Karl Pearson introduced the term "Random Walk". He was interested in describing the spatial/temporal evolutions of mosquito populations invading cleared jungle regions. He found it too complex to model deterministically, so he conceptualized a simple random model.

Pearson posed his problem in

Nature(27 July 1905):

A man starts from a point 0 and walks l yards in a straight line; he then turns through any angle whatever and walks another l yards in a second straight line. He repeats this process n times. I require the probability that after n of these stretches he is at a distance between r and r 'r from his starting point.