Mathematics often provides the proper level of abstraction, enabling the researcher to see and exploit hidden connections between disparate problems in different subjects. For example, consider the classical geometric problem: How many lines meet 4 lines in space? The picture at right illustrates the solution: there are two such lines. (The given lines are in blue, the solution lines in green, and the saddle surface is an auxiliary construction that helps solve the problem.)
    Understanding generalizations of this problem continues to be important in mathematics. (Link to a recent scientific meeting in this subject.)  Interestingly, solutions to this very problem arise in other subjects, often in a disguised form:
  1. The feedback laws solving a problem of controlling a particular system in electrical engineering,
  2. the rational functions having prescribed critical points,   and
  3. indeterminate lines of sight to objects whose edges include the four lines.
This last example is the most direct; it is precisely along the solution lines that the four lines outlining the objects appear to coincide. Here is a web page devoted to a similar geometric problem arising from computational vision.