I can remember when the word “problem” referred to either (a) a mathematical challenge or (b) some kind of difficult development that could probably be solved with sufficient smarts and patience and whatnot. It was almost synonymous with “issue” and next door to “riddle.” Then it became an aggressive allusion to an argument or annoying behavior — “What’s your problem?” or more precisely “What’s your effing problem?” For the last 20 or 25 years “problem” has lost almost all of its currency in the mathematical realm and has come to mean (a) a major personality deficiency and/or (b) a very dark situation that could involve death or torture or some other form of devastation.
When an old mafia goon was explaining to Robert DeNiro in Goodfellas why Joe Pesci had just been whacked, he began by saying “well, we had this problem.” When Brad Pitt called Michael Fassbender in The Counselor to explain that a cocaine shipment they’ve invested in has been hijacked, he began with “we have a problem” or something close to that. If a character in a film has a “problem,” it doesn’t mean things have taken a turn for the worse as much as he/she might be toast.