In 1988, Harvard mathematician Steven Strogatz hit on a new way to teach differential equations. Juliet loves Romeo, but Romeo is fickle: The more she warms to him, the colder he becomes, but when her interest wanes his feelings grow. She, on the other hand, tends to echo his feeling for her, returning love for love and hate for hate:

dr/dt = –aj, dj/dt = br,

where

r(t) = Romeo’s love/hate for Juliet at time t
j(t) = Juliet’s love/hate for Romeo at time t.

Positive values of r, j signify love, negative values signify hate, and the parameters a, b are positive, to be consistent with the story.

“The sad outcome of their affair is, of course, a neverending cycle of love and hate; their governing equations are those of a simple harmonic oscillator. At least they manage to achieve simultaneous love one-quarter of the time.”

The same idea can be pursued in other variations. He adds, “the term ‘many-body problem’ takes on new meaning in this context.”

(Steven H. Strogatz, “Love Affairs and Differential Equations,” Mathematics Magazine 61:1 [February 1988], 35.)