ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Benoit Mandelbrot, Mathematician

Updated on December 30, 2010
A Unit of a Koch Snowflake.  Mandelbrot suggested this as a symbol for 'fractal-man'.
A Unit of a Koch Snowflake. Mandelbrot suggested this as a symbol for 'fractal-man'.
Benoit Mandelbrot
Benoit Mandelbrot

The mathematician Benoit Mandelbrot (1924 – 2010) is best-known as the father of fractal geometry. He was born in Warsaw, Poland of a Jewish-Lithuanian family. They moved to France in 1936 to follow his uncle and escape Nazism, and Mandelbrot never received a formal secondary education. He was largely self-taught. He studied in France during World War II, and later moved to the United States. He married Aliette Kagan in 1955 and they had two children. In the 1950s he worked both in France and in the US. He worked for 35 years for IBM in New York and Massachusetts, and later taught at Yale in Connecticut. In 2010 he died of pancreatic cancer in Cambridge, Massachusetts.

Mandelbrot’s father traded clothing, his mother was a physician and both his uncles were mathematicians. In France, the war and the need to survive often kept Mandelbrot away from school. Nevertheless, he had an uncanny ability to visualize mathematical questions. He would solve problems with leaps of geometric intuition rather than using the “proper” techniques of strict logical analysis.

Szolem Mandelbrojt, Benoit Mandelbrot's uncle
Szolem Mandelbrojt, Benoit Mandelbrot's uncle

One of his uncles, Szolem Mandelbrojt, had a strong influence on the young Mandelbrot. Szolem had become an “intellectual refugee” from the academies in Poland that were influenced by Waclaw Sierpinski. He moved to Paris and became part of a group of French mathematicians who believed in “pure mathematics”, known for its rigor and abstraction, as opposed to “applied mathematics”, which concerns applying mathematics to other fields. Mandelbrot reacted against his uncle; he was a strong advocate of applied mathematics. Writing in 1987, Mandelbrot said, “While I was fond of my uncle, many aspects of his story somehow repelled me intensely. My uncle, in turn, always felt that I had squandered my intellectual gifts. Lately, however, it is becoming clear to me that in some essential ways we are alike.” This rift with French academics, where the logic and rigor of pure mathematics were strongly ingrained, eventually caused Mandelbrot to leave France for the US and become an “intellectual refugee”, just like his uncle had been.

The Face of War, by Salvador Dali.  This painting inspired Mandelbrot, with its self-similarity of faces within faces, to infinity.
The Face of War, by Salvador Dali. This painting inspired Mandelbrot, with its self-similarity of faces within faces, to infinity.

Working for IBM, Mandelbrot was allowed the freedom to study many diverse fields. He made a conscious effort to become an expert in various unrelated areas, making contributions in fluid dynamics, information theory, cosmology and the behavior of stock markets. Looking back in 1987, he wrote: “…certain problems than others had the same “taste” to me… I always moved in hot pursuit of a technical problem that was congenial because its “taste” was the same as that of a problem I had met elsewhere and had liked.” He began to notice similar patterns in these various disciplines. When looking carefully into the detailed data, he noticed that no matter how closely he looked, there was always more detail. Also, there was a self-similarity in the patterns at different levels of magnification.

Points in the black area are in the Mandelbrot set.
Points in the black area are in the Mandelbrot set.

The achievements Mandelbrot is best-known for today are the discovery of the remarkable and elegant Mandelbrot set and the development of fractal geometry. Fractal geometry stands in contrast to classical Euclidean geometry, which involves smooth shapes like triangles, circles and spheres. Fractals are rough, and more closely describe the shapes found in nature. The defining works are “How Long is the Coast of England?” in 1967 (answer: “it depends”) and “The Fractal Geometry of Nature” in French in 1975. In 1980 Mandelbrot explained the term ‘fractal’, which he coined: “The word is related to the Latin verb frangere, which means “to break.” In the Roman mind, frangere may have evoked the action of breaking a stone, since the adjective derived from it combines the two most obvious properties of broken stones, irregularity and fragmentation. This adjective is fractus, which led to fractal.”

Benoit Mandelbrot
Benoit Mandelbrot

This quote from an address by Peter Clark describes some unsolved geometric problems from the early 1900’s. (Note the mention of Sierpinski, ironically the same Waclaw Sierpinski who was part of the reason his uncle had left Poland.) --

“…Now lurking about so to speak in the undergrowth of that achievement lay certain very extraordinary geometric objects indeed. To all at the time, they seemed strange, indeed rather pathological monsters. Odd indeed they were, there were curves - one dimensional lines in effect - which filled two dimensional spaces, there were curves which were well behaved, that is nice and continuous but which had no slope at any point (not just some points, ANY points) and they went by strange names, the Peano Space filling curve, the Sierpinski gasket, the Koch curve, the Cantor Ternary set. Despite their pathological qualities, their extraordinary complexity, especially when viewed in greater and greater detail, they were often very simple to describe in the sense that the rules which generated them were absurdly simple to state. So odd were these objects that mathematicians set about barring these monsters and they were set aside as too strange to be of interest. That is until our honorary graduand [Benoit Mandelbrot] created out of them an entirely new science, the theory of fractal geometry: it was his insight and vision which saw in those objects and the many new ones he discovered, some of which now bear his name, not mathematical curiosities, but signposts to a new mathematical universe, a new geometry with as much system and generality as that of Euclid and a new physical science.”

“Being a language, mathematics may be used not only to inform but also, among other things, to seduce.” – Benoit Mandelbrot, 1977.


Find out more:


Mandelbrot's home page at Yale University

Biography at the University of St. Andrew's, Scotland

Fun and easy program for zooming into the Mandelbrot set:


This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

Show Details
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
ClickscoThis is a data management platform studying reader behavior (Privacy Policy)