Origins
The word 'problem' preserves one of Greek's most physical metaphors for intellectual difficulty: an obstacle hurled into your path. It enters English in the late fourteenth century from Old French 'problème,' from Latin 'problēma,' from Greek 'próblēma' (πρόβλημα). The Greek noun derives from the verb 'probállein' (προβάλλειν, to throw forward, to put forth), composed of 'pro-' (πρό, forward, before) and 'bállein' (βάλλειν, to throw). In its most literal sense, a 'próblēma' was something thrown forward — a projection, a barrier, a thing placed in front of someone as an obstacle or a challenge.
The metaphorical extension from physical obstacle to intellectual challenge was already complete in classical Greek. Aristotle used 'próblēma' in his logical and scientific works to mean a question put forward for discussion or investigation. In Greek geometry, the word had a precise technical meaning that distinguished it from 'theōrēma' (θεώρημα, a proposition to be contemplated and proved). A 'próblēma' was a construction task — something requiring the geometer to produce a figure satisfying given conditions (e.g., 'construct an equilateral triangle on a given line segment'). A 'theōrēma' was a truth to be demonstrated through proof. Euclid's Elements carefully maintains this distinction: propositions are classified as either problems (requiring construction) or theorems (requiring proof). Modern mathematics has collapsed both into 'problems,' losing a distinction the Greeks considered essential.
The Greek verb 'bállein' (to throw) is the ancestor of a large and varied English word family. 'Symbol' (σύμβολον) is 'syn-' (together) + 'bállein' — something 'thrown together' as a token of identity or meaning. 'Parable' (παραβολή) is 'pará' (beside) + 'bállein' — something 'thrown beside' another thing for comparison, a story placed alongside reality to illuminate it. 'Hyperbole' (ὑπερβολή) is 'hypér' (beyond, over) + 'bállein' — a 'throwing beyond,' an overshooting, an exaggeration. 'Emblem' (ἔμβλημα) is 'en-' (in) + 'bállein' — something 'thrown in' or inserted, originally an inlaid ornament. 'Metabolism' (μεταβολή) is 'metá' (change, after) + 'bállein' — a 'throwing into change,' a transformation. 'Ballistic' derives directly from 'bállein' — the science of projectiles, things thrown.
Development
The word 'diábolos' (devil) also belongs to this family: 'diá' (across) + 'bállein' — one who 'throws across,' who casts accusations and sows division. The devil and the problem are etymological cousins, both things thrown — one across your reputation, the other into your path.
In English, 'problem' initially referred primarily to intellectual puzzles and academic questions. The sense of 'a difficulty in practical life, a source of trouble' developed gradually during the seventeenth and eighteenth centuries. By the nineteenth century, social reformers spoke routinely of 'the problem of poverty,' 'the Irish problem,' and 'the labor problem,' extending the word from the academic study to the condition being studied. The twentieth century saw 'problem' become one of the most common words in English, applied to everything from existential dilemmas to minor inconveniences.
The adjective 'problematic' (from Greek 'problēmatikós') entered English in the seventeenth century meaning 'of the nature of a problem, questionable, uncertain.' Its recent expansion in academic and social discourse — where 'problematic' has become a near-synonym for 'ethically objectionable' — represents a significant semantic shift from 'uncertain or debatable' to 'definitely wrong,' almost inverting the word's original connotation of open inquiry.