prob·lem / ˈpräbləm/ • n. 1. a matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome: mental health problems| [as adj.] city planners consider it a problem district. ∎ a thing that is difficult to achieve or accomplish: motivation of staff can also be a problem.2. Physics & Math. an inquiry starting from given conditions to investigate or demonstrate a fact, result, or law. ∎ Geom. a proposition in which something has to be constructed. Compare with theorem. ∎ (in various games, esp. chess) an arrangement of pieces in which the solver has to achieve a specified result.PHRASES: have a problem with disagree with or have an objection to: I have no problem with shopping on Sundays.no problem used to express one's agreement or acquiescence: “Can you help?” “No problem.”that's your (or his, or her, etc.) problem (said with emphatic stress on pronoun) used to express one's lack of interest in or sympathy with the problems or misfortunes of another person: he'd made a mistake but that was his problem.