'reductio ad absurdum' originates from Latin, specifically the words 'reductio' (from 'reducere'), 'ad', and 'absurdum', where 'reducere' meant 'to lead back', 'ad' meant 'to/toward', and 'absurdum' meant 'out of tune, senseless'.

'reductio ad absurdum' entered English as a technical Latin phrase via Medieval Latin and the scholastic tradition in logic and rhetoric; it has been used in philosophical and mathematical writing since the Middle Ages and into modern scholarly English largely unchanged.

Initially it referred to the act of 'leading back to the absurd' in Latin scholastic usage; over time it retained that technical sense and is now used in English to mean the logical method of showing a claim leads to absurdity or contradiction.