If people like Benoît B. Mandelbrot would have never decided to research Fractals then many modern movies wouldn't be possible, as they rely on fractal landscape algorithms. Yet, at the time Benoît B. Mandelbrot conducted his research it was not foreseeable that his work would have any real-world applications.

Addendum (via 17 Equations that changed the world)

In many ways, this is a book about hindsight. Pythagoras could not have imagined the uses to which his equation would be put (if, indeed, he ever came up with the equation himself in the first place). The same applies to almost all of the equations in this book. They were studied/discovered/developed by mathematicians and mathematical physicists who were investigating subjects that fascinated them deeply, not because they imagined that two hundred years later the work would lead to electric light bulbs or GPS or the internet, but rather because they were genuinely curious.

(emphasis mine)