Here's one example. In Darwin's "Origin of Species", a key principle which Darwin talks about at great length is the so-called Knight-Darwin Law, the observation that even in apparently asexual species, sexual reproduction still occasionally occurs, if only after long spans of time. In an article in Acta Biotheoretica, I argued this is in fact an infinite graph-theoretical principle. If G is the directed graph of all organisms, where an edge from x to y means that x is a parent of y, then (Darwin theorizes that) there is no infinite directed path through G all of whose vertices have indegree 1. (A vertex has indegree 1 if it has exactly 1 parent.) The low-hanging fruit (some of which I picked in my paper): Investigate the mathematical implications of the above property (esp. if G also has other biologically motivated properties).

The Knight-Darwin law seems to have vanished completely from the literature around the start of the 20th century, until I cited it. Almost as if no-one has actually been reading Darwin in all that time.

To generalize: If you want to find low-hanging fruit, read non-fiction classics like Darwin and constantly be asking, "Is this some unrecognized mathematics in disguise?"