Benoît Mandelbrot passed away recently at age 85. He coined the term "fractal" and pushed the boundaries of iterative and chaotic mathematics.
(from the article) "Dr. 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, depends on how closely one looks. 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,' Dr. Mandelbrot [said]."