Benoit Mandelbrot, a French-American mathematician who explored a new class of mathematical shapes known as "fractals," has died at age 85 in Cambridge, Massachusetts, his family said.
The cause of death was cancer, his family said in a statement.
His seminal book, "The Fractal Geometry of Nature," published in 1982, argued that irregular mathematical objects once dismissed as "pathological" were a reflection of nature.
The fractal geometry he developed would be used to measure natural phenomena like clouds or coastlines that once were believed to be unmeasurable.
He applied the theory to physics, biology, finance and many other fields of study.
"Fractals are easy to explain, it's like a romanesco cauliflower, which is to say that each small part of it is exactly the same as the entire cauliflower itself," Catherine Hill, a statistician at the Gustave Roussy Institute, told AFP.
"It's a curve that reproduces itself to infinity. Every time you zoom in further, you find the same curve," she said.
French President Nicolas Sarkozy paid tribute to Mandelbrot, saying he had "a powerful, original mind that never shied away from innovation and battering preconceived ideas," according to a statement published by his office.
"His work, which was entirely developed outside the main research channels, led to a modern information theory," Sarkozy added.
Mandelbrot had been "very critical of the prevailing banking models," adding that his "warnings were not heeded," Sarkozy said.
"France is proud to have received Benoit Mandelbrot and to have allowed him to benefit from the best education."
A professor emeritus at Yale University, Mandelbrot was born in Poland but as a child moved with his family to France where he was educated.
In the United States and around the world, his work attracted the attention of academics, but also pop culture because the fractals he uncovered could be illustrated in stunningly beautiful, multi-colored representations.
"Mandelbrot spent most of his professional life working at IBM's main research laboratory at Yorktown Heights, New York," the family statement said.
"He also taught mathematics for many years at Yale University; he was Sterling Professor Emeritus of Mathematical Sciences."
He was awarded the Wolf Prize for Physics in 1993, and the 2003 Japan Prize for Science and Technology.
David Mumford, a professor of mathematics at Brown University, told the New York Times that Mandelbrot revolutionized his field.
"Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found," the Times quoted him as saying.
"He was one of the primary people who realized these were legitimate objects," Mumford added.
Mathematicians and economists were among those who reacted swiftly to Mandelbrot's death on the Internet.
Nassim Nicholas Taleb, the statistician and philosopher best known for the book "The Black Swan," turned over his website to mourn Mandelbrot's passing.
The page featured only the words: "Benoit Mandelbrot, 1924-2010, A Greek among Romans."
Chris Anderson, the organizer of the TED conferences that feature addresses from prominent thinkers drawn from a variety of fields, also offered his condolences.
He described Mandelbrot, who addressed the Technology, Entertainment, Design conference earlier this year, as "an icon who changed how we see the world" on the TED blog.
Mandelbrot leaves behind his wife, Aliette, two sons and three grandchildren.