problemyoudaoicibaDictYouDict[problem 词源字典]
problem: [14] A problem is etymologically something ‘thrown forward’. The word comes via Old French probleme and Latin problēma from Greek próblēma, a derivative of probállein ‘throw forward’. This was a compound verb formed from the prefix pro- ‘forward’ and bállein ‘throw’ (source of English ballistic, emblem, parable, etc). Things that are ‘thrown out’ project and can get in the way and hinder one, and so próblēma came to be used for an ‘obstacle’ or ‘problem’ – senses carried through into English problem.
=> ballistic, emblem, parable, symbol[problem etymology, problem origin, 英语词源]
problem (n.)youdaoicibaDictYouDict
late 14c., "a difficult question proposed for solution," from Old French problème (14c.) and directly from Latin problema, from Greek problema "a task, that which is proposed, a question;" also "anything projecting, headland, promontory; fence, barrier;" also "a problem in geometry," literally "thing put forward," from proballein "propose," from pro "forward" (see pro-) + ballein "to throw" (see ballistics).

Meaning "a difficulty" is mid-15c. Mathematical sense is from 1560s in English. Problem child first recorded 1920. Phrase _______ problem in reference to a persistent and seemingly insoluble difficulty is attested at least from 1882, in Jewish problem. Response no problem "that is acceptable; that can be done without difficulty" is recorded from 1968.