Obituary: Benoît B Mandelbrot, mathematician

Benot Mandelbrot was a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields.

Graphic representations of the Mandelbrot set have been implanted in popular culture, gracing T-shirts and album covers.

He coined the term "fractal" to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature.

In a seminal book, The Fractal Geometry of Nature, published in 1982, Mandelbrot defended mathematical objects that he said others had dismissed as "monstrous" and "pathological". Using fractal geometry, he argued, the complex outlines of clouds and coastlines, once considered unmeasurable, could now "be approached in rigorous and vigorous quantitative fashion".

For most of his career, he had a reputation as an outsider to the mathematical establishment. From his perch as a researcher for IBM in New York, where he worked for decades before accepting a position at Yale University, he noticed patterns other researchers may have overlooked in their own data, then often swooped in to collaborate.

Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain? The answer, he was surprised to discover, depended on how closely one looked. On a map, an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.

"Here is a question, a staple of grade-school geometry, that, if you think about it, is impossible," he said earlier this year. "The length of the coastline, in a sense, is infinite."

In the 1950s, Mandelbrot proposed a simple but radical way to quantify the crookedness of such an object by assigning it a "fractal dimension", an insight that has proved useful well beyond the field of cartography.

Over nearly seven decades, working with dozens of scientists, he contributed to the fields of geology, medicine, cosmology and engineering. He used the geometry of fractals to explain how galaxies cluster, how wheat prices change over time and how mammalian brains fold as they grow, among other phenomena.

His influence was also felt within the field of geometry, where he was one of the first to use computer graphics to study mathematical objects like the Mandelbrot set, which was named in his honour.

Benot B Mandelbrot (he added the middle initial himself, though it does not stand for a middle name) was born to a Lithuanian Jewish family in Warsaw. In 1936, they fled the Nazis, first to Paris, then to the south of France, where he tended horses and fixed tools.After the war, he enrolled in the cole Polytechnique in Paris, and his career soon spanned the Atlantic. He earned a master's degree in aeronautics at the California Institute of Technology, returned to Paris for his doctorate in mathematics in 1952, then went on to the Institute for Advanced Study in Princeton, New Jersey, for a postdoctoral degree under the mathematician John von Neumann. He was hired by IBM in 1958.

Mandelbrot, who received more than 15 honorary doctorates, is survived by his wife and two sons.