There are very, very few people who invent truly new shapes and ideas that come mainstream and change the way people think within their own lifetime. However, Benoit Mandelbrot (who died last Thursday) can be said to be one of these very, very few. He both named and created the field of fractal mathematics.
Whilst he didn’t discover the basic maths of fractals, he found an obscure, almost unknown concept of exploring the world between two dimensions and three dimensions and showed its fundamental role in the fabric of the universe.
Wikipedia has a great entry on what both fractals and Mandelbrot’s other work have done for mathematics.
Benoit Mandlebrot RIP