Benoît Mandelbrot: Quotes about mathematics

Benoît Mandelbrot was Polish-born, French and American mathematician. Explore interesting quotes on mathematics.
Benoît Mandelbrot: 112   quotes 2   likes

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

Benoît Mandelbrot

Source: The (Mis)Behavior of Markets (2004, 2008), Ch. 7, p. 125
Context: Contrary to popular opinion, mathematics is about simplifying life, not complicating it. A child learns a bag of candies can be shared fairly by counting them out: That is numeracy. She abstracts that notion to dividing a candy bar into equal pieces: arithmetic. Then, she learns how to calculate how much cocoa and sugar she will need to make enough chocolate for fifteen friends: algebra.

Life , Mathematics

“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

“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

“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 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

“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

“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)

Mathematics , Reality , Study

“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)

Life , People , Age , Hope