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Benoit Mandelbrot

Benoit Mandelbrot Books

Mathematician

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“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."”

DifferentFormScienceUsedTermChallengesLevelsExistenceStudyHigherDegreesStandardsClaimsPatternsComplexityGeometryExhibitsDifferent LevelsFragmentedEuclidMorphology
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“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).”

IfsWellsTwoPastScienceNatureNaturalSawsCenturyFunctionAssumingPhysicsMathematicalEngineeringEquationsHammersContinuityDifferential Equations
Book:The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward
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“I was asking questions which nobody else had asked before, because nobody else had actually looked at certain structures. Therefore, as I will tell, the advent of the computer, not as a computer but as a drawing machine, was for me a major event in my life. That's why I was motivated to participate in the birth of computer graphics, because for me computer graphics was a way of extending my hand, extending it and being able to draw things which my hand by itself, and the hands of nobody else before, would not have been able to represent.”

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“If you look at coastlines, if you look at that them from far away, from an airplane, well, you don't see details, you see a certain complication. When you come closer, the complication becomes more local, but again continues. And come closer and closer and closer, the coastline becomes longer and longer and longer because it has more detail entering in.”

IfsWellsLooksCertainDetailsLocalsAirplaneFar AwayEnteringComplicationCoastline
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“The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may not be true. And that idea is still unproven. It is the foundation, what started me and what everybody failed to **** prove has so far defeated the greatest efforts by experts to be proven.”

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“Many painters had a clear idea of what fractals are. Take a French classic painter named Poussin. Now, he painted beautiful landscapes, completely artificial ones, imaginary landscapes. And how did he choose them? Well, he had the balance of trees, of lawns, of houses in the distance. He had a balance of small objects, big objects, big trees in front and his balance of objects at every scale is what gives to Poussin a special feeling.”

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“It was a very big gamble. I lost my job in France, I received a job in which was extremely uncertain, how long would IBM be interested in research, but the gamble was taken and very shortly afterwards, I had this extraordinary fortune of stopping at Harvard to do a lecture and learning about the price variation in just the right way.”

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“One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining pure mathematics, very pure mathematics with very hard things which had been long a nuisance to scientists and to engineers, that this combination was possible and I put together this new geometry of nature, the fractal geometry of nature.”

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“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.”

IfsWould BeScienceChoicesSportsDisciplineEssentialsIntellectualAccountsCompetitionIntellectDefinedWelfareScholarRuinedNomadSpecialtyWithdrawing
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“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.”

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