I once was on a workshop organised by and for mathematicians which supposed to be about biology. There was a talk where guy was discussing PDE system describing some colony growth; at some point near the beginning he concluded that the results for real input are "boring", and one can get "intriguing chaotic behaviour" with negative cell number, and continued with that assumption (;
Many similar experiences, from having someone say "I was under the impression this was interesting for its own sake" at an applied math talk, or asking a group of mathematicians how to actually implement their biologically (and logistically) impossible solution to influenza containment.
