

A Theory of Roughness (2004)

Way , Feeling , Problem , Effort

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

Benoît Mandelbrot book The Fractal Geometry of Nature

The Fractal Geometry of Nature (1982)

World , Mathematics , Help

“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.”

Benoît Mandelbrot

Source: The Fractalist (2012), Ch. 29, p. 299

World , Sea

“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.”

Benoît Mandelbrot

New Scientist interview (2004)

Feeling , Motivation , Idea

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

Benoît Mandelbrot

As quoted in "Fractal Finance" by Greg Phelan in Yale Economic Review (Fall 2005)

“One of my conjectures was solved in six months, a second in five years, a third in ten. But the basic conjecture, despite heroic efforts rewarded by two Fields Medals, remains a conjecture, now called MLC: the Mandelbrot Set is locally connected. The notion that these conjectures might have been reached by pure thought — with no picture — is simply inconceivable.”

Benoît Mandelbrot

A Theory of Roughness (2004)

Effort

“The most important thing I have done is to combine something esoteric with a practical issue that affects many people. In this spirit, the stock market is one of the most attractive things imaginable. Stock-market data is abundant so I can check everything. Financial markets are very influential and I want to be part of this field now that it is maturing.”

Benoît Mandelbrot

New Scientist interview (2004)

People , Imagination , Parting

“Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of competition by withdrawing entirely into narrowly defined specialties. The rare scholars who are nomads by choice are essential to the intellectual welfare of the subtle disciplines”

Benoît Mandelbrot

Benoit Mandelbrot cited in James Gleick (1987) Chaos: Making a New Science p. 70

Sport , Science

“This difficulty — am I a mathematician because my degree says so? Am I an engineer because I'm interested in things? Am I a social scientist because I don't think there's a difference between the turbulence in stock markets in terms of unpredictability? At IBM I wouldn't have to worry about that. The names of departments were totally strange and totally meaningless, so it looked like a promising situation for a short time. As it turned out I was going to spend thirty-five years and twelve days at IBM, almost from the beginning to the day when IBM decided that successful research was no longer going to be carried on in that division.”

Benoît Mandelbrot

Segment 44
Peoples Archive interview

Thinking , Time , Success

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

Benoît Mandelbrot

Fractals : Form, chance and dimension (1977)

Mathematics

“A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that. 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.”

Benoît Mandelbrot

A Theory of Roughness (2004)

Parting

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

Benoît Mandelbrot book The Fractal Geometry of Nature

The Fractal Geometry of Nature (1982)

“A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…”

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

Mathematics

“My ambition was not to create a new field, but I would have welcomed a permanent group of people having interests close to mine and therefore breaking the disastrous tendency towards increasingly well-defined fields. Unfortunately, I failed on this essential point, very badly. Order doesn't come by itself.”

Benoît Mandelbrot

A Theory of Roughness (2004)

People

“Britain for a long time had a reflection of its class structure which meant that people like, well, J. B. S. Haldane who was the nephew of Lord Haldane, or Bertrand Russell who became Lord Russell, could do what they pleased, and it's interesting to think that Bertrand Russell never had a job, he never had to compete for a job. Haldane had four or five different jobs in his life, totally different. He probably could have — if he had been bothered — have just abandoned his job and went on to live otherwise. … But this no longer exists. IBM no longer exists. I don't see a place now where somebody like myself who combined, let's say, unusual gifts and unusual tastes and, who everybody said has promise, was certainly a misfit of the worst kind could find a position at this point and I think that a tragedy.”

Benoît Mandelbrot

Segment 45
Peoples Archive interview

Life , People , Thinking , Time

“Georg Cantor claimed the essence of mathematics lies in its freedom. But mathematicians do not pick problems from thin air for the pleasure of solving them. To the contrary, a mark of greatness resides in the ability to identify the most interesting problems in the framework of what is already known.”

Benoît Mandelbrot

Source: The Fractalist (2012), Ch. 17, p. 178

Pleasure , Mathematics , Problem , Freedom

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

Benoît Mandelbrot

Lecture at the University of Maryland (March 2005)

Life , Personality