1660s, from Modern Latin divergere "go in different directions," from dis- "apart" (see dis-) + vergere "to bend, turn" (see verge (v.)). Originally a term in optics; the figurative sense is 19c. Related: Diverged; diverging.
If a series of approximations to some value get progressively further from it then the series is said to diverge. The reduction of some term under some evaluation strategy diverges if it does not reach a normal form after a finite number of reductions. (1994-12-08)