Both cease doing and cease to do are correct, but they differ subtly in focus
and usage.
1. Cease doing (something)
Emphasizes stopping an ongoing activity.
More common in everyday use.
Example: He ceased smoking after the doctor's warning.
→ He stopped the continuous habit.
2. Cease to do (something)
Often used in more formal, literary, or abstract contexts.
Emphasizes reaching a point where an action no longer happens.
Example: The noise ceased to disturb us.
→ At some point, the noise stopped having that effect.
3. Overlap
In many cases, both can be used with little difference in meaning:
She ceased talking. = She ceased to talk.
But nuance:
cease doing → stresses the activity itself.
cease to do → stresses the result/state of not doing.
Summary:
cease doing → focus on the ongoing action/habit.
cease to do → focus on the point where the action no longer occurs, often
more formal.
Recommendation: Use cease doing in practical, everyday contexts; reserve
cease to do for formal, abstract, or written style.