Scientific thought is characterized in general as methodical and rational. I would like to present here an opposing view, which treats science as a non-systematic activity, where serendipity, tinkering and imitation, rather than so-called rational thought, characterizes it. All these kinds of acts, which are considered to be a-rational, are related to an evolutionary view of science. Here I deal with a version of evolutionary epistemology as applied to science, integrated with the concept of ‘meme’. Richard Dawkins, who coined the term, treats memes as units of information that propagate in the meme pool by leaping from brain to brain. Memetics is the counterpart of genetics in the cultural arena. In its application to science, it deals with the manner in which memes/ideas spread in scientific communities. Memes (ideas) replicate through imitation. Examples of this phenomenon in science are illustrated by some historical cases. In particular, I deal with the evolution of theories of ‘internal symmetries’ in particle physics.