I'm surprised that no one has mentioned the Mandelbrot set yet, arguably the
most famous new mathematical object of the last 30 years, at least among the
general public. Benoit Mandelbrot discovered it in 1979 as a result of
computer experiments. He says that when he first saw it he was so surprised by
its appearance that he thought it must be the result of a computer
malfunction. In his book *Fractals and Chaos*, Mandelbrot argues that his
discovery of the Mandelbrot set contributed to the revival of experimental
mathematics and led to a general change in the attitude of mathematicians to
experiments in mathematics. [On page 25 he writes][1]:

"The culture of mathematics during the 1960s and 1970s

Within that culture the Mandelbrot set could not have been discovered. Hence its discovery marked a historical departure. Today -- but not yesterday -- only a minority among mathematicians would agree with the opinion due to someone who did not discover that set, that the study of M reflects "a rather infantile and somewhat dull mathematical sensibility" (Brooks 1989)."


  [1]: http://tinyurl.com/yd57hgu