Benoit Mandelbrot Quotes about Science

Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.

Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.

Benoit Mandelbrot

Nature, Lying, Science

"Benoît Mandelbrot obituary' by Nigel Lesmoir-Gordon, www.theguardian.com. October 17, 2010.

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

Benoit Mandelbrot

Science, Engineering, May

"Fractals: Form, Chance and Dimension". Book by Benoit Mandelbrot, 1977.

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.

Benoit Mandelbrot

Powerful, Science, Tools

Benoit B. Mandelbrot (2013). “Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E”, p.16, Springer Science & Business Media

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."

Benoit Mandelbrot

Science, Challenges, Different

The American Mathematical Monthly, Vol. 91, No. 9, (p. 594), November 1984.

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.

Benoit Mandelbrot

Science, Numbers, Nomenclature

A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales...

Benoit Mandelbrot

Science, Definitions, Scales

The American Mathematical Monthly, Vol. 91, No. 9, (p. 594), November 1984.

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 settled disciplines.

Benoit Mandelbrot

Sports, Science, Discipline

"Chaos: Making a New Science". Book by James Gleick, p. 70, 1987.

The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

Benoit Mandelbrot

Nature, Science, Challenges

Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.

Benoit Mandelbrot

Science, Order, Facts

If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).

Benoit Mandelbrot

Nature, Science, Past

Benoit B. Mandelbrot, Richard L. Hudson (2010). “The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward”, p.86, Profile Books